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Rice University
1.
Buras, Eric.
A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs.
Degree: MA, Engineering, 2016, Rice University
URL: http://hdl.handle.net/1911/96624 
► The Laplacian matrix, L, of a graph, G, contains degree and edge information of a given network. Solving a Laplacian linear system Lx = b…
(more)
▼ The Laplacian matrix, L, of a graph, G, contains degree and edge information of a given network. Solving a Laplacian linear system Lx = b provides information about flow through the network, and in specific cases, how that information orders the nodes in the network. I propose a novel way to solve this linear system by first partitioning G into its maximum locally-connected subgraph and a small subgraph of the remaining so-called "teleportation" edges. I then apply optimal
multigrid solves to the locally-connected subgraph, and linear algebra and a solve on the teleportation subgraph to solve the original linear system. I show results for this method on real-world graphs from the biological systems of the C. Elegans worm, Facebook friend networks, and the power grid of the Western United States.
Advisors/Committee Members: Knepley, Matthew G (advisor).
Subjects/Keywords: Laplacian; Multigrid
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APA (6th Edition):
Buras, E. (2016). A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs. (Masters Thesis). Rice University. Retrieved from http://hdl.handle.net/1911/96624
Chicago Manual of Style (16th Edition):
Buras, Eric. “A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs.” 2016. Masters Thesis, Rice University. Accessed April 11, 2021.
http://hdl.handle.net/1911/96624.
MLA Handbook (7th Edition):
Buras, Eric. “A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs.” 2016. Web. 11 Apr 2021.
Vancouver:
Buras E. A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs. [Internet] [Masters thesis]. Rice University; 2016. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1911/96624.
Council of Science Editors:
Buras E. A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs. [Masters Thesis]. Rice University; 2016. Available from: http://hdl.handle.net/1911/96624
University of Colorado
2.
Park, Minho.
Relaxation-Corrected Bootstrap Algebraic Multigrid (rBAMG).
Degree: PhD, Applied Mathematics, 2010, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/10
► Bootstrap Algebraic Multigrid (BAMG) is a multigrid-based solver for matrix equations of the form Ax = b. Its aim is to automatically determine the…
(more)
▼ Bootstrap Algebraic
Multigrid (BAMG) is a
multigrid-based solver for matrix equations of the form Ax = b. Its aim is to automatically determine the interpolation weights used in algebraic
multigrid (AMG) by locally fitting a set of test vectors that have been relaxed as solutions to the corresponding homogeneous equation, Ax = 0. This thesis introduces an indirect operator based interpolation scheme for BAMG that determines the interpolation weights indirectly by “collapsing” the unwanted connections in “operator interpolation”. Compared to BAMG, this
indirect BAMG approach (
iBAMG) is more in the spirit of classical AMG, which collapses unwanted connections in operator interpolation based on the (restrictive) assumption that smooth error is locally constant.
This thesis also develops another form of BAMG, called
rBAMG, that involves modifying the least-squares process by temporarily relaxing on the test vectors at the fine-grid interpolation points. The theory here shows that, under fairly general conditions,
iBAMG and
rBAMG are equivalent. Simplicity and potentially greater generality favor
rBAMG, so this algorithm is at the focus of the numerical performance study here.
The
rBAMG setup process involves several components that are developed in this thesis.
Besides the new least-squares principle involving the residuals of the test vectors, a simple extrapolation scheme is developed to accurately estimate the convergence factors of the evolving AMG solver. Such a capability is essential to effective development of a fast solver, and the approach introduced here proves to be much more effective than the conventional approach of just observing successive error reduction factors. Another component of the setup process is the use of the current V-cycle to ensure its effectiveness or, when poor convergence is observed, to expose error components that are not being properly attenuated. How we coordinate use of these evolving error components together with the original test vectors to direct the setup process is a critical issue to
rBAMG’s effectiveness. Another related component is the scaling and recombination Ritz process that targets the so-called weak approximation property in an attempt to reveal the important elements of these evolving error and test vector spaces. The details of the components used here are spelled out in what follows.
The study of
rBAMG here is an attempt to systematically analyze the behavior of the algorithm in terms relative to several parameters. The focus here is on the number of test vectors, the number of relaxations applied to them, and the dimension of the matrix to which the scheme is applied. A large number of other parameters and options could also be considered, including different cycling strategies, other coarsening strategies (e. g., computing several eigenvector approximations on coarse levels), different numbers of relaxation sweeps on coarse levels, different…
Advisors/Committee Members: Stephen F. McCormick, Thomas A. Manteuffel, Marian Brezina.
Subjects/Keywords: Adaptive Multigrid; Algebraic Multigrid; Bootstrap Algebraic Multigrid; Convergence Estimate; Iterative Methods; Multigrid; Applied Mathematics
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APA (6th Edition):
Park, M. (2010). Relaxation-Corrected Bootstrap Algebraic Multigrid (rBAMG). (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/10
Chicago Manual of Style (16th Edition):
Park, Minho. “Relaxation-Corrected Bootstrap Algebraic Multigrid (rBAMG).” 2010. Doctoral Dissertation, University of Colorado. Accessed April 11, 2021.
https://scholar.colorado.edu/appm_gradetds/10.
MLA Handbook (7th Edition):
Park, Minho. “Relaxation-Corrected Bootstrap Algebraic Multigrid (rBAMG).” 2010. Web. 11 Apr 2021.
Vancouver:
Park M. Relaxation-Corrected Bootstrap Algebraic Multigrid (rBAMG). [Internet] [Doctoral dissertation]. University of Colorado; 2010. [cited 2021 Apr 11].
Available from: https://scholar.colorado.edu/appm_gradetds/10.
Council of Science Editors:
Park M. Relaxation-Corrected Bootstrap Algebraic Multigrid (rBAMG). [Doctoral Dissertation]. University of Colorado; 2010. Available from: https://scholar.colorado.edu/appm_gradetds/10
University of Utah
3.
Lewis, Thomas James.
A GPU-based maximal independent set aggregation strategy: algorithms, comparisons, and applications withing algebraic multigrid.
Degree: MS, Computing (School of), 2014, University of Utah
URL: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3132/rec/44
► The algebraic multigrid (AMG) method is often used as a preconditioner in Krylov subspace solvers such as the conjugate gradient method. An AMG preconditionerhierarchically aggregates…
(more)
▼ The algebraic multigrid (AMG) method is often used as a preconditioner in Krylov subspace solvers such as the conjugate gradient method. An AMG preconditionerhierarchically aggregates the degrees of freedom during the coarsening phase in order to eciently account for lower-frequency errors. Each degree of freedom in the coarser level corresponds to one of the aggregates in the ner level. The aggregation in each level in the hierarchy has a signicant impact on the eectiveness of AMG as a preconditioner. The aggregation can be formulated as a partitioning problem on the graph induced from the matrix representation of a linear system. The contributions of this work are as follows: rst, a GPU implementation of a \bottom-up" partitioning scheme based on maximal independent sets (MIS), including an ecient conditioning scheme for enforcing partition size constraints; second, three novel topological metrics, convexity, eccentricity, and minimum enclosing ball, for measuring partition quality; third, empirical test results comparing our MIS-Based aggregation methods with the MeTis graph partioning library, showing that the metrics correlate more strongly with AMG performance than the commonly used edge-cut metric, and that for ner aggregations, MIS-based aggregation is better suited for AMG coarsening than is the \top down" MeTis graph partitioning library, but that for coarser aggregations, MeTis performs better.
Subjects/Keywords: GPU; Maximal independent set; Multigrid
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APA (6th Edition):
Lewis, T. J. (2014). A GPU-based maximal independent set aggregation strategy: algorithms, comparisons, and applications withing algebraic multigrid. (Masters Thesis). University of Utah. Retrieved from http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3132/rec/44
Chicago Manual of Style (16th Edition):
Lewis, Thomas James. “A GPU-based maximal independent set aggregation strategy: algorithms, comparisons, and applications withing algebraic multigrid.” 2014. Masters Thesis, University of Utah. Accessed April 11, 2021.
http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3132/rec/44.
MLA Handbook (7th Edition):
Lewis, Thomas James. “A GPU-based maximal independent set aggregation strategy: algorithms, comparisons, and applications withing algebraic multigrid.” 2014. Web. 11 Apr 2021.
Vancouver:
Lewis TJ. A GPU-based maximal independent set aggregation strategy: algorithms, comparisons, and applications withing algebraic multigrid. [Internet] [Masters thesis]. University of Utah; 2014. [cited 2021 Apr 11].
Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3132/rec/44.
Council of Science Editors:
Lewis TJ. A GPU-based maximal independent set aggregation strategy: algorithms, comparisons, and applications withing algebraic multigrid. [Masters Thesis]. University of Utah; 2014. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3132/rec/44
Penn State University
4.
Wang, Lu.
the auxiliary space solvers and their applications.
Degree: 2014, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/23592
► Developing efficient iterative methods and parallel algorithms for solving sparse linear sys- tems discretized from partial differential equations (PDEs) is still a challenging task in…
(more)
▼ Developing efficient iterative methods and parallel algorithms for solving sparse linear sys- tems discretized from partial differential equations (PDEs) is still a challenging task in scien- tific computing and practical applications. Although many mathematically optimal solvers, such as the
multigrid methods, have been analyzed and developed, the unfortunate reality is that these solvers have not been used much in practical applications. In order to narrow the gap between theory and practice, we develop, formulate, and analyze mathematically optimal solvers that are robust and easy to use in practice based on the methodology of Fast Auxiliary Space Preconditioning (FASP).
We develop a
multigrid method on unstructured shape-regular grids by the construction of an auxiliary coarse grid hierarchy on which the
multigrid method can be applied by using the FASP technique. Such a construction is realized by a cluster tree which can be obtained in O(N log N ) operations for a grid of N nodes. This tree structure is used for the definition of the grid hierarchy from coarse to fine. For the constructed grid hierarchy, we prove that the condition number of the preconditioned system for an elliptic PDE is O(logN). Then, we present a new colored block Gauss-Seidel method for general unstructured grids. By constructing the auxiliary grid, we can aggregate the degree of freedoms in the same cells of the auxiliary girds into one block. By developing and a parallel coloring algorithm for the tree structure, a colored block Gauss-Seidel method can be applied with the aggregates serving as non-overlapping blocks. On the other hand, we also develop a new parallel unsmoothed aggregation algebraic
multigrid method for the PDEs defined on an unstructured mesh from the auxiliary grid. It provides (nearly) optimal load balance and predictable communication patterns factors that make our new algorithm suitable for parallel computing.
Furthermore, we extend the FASP techniques to saddle point and indefinite problems. Two auxiliary space preconditioners are presented. An abstract framework of the symmetric positive definite auxiliary preconditioner is presented so that the optimal
multigrid method could be applied for the indefinite problem on the unstructured grid. We also numerically verify the optimality of the two preconditioners for the Stokes equations.
Advisors/Committee Members: Jinchao Xu, Dissertation Advisor/Co-Advisor, James Joseph Brannick, Committee Member, Ludmil Tomov Zikatanov, Committee Member, Chao Yang Wang, Special Member.
Subjects/Keywords: multigrid; auxiliary space; solver
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APA (6th Edition):
Wang, L. (2014). the auxiliary space solvers and their applications. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/23592
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Wang, Lu. “the auxiliary space solvers and their applications.” 2014. Thesis, Penn State University. Accessed April 11, 2021.
https://submit-etda.libraries.psu.edu/catalog/23592.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Wang, Lu. “the auxiliary space solvers and their applications.” 2014. Web. 11 Apr 2021.
Vancouver:
Wang L. the auxiliary space solvers and their applications. [Internet] [Thesis]. Penn State University; 2014. [cited 2021 Apr 11].
Available from: https://submit-etda.libraries.psu.edu/catalog/23592.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Wang L. the auxiliary space solvers and their applications. [Thesis]. Penn State University; 2014. Available from: https://submit-etda.libraries.psu.edu/catalog/23592
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Georgia Tech
5.
Henneking, Stefan.
Implementation and analysis of a parallel vertex-centered finite element segmental refinement multigrid solver.
Degree: MS, Computational Science and Engineering, 2016, Georgia Tech
URL: http://hdl.handle.net/1853/55050
► In a parallel vertex-centered finite element multigrid solver, segmental refinement can be used to avoid all inter-process communication on the fine grids. While domain decomposition…
(more)
▼ In a parallel vertex-centered finite element
multigrid solver, segmental refinement can be used to avoid all inter-process communication on the fine grids. While domain decomposition methods generally require coupled subdomain processing for the numerical solution to a nonlinear elliptic boundary value problem, segmental refinement exploits that subdomains are almost decoupled with respect to high-frequency error components. This allows to perform
multigrid with fully decoupled subdomains on the fine grids, which was proposed as a sequential low-storage algorithm by Brandt in the 1970s, and as a parallel algorithm by Brandt and Diskin in 1994. Adams published the first numerical results from a multilevel segmental refinement solver in 2014, confirming the asymptotic exactness of the scheme for a cell-centered finite volume implementation. We continue Brandt’s and Adams’ research by experimentally investigating the scheme’s accuracy with a vertex-centered finite element segmental refinement solver. We confirm that full
multigrid accuracy can be preserved for a few segmental refinement levels, although we observe a different dependency on the segmental refinement parameter space. We show that various strategies for the grid transfers between the finest conventional
multigrid level and the segmental refinement subdomains affect the solver accuracy. Scaling results are reported for a Cray XC30 with up to 4096 cores.
Advisors/Committee Members: Vuduc, Richard (advisor), Chow, Edmond (committee member), Zhou, Hao-Min (committee member), Adams, Mark F. (committee member).
Subjects/Keywords: Multigrid; Segmental refinement; Communication-avoiding
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APA (6th Edition):
Henneking, S. (2016). Implementation and analysis of a parallel vertex-centered finite element segmental refinement multigrid solver. (Masters Thesis). Georgia Tech. Retrieved from http://hdl.handle.net/1853/55050
Chicago Manual of Style (16th Edition):
Henneking, Stefan. “Implementation and analysis of a parallel vertex-centered finite element segmental refinement multigrid solver.” 2016. Masters Thesis, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/55050.
MLA Handbook (7th Edition):
Henneking, Stefan. “Implementation and analysis of a parallel vertex-centered finite element segmental refinement multigrid solver.” 2016. Web. 11 Apr 2021.
Vancouver:
Henneking S. Implementation and analysis of a parallel vertex-centered finite element segmental refinement multigrid solver. [Internet] [Masters thesis]. Georgia Tech; 2016. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/55050.
Council of Science Editors:
Henneking S. Implementation and analysis of a parallel vertex-centered finite element segmental refinement multigrid solver. [Masters Thesis]. Georgia Tech; 2016. Available from: http://hdl.handle.net/1853/55050
Brunel University
6.
Dyson, Joshua.
GPU accelerated linear system solvers for OpenFOAM and their application to sprays.
Degree: PhD, 2018, Brunel University
URL: http://bura.brunel.ac.uk/handle/2438/16005
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.764958
► This thesis presents the development of GPU accelerated solvers for use in simulation of the primary atomization phenomenon. By using the open source continuum mechanics…
(more)
▼ This thesis presents the development of GPU accelerated solvers for use in simulation of the primary atomization phenomenon. By using the open source continuum mechanics library, OpenFOAM, as a basis along with the NVidia CUDA API linear system solvers have been developed so that the multiphase solver runs in part on GPUs. This aims to reduce the enormous computational cost associated with modelling primary atomization. The modelling of such is vital to understanding the mechanisms that make combustion efficient. Firstly, the OpenFOAM code is benchmarked to assess both its suitability for atomization problems and to establish efficient operating parameters for comparison to GPU accelerations. This benchmarking then culminates in a comparison to an experimental test case, from the literature, dominated by surface tension, in 3D. Finally, a comparison is made with a primary atomizing liquid sheet as published in the literature. A geometric multigrid method is employed to solve the pressure Poisson equations, the first use of a geometric multigrid method in 3D GPU accelerated VOF simulation. Detailed investigations are made into the compute efficiency of the GPU accelerated solver, comparing memory bandwidth usage to hardware maximums as well as GPU idling time. In addition, the components of the multigrid method are also investigated, including the effect of residual scaling. While the GPU based multigrid method shows some improvement over the equivalent CPU implementation, the costs associated with running on GPU cause this to not be significantly greater.
Subjects/Keywords: 620.1; Primary atomization; OpenFOAM; Multigrid
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APA (6th Edition):
Dyson, J. (2018). GPU accelerated linear system solvers for OpenFOAM and their application to sprays. (Doctoral Dissertation). Brunel University. Retrieved from http://bura.brunel.ac.uk/handle/2438/16005 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.764958
Chicago Manual of Style (16th Edition):
Dyson, Joshua. “GPU accelerated linear system solvers for OpenFOAM and their application to sprays.” 2018. Doctoral Dissertation, Brunel University. Accessed April 11, 2021.
http://bura.brunel.ac.uk/handle/2438/16005 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.764958.
MLA Handbook (7th Edition):
Dyson, Joshua. “GPU accelerated linear system solvers for OpenFOAM and their application to sprays.” 2018. Web. 11 Apr 2021.
Vancouver:
Dyson J. GPU accelerated linear system solvers for OpenFOAM and their application to sprays. [Internet] [Doctoral dissertation]. Brunel University; 2018. [cited 2021 Apr 11].
Available from: http://bura.brunel.ac.uk/handle/2438/16005 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.764958.
Council of Science Editors:
Dyson J. GPU accelerated linear system solvers for OpenFOAM and their application to sprays. [Doctoral Dissertation]. Brunel University; 2018. Available from: http://bura.brunel.ac.uk/handle/2438/16005 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.764958
Texas A&M University
7.
Hanophy, Joshua Thomas.
Performance of Parallel Approximate Ideal Restriction Multigrid for Transport Applications.
Degree: MS, Nuclear Engineering, 2019, Texas A&M University
URL: http://hdl.handle.net/1969.1/187540
► Algebraic multigrid (AMG) methods have been widely used to solve systems arising from the discretization of elliptic partial differential equations. In serial, AMG algorithms scale…
(more)
▼ Algebraic
multigrid (AMG) methods have been widely used to solve systems arising from the discretization of elliptic partial differential equations. In serial, AMG algorithms scale linearly with problem size. In parallel, communication costs scale logarithmically with the number of processors. Recently, a classical AMG method based on approximate ideal restriction (AIR) was developed for nonsymmetric matrices. AIR has already been shown to be effective for solving the linear systems arising from upwind discontinuous Galerkin (DG) finite element discretization of advection-diffusion problems, including the hyperbolic limit of pure advection. A new parallel version of AIR, pAIR, has been implemented in the hypre library.
In this thesis, pAIR is tested for use solving the source iteration equations of the SN approximations to the transport equation. The performance is investigated with various meshes in two and three dimensions. Detailed profiling of parallel performance is also conducted to identify the most important areas for algorithm improvements. An improvement to the Local Ideal Approximate Restriction algorithm is introduced and discussed. Weak scaling results to 4,096 processors are presented. These results show total solve growing logarithmically with the number of processors used. Importantly, this result is shown on both uniform grids and unstructured grids in three dimensions. The unstructured mesh did not include reentrant cells.
Advisors/Committee Members: Morel, Jim (advisor), Ragusa, Jean (committee member), Lazarov, Raytcho (committee member).
Subjects/Keywords: transport; multigrid; parallel multigrid; AMG; Approximate Ideal Restriction
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APA (6th Edition):
Hanophy, J. T. (2019). Performance of Parallel Approximate Ideal Restriction Multigrid for Transport Applications. (Masters Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/187540
Chicago Manual of Style (16th Edition):
Hanophy, Joshua Thomas. “Performance of Parallel Approximate Ideal Restriction Multigrid for Transport Applications.” 2019. Masters Thesis, Texas A&M University. Accessed April 11, 2021.
http://hdl.handle.net/1969.1/187540.
MLA Handbook (7th Edition):
Hanophy, Joshua Thomas. “Performance of Parallel Approximate Ideal Restriction Multigrid for Transport Applications.” 2019. Web. 11 Apr 2021.
Vancouver:
Hanophy JT. Performance of Parallel Approximate Ideal Restriction Multigrid for Transport Applications. [Internet] [Masters thesis]. Texas A&M University; 2019. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1969.1/187540.
Council of Science Editors:
Hanophy JT. Performance of Parallel Approximate Ideal Restriction Multigrid for Transport Applications. [Masters Thesis]. Texas A&M University; 2019. Available from: http://hdl.handle.net/1969.1/187540
Penn State University
8.
Cao, Fei.
Generalized Bootstrap Algebraic Multigrid.
Degree: 2017, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/14776fwc5045
► In this thesis, we consider a classical algebraic multigrid form of optimal interpolation that directly minimizes the two-grid convergence rate and compare it with a…
(more)
▼ In this thesis, we consider a classical algebraic
multigrid form of optimal interpolation that directly minimizes the two-grid convergence rate and compare it with a so-called ideal interpolation that minimizes a certain weak approximation property of the coarse space. We study compatible relaxation type estimates for the quality of the coarse grid and derive a new sharp measure using optimal interpolation that provides a guaranteed lower bound on the convergence rate of the resulting two-grid method for a given grid. Also we design an adaptive coarsening algorithm based on this sharp form of compatible relaxation. The resulting coarsening algorithm aims to find a sparse representation (changing of basis) for the coarse space defined by the optimal interpolation operator. In addition, we design a generalized bootstrap algebraic
multigrid setup algorithm that computes a sparse approximation to the optimal interpolation matrix. We demonstrate numerically that the bootstrap algebraic
multigrid method with sparse interpolation matrix
(and spanning multiple levels) converges faster than the two-grid method with the standard ideal interpolation (a dense matrix) for various scalar diffusion problems with highly varying diffusion coefficient and we show the general usage of our algorithm by applying also to elasticity problem.
Advisors/Committee Members: James Joseph Brannick, Dissertation Advisor/Co-Advisor, James Joseph Brannick, Committee Chair/Co-Chair, Jinchao Xu, Committee Member, Yuxi Zheng, Committee Member, Lyle Norman Long, Outside Member.
Subjects/Keywords: algebraic multigrid; compatible relaxation; bootstrap algebraic multigrid; optimal interpolation
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APA (6th Edition):
Cao, F. (2017). Generalized Bootstrap Algebraic Multigrid. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/14776fwc5045
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Cao, Fei. “Generalized Bootstrap Algebraic Multigrid.” 2017. Thesis, Penn State University. Accessed April 11, 2021.
https://submit-etda.libraries.psu.edu/catalog/14776fwc5045.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Cao, Fei. “Generalized Bootstrap Algebraic Multigrid.” 2017. Web. 11 Apr 2021.
Vancouver:
Cao F. Generalized Bootstrap Algebraic Multigrid. [Internet] [Thesis]. Penn State University; 2017. [cited 2021 Apr 11].
Available from: https://submit-etda.libraries.psu.edu/catalog/14776fwc5045.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Cao F. Generalized Bootstrap Algebraic Multigrid. [Thesis]. Penn State University; 2017. Available from: https://submit-etda.libraries.psu.edu/catalog/14776fwc5045
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Rochester Institute of Technology
9.
Parker, Benjamin Quanah.
Multigrid Solution of the Debye-Hückel Equation.
Degree: MS, School of Mathematical Sciences (COS), 2013, Rochester Institute of Technology
URL: https://scholarworks.rit.edu/theses/8573
► Multigrid algorithms are fast solvers for elliptic partial differential equations. In this thesis, we apply multigrid methods to the model of protein charge-regulation of…
(more)
▼ Multigrid algorithms are fast solvers for elliptic partial differential equations. In this thesis, we apply
multigrid methods to the model of protein charge-regulation of Hollenbeck, et al. The model of protein charge-regulation requires computing work of charging matrices for two low dielectric spheres in a salt solution, which in turn requires many solutions of the linearized Poisson-Boltzmann equation, or the Debye-Huckel equation. We use
multigrid methods to reduce the run time of computing solutions to the Debye-Huckel equation, and compare the results of some simple and more complicated examples. Using the work of Brandt and others, we also construct an interpolation scheme that takes the potentially complicated behavior of the coefficient into account
Advisors/Committee Members: David S. Ross.
Subjects/Keywords: Debye-Huckel; elliptic; interpolation; multigrid; Poisson-Boltzmann
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APA (6th Edition):
Parker, B. Q. (2013). Multigrid Solution of the Debye-Hückel Equation. (Masters Thesis). Rochester Institute of Technology. Retrieved from https://scholarworks.rit.edu/theses/8573
Chicago Manual of Style (16th Edition):
Parker, Benjamin Quanah. “Multigrid Solution of the Debye-Hückel Equation.” 2013. Masters Thesis, Rochester Institute of Technology. Accessed April 11, 2021.
https://scholarworks.rit.edu/theses/8573.
MLA Handbook (7th Edition):
Parker, Benjamin Quanah. “Multigrid Solution of the Debye-Hückel Equation.” 2013. Web. 11 Apr 2021.
Vancouver:
Parker BQ. Multigrid Solution of the Debye-Hückel Equation. [Internet] [Masters thesis]. Rochester Institute of Technology; 2013. [cited 2021 Apr 11].
Available from: https://scholarworks.rit.edu/theses/8573.
Council of Science Editors:
Parker BQ. Multigrid Solution of the Debye-Hückel Equation. [Masters Thesis]. Rochester Institute of Technology; 2013. Available from: https://scholarworks.rit.edu/theses/8573
Texas A&M University
10.
Kliewer, John David.
Non-Linear Spatial Multigrid Method For Non-Linear S2 Acceleration.
Degree: MS, Nuclear Engineering, 2018, Texas A&M University
URL: http://hdl.handle.net/1969.1/173382
► A nonlinear spatial multigrid algorithm was developed and explored as a technique to efficiently solve the nonlinear S2 acceleration equations for SN neutron transport calculations…
(more)
▼ A nonlinear spatial
multigrid algorithm was developed and explored as a technique to efficiently
solve the nonlinear S2 acceleration equations for SN neutron transport calculations in 1-D
slabs. Acceleration of the basic source iteration process in SN calculations is necessary in problems
with highly diffusive regions. Direct inversion would be a more efficient method in 1-D, but a
multigrid method has the potential to be far more efficient than other techniques in 2-D. This work
is a first step toward a 2-D
multigrid algorithm. The computational results show that this scheme
works well for optically-thin cells on the fine mesh, but degrades significantly for optically-thick
cells on the fine mesh.
Advisors/Committee Members: Morel, Jim E (advisor), Ragusa, Jean C (committee member), Popov, Bojan (committee member).
Subjects/Keywords: neutron transport; spatial multigrid; SN; S2; acceleration
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APA (6th Edition):
Kliewer, J. D. (2018). Non-Linear Spatial Multigrid Method For Non-Linear S2 Acceleration. (Masters Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/173382
Chicago Manual of Style (16th Edition):
Kliewer, John David. “Non-Linear Spatial Multigrid Method For Non-Linear S2 Acceleration.” 2018. Masters Thesis, Texas A&M University. Accessed April 11, 2021.
http://hdl.handle.net/1969.1/173382.
MLA Handbook (7th Edition):
Kliewer, John David. “Non-Linear Spatial Multigrid Method For Non-Linear S2 Acceleration.” 2018. Web. 11 Apr 2021.
Vancouver:
Kliewer JD. Non-Linear Spatial Multigrid Method For Non-Linear S2 Acceleration. [Internet] [Masters thesis]. Texas A&M University; 2018. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1969.1/173382.
Council of Science Editors:
Kliewer JD. Non-Linear Spatial Multigrid Method For Non-Linear S2 Acceleration. [Masters Thesis]. Texas A&M University; 2018. Available from: http://hdl.handle.net/1969.1/173382
Penn State University
11.
Urschel, John Cameron.
Graph-based Topics in Applied Mathematics.
Degree: 2013, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/17554
► Computational problems in applied mathematics often have strong ties to graph/grid based structures. We treat graph-based problems in applied mathematics. We consider the spectral bisection…
(more)
▼ Computational problems in applied mathematics often have strong ties to graph/grid based structures. We treat graph-based problems in applied mathematics. We consider the spectral bisection problem for general graphs, and extend Miroslav Fiedler's results to more general graphs, using the theory of irreducible matrices. In addition, we apply the spectral bisection theory to graph partitioning, and create a cascadic
Multigrid algorithm to solve for the Fiedler vector of a graph Laplacian, thus producing a bisection. We give convergence results for a sub class of graphs for our method. Finally, we consider the numerical computation of the fair price of barrier options. In practice, this becomes a problem of solving a partial differential equation numerically. We introduce a technique where the grid is treated in space and time simultaneously. We use a
Multigrid V-cycle, in which the coarse grids are chosen adaptively, based on the properties of the finer structured graph.
Advisors/Committee Members: Victor Nistor, Thesis Advisor/Co-Advisor, Jinchao Xu, Thesis Advisor/Co-Advisor, Ludmil Tomov Zikatanov, Thesis Advisor/Co-Advisor.
Subjects/Keywords: Multigrid; Spectral Bisection; Fiedler Vector; Barrier Option
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APA (6th Edition):
Urschel, J. C. (2013). Graph-based Topics in Applied Mathematics. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/17554
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Urschel, John Cameron. “Graph-based Topics in Applied Mathematics.” 2013. Thesis, Penn State University. Accessed April 11, 2021.
https://submit-etda.libraries.psu.edu/catalog/17554.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Urschel, John Cameron. “Graph-based Topics in Applied Mathematics.” 2013. Web. 11 Apr 2021.
Vancouver:
Urschel JC. Graph-based Topics in Applied Mathematics. [Internet] [Thesis]. Penn State University; 2013. [cited 2021 Apr 11].
Available from: https://submit-etda.libraries.psu.edu/catalog/17554.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Urschel JC. Graph-based Topics in Applied Mathematics. [Thesis]. Penn State University; 2013. Available from: https://submit-etda.libraries.psu.edu/catalog/17554
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Penn State University
12.
Zhang, Hongxuan.
ALGEBRAIC MULTIGRID METHODS AND THEIR APPLICATIONS.
Degree: 2017, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/14766huz114
► Algebraic MultiGrid (AMG) method, is one of the most efficient numerical techniques to solve large-scale linear system, especially for those arising from discretization of systems…
(more)
▼ Algebraic
MultiGrid (AMG) method, is one of the most efficient numerical techniques to solve large-scale linear system, especially for those arising from discretization of systems of partial differential equations (PDEs). In this work, we try to understand how and why an algebraic
multigrid method in a more abstract level. We develop a unified framework and theory that can be used to derive and analyze different algebraic
multigrid methods in a coherent manner. Given a smoother R for a matrix A, such as Gauss-Seidel or Jacobi, it is well-known that the optimal coarse space of dimension n
c is the span of the eigen-vectors corresponding to the first n
c eigen-values of \bar RA (with \bar R=R+R
T-RTAR). We prove that this optimal coarse space can be obtained by a constrained trace-minimization problem for a matrix associated with \bar RA and demonstrate that coarse spaces of most of existing AMG methods can be viewed some approximate solution of this trace-minimization problem. Furthermore, we develop a general approach to the construction of a quasi-optimal coarse space and we prove that under appropriate assumptions the resulting two-level AMG method for the underlying linear system converges uniformly with respect to the size of the problem, the coefficient variation, and the anisotropy. Our theory applies to most existing
multigrid methods, including the standard geometric
multigrid method, the classic AMG, energy-minimization AMG, unsmoothed and smoothed aggregation AMG, and spectral AMGe. Finally, we apply AMG methods to two application problems, one is on electrokinetics flow and the other is on reservoir simulation, which provide numerical results to demonstrate the efficiency and robustness of AMG methods.
Advisors/Committee Members: Jinchao Xu, Dissertation Advisor/Co-Advisor, Jinchao Xu, Committee Chair/Co-Chair, Ludmil Tomov Zikatanov, Committee Member, James Joseph Brannick, Committee Member, Yilin Wang, Outside Member.
Subjects/Keywords: Algebraic Multigrid; Numerical Linear Algebra; Numerical Analysis
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Export
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APA (6th Edition):
Zhang, H. (2017). ALGEBRAIC MULTIGRID METHODS AND THEIR APPLICATIONS. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/14766huz114
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Zhang, Hongxuan. “ALGEBRAIC MULTIGRID METHODS AND THEIR APPLICATIONS.” 2017. Thesis, Penn State University. Accessed April 11, 2021.
https://submit-etda.libraries.psu.edu/catalog/14766huz114.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Zhang, Hongxuan. “ALGEBRAIC MULTIGRID METHODS AND THEIR APPLICATIONS.” 2017. Web. 11 Apr 2021.
Vancouver:
Zhang H. ALGEBRAIC MULTIGRID METHODS AND THEIR APPLICATIONS. [Internet] [Thesis]. Penn State University; 2017. [cited 2021 Apr 11].
Available from: https://submit-etda.libraries.psu.edu/catalog/14766huz114.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Zhang H. ALGEBRAIC MULTIGRID METHODS AND THEIR APPLICATIONS. [Thesis]. Penn State University; 2017. Available from: https://submit-etda.libraries.psu.edu/catalog/14766huz114
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Penn State University
13.
Chen, Yao.
Algebraic Multilevel Methods for Graph Laplacians.
Degree: 2012, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/15362
► This dissertation presents estimates of the convergence rate and computational complexity of an algebraic multilevel preconditioner of graph Laplacian problems. The aim is to construct…
(more)
▼ This dissertation presents estimates of the convergence rate and computational complexity of an algebraic multilevel preconditioner of graph Laplacian problems. The aim is to construct fast and robust multilevel solvers, and this is achieved by balancing the convergence rate and the complexity of an aggregation based multilevel method. The main theoretical result consists of two parts: first, the relation between a graph partitioning and the convergence rate of the corresponding aggregation based two-level method is established; next, a multilevel method with polynomial coarse level corrections is constructed in the way that both its convergence rate and its complexity can be estimated simultaneously. Numerical tests further indicate the sharpness of the theoretical estimates. Some other interesting results, including a generalized definition of strength of connection, an optimal convergence condition of the algebraic multilevel iterations, and parallel implementations of the numerical solvers, are also addressed.
Advisors/Committee Members: James Joseph Brannick, Committee Chair/Co-Chair, Ludmil Tomov Zikatanov, Dissertation Advisor/Co-Advisor, Jinchao Xu, Committee Member, Jesse Louis Barlow, Special Member.
Subjects/Keywords: Algebraic Multigrid Methods; Graph Laplacians; Parallel Algorithms
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MLA ·
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CSE |
Export
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APA (6th Edition):
Chen, Y. (2012). Algebraic Multilevel Methods for Graph Laplacians. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/15362
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Chen, Yao. “Algebraic Multilevel Methods for Graph Laplacians.” 2012. Thesis, Penn State University. Accessed April 11, 2021.
https://submit-etda.libraries.psu.edu/catalog/15362.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Chen, Yao. “Algebraic Multilevel Methods for Graph Laplacians.” 2012. Web. 11 Apr 2021.
Vancouver:
Chen Y. Algebraic Multilevel Methods for Graph Laplacians. [Internet] [Thesis]. Penn State University; 2012. [cited 2021 Apr 11].
Available from: https://submit-etda.libraries.psu.edu/catalog/15362.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Chen Y. Algebraic Multilevel Methods for Graph Laplacians. [Thesis]. Penn State University; 2012. Available from: https://submit-etda.libraries.psu.edu/catalog/15362
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Colorado
14.
Glugla, Andrew.
Improving Robustness of Smoothed Aggregation Multigrid for Problems with Anisotropies.
Degree: MS, Applied Mathematics, 2011, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/12
► The application of multilevel methods to solving large algebraic systems obtained by discretization of PDEs has seen great success. However, these methods often perform…
(more)
▼ The application of multilevel methods to solving large algebraic systems obtained by discretization of PDEs has seen great success. However, these methods often perform sub-optimally when treating problems with anisotropies. For problems posed over unstructured meshes, optimal automatic
multigrid coarsening is not a fully solved problem for the smoothed aggregation
multigrid.
The focus of this thesis is on enhancing robustness of the coarsening in the Smoothed Aggregation (SA)
multigrid. We focus on improving the standard detection of coupling, on which the coarsening decisions in SA are based. Our approach takes the form of a two-pass test which allows for a more robust local control over the coupling detection, as well as added exibility permitting utilization of new coupling detection measures in a more systematic way.
For isotropic problems, smoothed aggregation coarsening is known to offer very favorable operator complexity, but achieving similar behavior in the presence of anisotropy is more challenging. Special attention is paid to addressing the issue of controlling the complexity of the method. We discuss several existing approaches to curbing coarse-level operator fill-in, and offer generalizations and improvements.
Numerical experiments are provided to demonstrate the performance of the improved coarsening on model examples of anisotropic problems featuring both cases where anisotropies are aligned with the grid, as well as cases where they are not.
Advisors/Committee Members: Marian Brezina, Thomas Manteuffel, Stephen McCormick.
Subjects/Keywords: anisotropies; multigrid coarsening; coupling detection; Applied Mathematics
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Export
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APA (6th Edition):
Glugla, A. (2011). Improving Robustness of Smoothed Aggregation Multigrid for Problems with Anisotropies. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/12
Chicago Manual of Style (16th Edition):
Glugla, Andrew. “Improving Robustness of Smoothed Aggregation Multigrid for Problems with Anisotropies.” 2011. Masters Thesis, University of Colorado. Accessed April 11, 2021.
https://scholar.colorado.edu/appm_gradetds/12.
MLA Handbook (7th Edition):
Glugla, Andrew. “Improving Robustness of Smoothed Aggregation Multigrid for Problems with Anisotropies.” 2011. Web. 11 Apr 2021.
Vancouver:
Glugla A. Improving Robustness of Smoothed Aggregation Multigrid for Problems with Anisotropies. [Internet] [Masters thesis]. University of Colorado; 2011. [cited 2021 Apr 11].
Available from: https://scholar.colorado.edu/appm_gradetds/12.
Council of Science Editors:
Glugla A. Improving Robustness of Smoothed Aggregation Multigrid for Problems with Anisotropies. [Masters Thesis]. University of Colorado; 2011. Available from: https://scholar.colorado.edu/appm_gradetds/12
University of Illinois – Urbana-Champaign
15.
Gahvari, Hormozd.
Improving the performance and scalability of algebraic multigrid solvers through applied performance modeling.
Degree: PhD, 0112, 2014, University of Illinois – Urbana-Champaign
URL: http://hdl.handle.net/2142/50516
► With single-core speeds no longer rising, dramatically increased parallelism is now the means of getting more performance from supercomputers. The current generation of algorithms run…
(more)
▼ With single-core speeds no longer rising, dramatically increased parallelism is now the means of getting more performance from supercomputers. The current generation of algorithms run on these machines will have to adapt to this new landscape. In this dissertation, we focus on algebraic
multigrid (AMG), a popular linear solver with many scientific and engineering applications. AMG has the attractive property of requiring work that is linear in the number of unknowns. However, it also has substantial communication requirements that impede its scalability on emerging architectures.
In our treatment of AMG, we make heavy use of performance modeling, developing a methodology we like to call, ``applied performance modeling,'' that drives how we analyze and adjust AMG to improve its performance and scalability. The fundamental idea is that straightforward performance models can be used to analyze applications and architectures and draw startlingly powerful conclusions about them. We develop such models for AMG and use them to explain performance difficulties on emerging machines, analyze a large body of past work in adapting
multigrid methods to massively parallel machines, and then perform a pair of practical tasks: guiding an algorithm that redistributes data to trade communication for computation, and informing the selection of thread/task mixes when using a hybrid programming model.
Our performance models accurately predict the performance of the AMG solve cycle on multiple platforms, capturing the application and architectural features behind the observed performance, and are easily extended to cover new platforms and AMG algorithms. The model-guided data redistribution yields significant improvements, and the suggestions provided for thread/task mixes enable users to avoid selecting ones that would perform poorly. We are encouraged by our results so far, and expect our work to be of continued use to AMG and to other applications in the future.
Advisors/Committee Members: Gropp, William D. (advisor), Gropp, William D. (Committee Chair), Heath, Michael T. (committee member), Olson, Luke N. (committee member), Vanka, Surya Pratap (committee member), Yang, Ulrike M. (committee member).
Subjects/Keywords: Algebraic Multigrid; Performance Modeling; Massively Parallel Architectures
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MLA ·
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Export
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Manager
APA (6th Edition):
Gahvari, H. (2014). Improving the performance and scalability of algebraic multigrid solvers through applied performance modeling. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50516
Chicago Manual of Style (16th Edition):
Gahvari, Hormozd. “Improving the performance and scalability of algebraic multigrid solvers through applied performance modeling.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed April 11, 2021.
http://hdl.handle.net/2142/50516.
MLA Handbook (7th Edition):
Gahvari, Hormozd. “Improving the performance and scalability of algebraic multigrid solvers through applied performance modeling.” 2014. Web. 11 Apr 2021.
Vancouver:
Gahvari H. Improving the performance and scalability of algebraic multigrid solvers through applied performance modeling. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/2142/50516.
Council of Science Editors:
Gahvari H. Improving the performance and scalability of algebraic multigrid solvers through applied performance modeling. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50516
16.
Bauer Petr.
Mathematical modelling of pollution transport in urban canopy
.
Degree: 2011, Czech University of Technology
URL: http://hdl.handle.net/10467/8037
Mathematical modelling of pollution transport in urban canopy; Mathematical modelling of pollution transport in urban canopy
Advisors/Committee Members: Jaňour Zbyněk (advisor).Subjects/Keywords: Navier-Stokes equations; advection-diffusion equation; multigrid
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Manager
APA (6th Edition):
Petr, B. (2011). Mathematical modelling of pollution transport in urban canopy
. (Thesis). Czech University of Technology. Retrieved from http://hdl.handle.net/10467/8037
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Petr, Bauer. “Mathematical modelling of pollution transport in urban canopy
.” 2011. Thesis, Czech University of Technology. Accessed April 11, 2021.
http://hdl.handle.net/10467/8037.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Petr, Bauer. “Mathematical modelling of pollution transport in urban canopy
.” 2011. Web. 11 Apr 2021.
Vancouver:
Petr B. Mathematical modelling of pollution transport in urban canopy
. [Internet] [Thesis]. Czech University of Technology; 2011. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/10467/8037.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Petr B. Mathematical modelling of pollution transport in urban canopy
. [Thesis]. Czech University of Technology; 2011. Available from: http://hdl.handle.net/10467/8037
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Clemson University
17.
Clevenger, Thomas Conrad.
A Parallel Geometric Multigrid Method for Adaptive Finite Elements.
Degree: PhD, Mathematical Sciences, 2019, Clemson University
URL: https://tigerprints.clemson.edu/all_dissertations/2523
► Applications in a variety of scientific disciplines use systems of Partial Differential Equations (PDEs) to model physical phenomena. Numerical solutions to these models are…
(more)
▼ Applications in a variety of scientific disciplines use systems of Partial Differential Equations (PDEs) to model physical phenomena. Numerical solutions to these models are often found using the Finite Element Method (FEM), where the problem is discretized and the solution of a large linear system is required, containing millions or even billions of unknowns. Often times, the domain of these solves will contain localized features that require very high resolution of the underlying finite element mesh to accurately solve, while a mesh with uniform resolution would require far too much computational time and memory overhead to be feasible on a modern machine. Therefore, techniques like adaptive mesh refinement, where one increases the resolution of the mesh only where it is necessary, must be used. Even with adaptive mesh refinement, these systems can still be on the order of much more than a million unknowns (large mantle convection applications like the ones in [90] show simulations on over 600 billion unknowns), and attempting to solve on a single processing unit is infeasible due to limited computational time and memory required. For this reason, any application code aimed at solving large problems must be built using a parallel framework, allowing the concurrent use of multiple processing units to solve a single problem, and the code must exhibit efficient scaling to large amounts of processing units.
Multigrid methods are currently the only known optimal solvers for linear systems arising from discretizations of elliptic boundary valued problems. These methods can be represented as an iterative scheme with contraction number less than one, independent of the resolution of the discretization [24, 54, 25, 103], with optimal complexity in the number of unknowns in the system [29]. Geometric
multigrid (GMG) methods, where the hierarchy of spaces are defined by linear systems of finite element discretizations on meshes of decreasing resolution, have been shown to be robust for many different problem formulations, giving mesh independent convergence for highly adaptive meshes [26, 61, 83, 18], but these methods require specific implementations for each type of equation, boundary condition, mesh, etc., required by the specific application. The implementation in a massively parallel environment is not obvious, and research into this topic is far from exhaustive.
We present an implementation of a massively parallel, adaptive geometric
multigrid (GMG) method used in the open-source finite element library deal.II [5], and perform extensive tests showing scaling of the v-cycle application on systems with up to 137 billion unknowns run on up to 65,536 processors, and demonstrating low communication overhead of the algorithms proposed. We then show the flexibility of the GMG by applying the method to four different PDE systems: the Poisson equation, linear elasticity, advection-diffusion, and the Stokes equations. For the Stokes equations, we implement a fully matrix-free, adaptive, GMG-based solver…
Advisors/Committee Members: Timo Heister, Qingshan Chen, Leo Rebholz, Fei Xue.
Subjects/Keywords: Geometric multigrid; Parallel computing; Stokes equations
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APA (6th Edition):
Clevenger, T. C. (2019). A Parallel Geometric Multigrid Method for Adaptive Finite Elements. (Doctoral Dissertation). Clemson University. Retrieved from https://tigerprints.clemson.edu/all_dissertations/2523
Chicago Manual of Style (16th Edition):
Clevenger, Thomas Conrad. “A Parallel Geometric Multigrid Method for Adaptive Finite Elements.” 2019. Doctoral Dissertation, Clemson University. Accessed April 11, 2021.
https://tigerprints.clemson.edu/all_dissertations/2523.
MLA Handbook (7th Edition):
Clevenger, Thomas Conrad. “A Parallel Geometric Multigrid Method for Adaptive Finite Elements.” 2019. Web. 11 Apr 2021.
Vancouver:
Clevenger TC. A Parallel Geometric Multigrid Method for Adaptive Finite Elements. [Internet] [Doctoral dissertation]. Clemson University; 2019. [cited 2021 Apr 11].
Available from: https://tigerprints.clemson.edu/all_dissertations/2523.
Council of Science Editors:
Clevenger TC. A Parallel Geometric Multigrid Method for Adaptive Finite Elements. [Doctoral Dissertation]. Clemson University; 2019. Available from: https://tigerprints.clemson.edu/all_dissertations/2523
18.
Senel, Gunes.
Multigrid method.
Degree: MS, Mathematics, 2017, The Ohio State University
URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1494347278971509
► The multigrid method is an algorithm aiming to provide a numerical solution to a system of equations. In this thesis we focus on its original…
(more)
▼ The
multigrid method is an algorithm aiming to provide
a numerical solution to a system of equations. In this thesis we
focus on its original purpose: solving differential equations. By
discretizing a differential equation, one obtains a system of
linear equations, which can be solved using
multigrid methods. We
will start our discussion in one dimension, considering ordinary
differential equations. First, we will review standard pointwise
relaxation methods, since they are a fundamental part of any
multigrid method. We will compare them in different settings and
see their shortcomings. This part also provides an insight of the
need for a better method, and one of the better methods is the
multigrid method. Then we will discuss elements of
multigrid method
in one dimension. We will apply the method on different problems,
compare and discuss the results, providing proofs and calculations
for easy but well-known phenomena, such as the reduction rate of
the error and the exact outcome of the method on the homogeneous
Poisson equation when damped Jacobi relaxation is chosen to be used
in the
multigrid method, and proof of the fact that the error for
the same equation can be totally eliminated in one single iteration
using the
multigrid method with the choice of red-black
Gauss-Seidel relaxation. We will consider a nontrivial ordinary
differential equation in order to be convinced that the problems
that the
multigrid method can deal with and the conclusions we have
arrived can be generalized. Afterwards we discuss the
multigrid
method in two dimensions, where it is mostly used in real life
applications. As we did in one dimension, we shortly review the
relaxation methods in two dimensions. Then we introduce the
elements of the
multigrid method in two dimensions. We apply the
multigrid method to some problems and tabulate the results, leaving
the redundant cases out. We discuss the results and compare them
with the one dimensional results.
Advisors/Committee Members: Overman, Edward (Advisor).
Subjects/Keywords: Mathematics; Multigrid
…4.
Multigrid in Two Dimensions . . . . . . . . . . . . . . . . . . . . . . . .
60
4.1… …Two Grid Method In Two Dimensions
V and W and Full Multigrid cycles . .
vii… …the end of first full multigrid cycle. e = 10. Started with
n = 128, went down the coarsest… …the end of first full multigrid cycle. e = 10. Started with
n = 128, went down the coarsest… …formalize
the equation and a chance to approximate the solution, whenever they can.
The multigrid…
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APA (6th Edition):
Senel, G. (2017). Multigrid method. (Masters Thesis). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1494347278971509
Chicago Manual of Style (16th Edition):
Senel, Gunes. “Multigrid method.” 2017. Masters Thesis, The Ohio State University. Accessed April 11, 2021.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1494347278971509.
MLA Handbook (7th Edition):
Senel, Gunes. “Multigrid method.” 2017. Web. 11 Apr 2021.
Vancouver:
Senel G. Multigrid method. [Internet] [Masters thesis]. The Ohio State University; 2017. [cited 2021 Apr 11].
Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1494347278971509.
Council of Science Editors:
Senel G. Multigrid method. [Masters Thesis]. The Ohio State University; 2017. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1494347278971509
King Abdullah University of Science and Technology
19.
Williams-Rioux, Bertrand.
Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries.
Degree: Biological and Environmental Sciences and Engineering (BESE) Division, 2012, King Abdullah University of Science and Technology
URL: http://hdl.handle.net/10754/209429
► Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell…
(more)
▼ Second order level set projection method for incompressible Navier-Stokes equations
is proposed to solve flow around arbitrary geometries. We used rectilinear grid
with collocated cell centered velocity and pressure. An explicit Godunov procedure
is used to address the nonlinear advection terms, and an implicit Crank-Nicholson
method to update viscous effects. An approximate pressure projection is implemented
at the end of the time stepping using
multigrid as a conventional fast iterative method.
The level set method developed by Osher and Sethian [17] is implemented to address
real momentum and pressure boundary conditions by the advection of a distance
function, as proposed by Aslam [3]. Numerical results for the Strouhal number and
drag coefficients validated the model with good accuracy for flow over a cylinder in
the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders
and an oscillating cylinder were performed, with the latter demonstrating our
methods ability to handle dynamic boundary conditions.
Advisors/Committee Members: Samtaney, Ravi (advisor), Stenchikov, Georgiy L. (committee member), Tempone, Raul (committee member).
Subjects/Keywords: level set; projection; incompressible; multigrid; navier-stokes
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APA ·
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APA (6th Edition):
Williams-Rioux, B. (2012). Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/209429
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Williams-Rioux, Bertrand. “Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries.” 2012. Thesis, King Abdullah University of Science and Technology. Accessed April 11, 2021.
http://hdl.handle.net/10754/209429.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Williams-Rioux, Bertrand. “Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries.” 2012. Web. 11 Apr 2021.
Vancouver:
Williams-Rioux B. Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2012. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/10754/209429.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Williams-Rioux B. Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries. [Thesis]. King Abdullah University of Science and Technology; 2012. Available from: http://hdl.handle.net/10754/209429
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
20.
Marline Ilha da Silva.
Estudo de métodos multigrid para solução de equações do tipo Poisson em malhas esféricas geodésicas icosaédricas.
Degree: 2014, University of São Paulo
URL: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-09042015-160400/
► O objetivo deste trabalho é o estudo de métodos multigrid para a solução de equações elípticas na esfera, discretizadas em malhas esféricas geodésicas icosaédricas. Malhas…
(more)
▼ O objetivo deste trabalho é o estudo de métodos multigrid para a solução de equações elípticas na esfera, discretizadas em malhas esféricas geodésicas icosaédricas. Malhas esféricas geradas a partir de sólidos platônicos receberam crescente atenção ao longo da última década, por serem razoavelmente uniformes e não apresentarem concentração de pontos em torno dos pólos como as tradicionais malhas latitude-longitude. Em especial, as malhas geodésicas icosaédricas (geradas a partir de um icosaedro inscrito na esfera com suas faces projetadas na superfície) têm sido adotadas no desenvolvimento de diversos modelos atmosféricos. Nestes é comum a necessidade de resolução de equações do tipo Poisson como parte do método de integração, motivando o nosso trabalho. Adotamos uma discretização do operador de Laplace baseada em volumes finitos. Para tal escrevemos o laplaciano como o divergente do gradiente. O divergente é discretizado com base nos fluxos nos
pontos médios das arestas das células computacionais (com o auxílio do teorema da divergência de Gauss) e no uso de diferenças centradas para aproximar as derivadas nesses pontos médios. Validamos a discretização para o operador de Laplace resolvendo uma equação de Poisson através dos métodos iterativos de Jacobi e Gauss-Seidel. Estes sabidamente não são eficientes computacionalmente, devido ao grande e crescente número de iterações necessárias para atingir a convergência ao refinar a malha. Uma alternativa muito eficiente para a resolução de equações elípticas é a métodologia multigrid. Investigamos alguns métodos multigrid propostos na literatura para a solução destas equações na malha esférica geodésica icosaédrica. A partir desse estudo, utilizando também como referência a Análise Local de Fourier para a equação de Poisson em malhas hexagonais uniformes, como uma aproximação para malhas geodésicas icosaédricas, escolhemos um algoritmo multigrid para implementação. Testamos
algumas opções para as componentes do esquema multigrid. Obtivemos taxas de convergência muito boas com V(1,1) ciclos com relaxação por Gauss-Seidel, restrição full weighting e interpolação linear.
This work is dedicated to the numerical solution of elliptic equations on the sphere, discretized on geodesic icosahedral grids. Spherical meshes generated from projections of platonic solids received considerable attention in the last decade, once they are almost isotropic and do not present a concentration of grid points around the poles, as traditional latitude-longitude grids. In particular, the geodesic icosahedral spherical grids have been adopted in the development of several atmospheric models. In these models, the necessity to solve Poisson type equations is very common, providing a motivation for our present work. We have employed a discretization of the Laplace operator based on finite volumes. We write the Laplacian as the divergent of the gradient operator and use Gauss
theorem to derive the discretization of the operator. We integrate the fluxes along the cell borders and…
Advisors/Committee Members: Saulo Rabello Maciel de Barros, Alice de Jesus Kozakevicius, Pedro da Silva Peixoto.
Subjects/Keywords: Discretização; Equação de Poisson; Malha icosaédrica; Multigrid; Discretization; Icosahedral grid; Multigrid; Poisson equation
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APA (6th Edition):
Silva, M. I. d. (2014). Estudo de métodos multigrid para solução de equações do tipo Poisson em malhas esféricas geodésicas icosaédricas. (Masters Thesis). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/45/45132/tde-09042015-160400/
Chicago Manual of Style (16th Edition):
Silva, Marline Ilha da. “Estudo de métodos multigrid para solução de equações do tipo Poisson em malhas esféricas geodésicas icosaédricas.” 2014. Masters Thesis, University of São Paulo. Accessed April 11, 2021.
http://www.teses.usp.br/teses/disponiveis/45/45132/tde-09042015-160400/.
MLA Handbook (7th Edition):
Silva, Marline Ilha da. “Estudo de métodos multigrid para solução de equações do tipo Poisson em malhas esféricas geodésicas icosaédricas.” 2014. Web. 11 Apr 2021.
Vancouver:
Silva MId. Estudo de métodos multigrid para solução de equações do tipo Poisson em malhas esféricas geodésicas icosaédricas. [Internet] [Masters thesis]. University of São Paulo; 2014. [cited 2021 Apr 11].
Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-09042015-160400/.
Council of Science Editors:
Silva MId. Estudo de métodos multigrid para solução de equações do tipo Poisson em malhas esféricas geodésicas icosaédricas. [Masters Thesis]. University of São Paulo; 2014. Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-09042015-160400/
21.
Millena Martins Villar.
Detailed Two-Dimensional Numerical Analysis of Multiphase Flows.
Degree: 2007, Federal University of Uberlândia
URL: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824
;
http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821
;
http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825
► The mathematical modeling of multiphase ows involves the interaction between deformable and moving geometries with the uid in which they are dispersed (immersed). This kind…
(more)
▼ The mathematical modeling of multiphase ows involves the interaction between deformable and moving geometries with the uid in which they are dispersed (immersed). This kind of interaction is present in many practical applications. A common approach to handle these problems is the so called Front-Tracking/Front-Capturing Hybrid Methods. This methodology consists in separating the problem into two domains: an eulerian domain, which is kept xed and is used to discretize the uid equations of both phases, and a lagrangian domain, which is used to solve the equations of motion of the interface. Since there is no geometric dependence between these two domains, the method can easily handle moving and deformable interfaces that are dispersed in the ow. Following this line of research, the present work aims to capture accurately details of such ows by resolving adequately the relevant physical scales in time and in space. This can be achieved by applying locally rened meshes which adapt dynamically to cover special ow regions, e.g. the vicinity of the uid-uid interfaces. To obtain the required resolution in time, a semi-implicit second order discretization to solve the Navier-Stokes equations is used. The turbulence modeling is introduced in the present work through Large Eddy Simulation. The eciency and robustness of the methodology applied are veried via convergence analysis, as well as with simulations of one-phase and two-phase ows for several Reynolds numbers. The results of two-phase ows, with one bubble and with multiple bubbles, are presented. The results obtained for a single bubble case are compared with Clift s shape diagram (Clift et al., 1978).
A modelagem matemÃtica de escoamentos multifÃsicos envolve a interaÃÃo de geometrias mÃveis e deformÃveis com o meio fluido que as envolve. Este tipo de interaÃÃo faz parte de uma extensa lista de aplicaÃÃes. Uma linha proposta para o tratamento num Ãrico deste tipo de problema sÃo os mÃtodos hÃbridos Front-Tracking/Front-Capturing. Esta abordagem leva à separaÃÃo do problema em dois domÃnios distintos (lÃquido/gÃs e lÃquido/lÃquido), um domÃnio fixo, euleriano, utilizado para discretizar as equaÃÃes de ambas as fases, e outro mÃvel, lagrangiano, usado para as interfaces. Para o presente trabalho, na metologia utilizada, ambos os domÃnios sÃo geometricamente independentes e nÃo apresentam restriÃÃo quanto ao movimento e à deformaÃÃo da fase dispersa. Seguindo esta linha, no presente trabalho propÃe-se capturar detalhes deste de tipo escoamento, resolvendo adequadamente as escalas fÃsicas do tempo e do espaÃo, utilizando malhas bloco estruturada refinadas localmente, as quais se adaptam dinamicamente para recobrir as regiÃes de interesse do escoamento (como, por exemplo, ao redor da interface fluido-fluido). Para se obter a resoluÃÃo necessÃria no tempo, à usada uma discretiza- ÃÃo semi-implÃcita de segunda ordem para solucionar as equaÃÃes de Navier-Stokes. A modelagem da turbulÃncia à introduzida no presente trabalho via SimulaÃÃo de Grandes Escalas. A eficiÃncia e a…
Advisors/Committee Members: Clovis Raimundo Maliska, SolidÃnio Rodrigues de Carvalho, Carlos Henrique Ataide, Aristeu da Silveira Neto, Alexandre Megiorin Roma, Carlos Roberto Ribeiro.
Subjects/Keywords: Turbulence; Adaptive mesh refinement; TurbulÃncia; Multigrid-multilevel; ENGENHARIA MECANICA; Escoamentos multifÃsicos; Mutltiphase flows; Multigrid-multinÃvel; Refinamento local adaptativo
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❌
APA ·
Chicago ·
MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Villar, M. M. (2007). Detailed Two-Dimensional Numerical Analysis of Multiphase Flows. (Thesis). Federal University of Uberlândia. Retrieved from http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Villar, Millena Martins. “Detailed Two-Dimensional Numerical Analysis of Multiphase Flows.” 2007. Thesis, Federal University of Uberlândia. Accessed April 11, 2021.
http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Villar, Millena Martins. “Detailed Two-Dimensional Numerical Analysis of Multiphase Flows.” 2007. Web. 11 Apr 2021.
Vancouver:
Villar MM. Detailed Two-Dimensional Numerical Analysis of Multiphase Flows. [Internet] [Thesis]. Federal University of Uberlândia; 2007. [cited 2021 Apr 11].
Available from: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Villar MM. Detailed Two-Dimensional Numerical Analysis of Multiphase Flows. [Thesis]. Federal University of Uberlândia; 2007. Available from: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
22.
Millena Martins Villar.
Análise numérica detalhada de escoamentos multifásicos bidimensionais.
Degree: 2007, Federal University of Uberlândia
URL: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821
;
http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824
;
http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825
► The mathematical modeling of multiphase flows involves the interaction between deformable and moving geometries with the fluid in which they are dispersed (immersed). This kind…
(more)
▼ The mathematical modeling of multiphase flows involves the interaction between deformable and moving geometries with the fluid in which they are dispersed (immersed). This kind of interaction is present in many practical applications. A common approach to handle these problems is the so called Front-Tracking/Front-Capturing Hybrid Methods. This methodology consists in separating the problem into two domains: an eulerian domain, which is kept fixed and is used to discretize the fluid equations of both phases, and a lagrangian domain, which is used to solve the equations of motion of the interface. Since there is no geometric dependence between these two domains, the method can easily handle moving and deformable interfaces that are dispersed in the flow. Following this line of research, the present work aims to capture accurately details of such flows by resolving adequately the relevant physical scales in time and in space. This can be achieved by applying locally refined meshes which adapt dynamically to cover special flow regions, e.g. the vicinity of the fluid-fluid interfaces. To obtain the required resolution in time, a semi-implicit second order discretization to solve the Navier-Stokes equations is used. The turbulence modeling is introduced in the present work through Large Eddy Simulation. The eficiency and robustness of the methodology applied are verified via convergence analysis, as well as with simulations of one-phase and two-phase flows for several Reynolds numbers. The results of two-phase flows, with one bubble and with multiple bubbles, are presented. The results obtained for a single bubble case are compared with Clift s shape diagram (Clift et al., 1978).
A modelagem matemática de escoamentos multifásicos envolve a interação de geometrias móveis e deformáveis com o meio fluido que as envolve. Este tipo de interação faz parte de uma extensa lista de aplicações. Uma linha proposta para o tratamento num érico deste tipo de problema são os métodos híbridos Front-Tracking/Front-Capturing. Esta abordagem leva à separação do problema em dois domínios distintos (líquido/gás e líquido/líquido), um domínio fixo, euleriano, utilizado para discretizar as equações de ambas as fases, e outro móvel, lagrangiano, usado para as interfaces. Para o presente trabalho, na metologia utilizada, ambos os domínios são geometricamente independentes e não apresentam restrição quanto ao movimento e à deformação da fase dispersa. Seguindo esta linha, no presente trabalho propõe-se capturar detalhes deste de tipo escoamento, resolvendo adequadamente as escalas físicas do tempo e do espaço, utilizando malhas bloco estruturada refinadas localmente, as quais se adaptam dinamicamente para recobrir as regiões de interesse do escoamento (como, por exemplo, ao redor da interface fluido-fluido). Para se obter a resolução necessária no tempo, é usada uma discretização semi-implícita de segunda ordem para solucionar as equações de Navier-Stokes. A modelagem da turbulência é introduzida no presente trabalho via Simulação de Grandes…
Advisors/Committee Members: Solidônio Rodrigues de Carvalho, Aristeu da Silveira Neto, Carlos Roberto Ribeiro, Alexandre Megiorin Roma, Clovis Raimundo Maliska, Carlos Henrique Ataide.
Subjects/Keywords: Multigrid-multinível; ENGENHARIA MECANICA; Escoamentos multifásicos; Turbulência; Refinamento local adaptativo; Adaptive mesh refinement; Mutltiphase flows; Turbulence; Multigrid-multilevel
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Record Details
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« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Villar, M. M. (2007). Análise numérica detalhada de escoamentos multifásicos bidimensionais. (Thesis). Federal University of Uberlândia. Retrieved from http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Villar, Millena Martins. “Análise numérica detalhada de escoamentos multifásicos bidimensionais.” 2007. Thesis, Federal University of Uberlândia. Accessed April 11, 2021.
http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Villar, Millena Martins. “Análise numérica detalhada de escoamentos multifásicos bidimensionais.” 2007. Web. 11 Apr 2021.
Vancouver:
Villar MM. Análise numérica detalhada de escoamentos multifásicos bidimensionais. [Internet] [Thesis]. Federal University of Uberlândia; 2007. [cited 2021 Apr 11].
Available from: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Villar MM. Análise numérica detalhada de escoamentos multifásicos bidimensionais. [Thesis]. Federal University of Uberlândia; 2007. Available from: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Delft University of Technology
23.
Diao, H. (author).
Fourier Analysis of Iterative Methods for the Helmholtz Problem.
Degree: 2012, Delft University of Technology
URL: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8
► This thesis attempts to explain the convergence behaviour of solving Helmholtz problem by investigating its spectral properties. Fourier analysis is employ to solve the eigenvalues…
(more)
▼ This thesis attempts to explain the convergence behaviour of solving Helmholtz problem by investigating its spectral properties. Fourier analysis is employ to solve the eigenvalues of the matrices that are involved in the iterative methods. The numerical experiment is conducted to verify the conclusions by Fourier analysis and also to reveal some other convergence behaviour.
Computer Simulation for Science and Engineering
Applied mathematics
Electrical Engineering, Mathematics and Computer Science
Advisors/Committee Members: Vuik, C. (mentor).
Subjects/Keywords: Helmholtz problem; Krylov subspace methods; multigrid method; multilevel Krylov multigrid method; shifted Laplacian preconditioner; deflation operator; Fourier analysis
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APA (6th Edition):
Diao, H. (. (2012). Fourier Analysis of Iterative Methods for the Helmholtz Problem. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8
Chicago Manual of Style (16th Edition):
Diao, H (author). “Fourier Analysis of Iterative Methods for the Helmholtz Problem.” 2012. Masters Thesis, Delft University of Technology. Accessed April 11, 2021.
http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8.
MLA Handbook (7th Edition):
Diao, H (author). “Fourier Analysis of Iterative Methods for the Helmholtz Problem.” 2012. Web. 11 Apr 2021.
Vancouver:
Diao H(. Fourier Analysis of Iterative Methods for the Helmholtz Problem. [Internet] [Masters thesis]. Delft University of Technology; 2012. [cited 2021 Apr 11].
Available from: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8.
Council of Science Editors:
Diao H(. Fourier Analysis of Iterative Methods for the Helmholtz Problem. [Masters Thesis]. Delft University of Technology; 2012. Available from: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8
University of New Mexico
24.
Sugiyama, Masumi.
Optimal Relaxation Weights for Multigrid Reduction In Time (MGRIT).
Degree: Mathematics & Statistics, 2019, University of New Mexico
URL: https://digitalrepository.unm.edu/math_etds/147
► Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are stagnate. This…
(more)
▼ Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are stagnate. This situation has created the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with
multigrid. In this work, we consider the scheme known as
multigrid-reduction-in-time (MGRIT), but note that there exist other parallel-in-time methods such as parareal and the parallel full approximation scheme in space and time (PFASST). MGRIT is a full multi-level method applied to the time dimension and computes multiple time-steps in parallel. Like all
multigrid methods, MGRIT relies on the complementary relationship between relaxation on a fine-grid and a correction from the coarse grid to solve the problem. In this work, we analyze and select relaxation weights for MGRIT using a convergence analysis and find that this is beneficial since it improves the convergence rate and consequently improves the efficiency of computation. We note that choosing appropriate weights for relaxation (here weighted-Jacobi) has a long history for improving the convergence of spatial
multigrid methods, and thus it is no surprise that such weight selection can be beneficial for MGRIT, too. Our numerical results demonstrate an improved convergence rate and lower iteration count for MGRIT when non-unitary weights are used for weighted-Jacobi.
Advisors/Committee Members: Jacob Schroder, Jehanzeb Chaudhry, Stephanie Friedhoff.
Subjects/Keywords: multigrid; multigrid-in-time; parallel-in-time; convergence theory; Applied Mathematics; Mathematics; Numerical Analysis and Computation
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APA (6th Edition):
Sugiyama, M. (2019). Optimal Relaxation Weights for Multigrid Reduction In Time (MGRIT). (Masters Thesis). University of New Mexico. Retrieved from https://digitalrepository.unm.edu/math_etds/147
Chicago Manual of Style (16th Edition):
Sugiyama, Masumi. “Optimal Relaxation Weights for Multigrid Reduction In Time (MGRIT).” 2019. Masters Thesis, University of New Mexico. Accessed April 11, 2021.
https://digitalrepository.unm.edu/math_etds/147.
MLA Handbook (7th Edition):
Sugiyama, Masumi. “Optimal Relaxation Weights for Multigrid Reduction In Time (MGRIT).” 2019. Web. 11 Apr 2021.
Vancouver:
Sugiyama M. Optimal Relaxation Weights for Multigrid Reduction In Time (MGRIT). [Internet] [Masters thesis]. University of New Mexico; 2019. [cited 2021 Apr 11].
Available from: https://digitalrepository.unm.edu/math_etds/147.
Council of Science Editors:
Sugiyama M. Optimal Relaxation Weights for Multigrid Reduction In Time (MGRIT). [Masters Thesis]. University of New Mexico; 2019. Available from: https://digitalrepository.unm.edu/math_etds/147
Brno University of Technology
25.
Sýkora, Ota.
Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems.
Degree: 2019, Brno University of Technology
URL: http://hdl.handle.net/11012/33105
► This bachelor thesis deals with the design and implementation of user interface of software application for simulation of elastohydrodynamic lubrication (EHL) problems. The first part…
(more)
▼ This bachelor thesis deals with the design and implementation of user interface of software application for simulation of elastohydrodynamic lubrication (EHL) problems. The first part of the thesis briefly reviews EHL simulations and describes the numerical method used for the application. The second part of the thesis provides an introduction into graphical user interfaces and describes the design and implemenation of the actual application in Qt Creator.
Advisors/Committee Members: Ficza, Ildikó (advisor), Poliščuk, Radek (referee).
Subjects/Keywords: elastohydrodynamické mazání; multigrid metoda; uživatelské prostředí; Qt Creator; elastohydrodynamic lubrication; multigrid method; user interface; Qt Creator
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APA ·
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APA (6th Edition):
Sýkora, O. (2019). Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/33105
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Sýkora, Ota. “Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems.” 2019. Thesis, Brno University of Technology. Accessed April 11, 2021.
http://hdl.handle.net/11012/33105.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Sýkora, Ota. “Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems.” 2019. Web. 11 Apr 2021.
Vancouver:
Sýkora O. Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems. [Internet] [Thesis]. Brno University of Technology; 2019. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/11012/33105.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Sýkora O. Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems. [Thesis]. Brno University of Technology; 2019. Available from: http://hdl.handle.net/11012/33105
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
26.
Nelson Leonardo Vidaurre Navarrete.
Paralelização de um modelo global de previsão do tempo em malhas localmente refinadas.
Degree: 2014, University of São Paulo
URL: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-23032015-110916/
► O objetivo principal deste trabalho é a paralelização de um modelo global de previsão do tempo em diferenças finitas com refinamento local. Este é baseado…
(more)
▼ O objetivo principal deste trabalho é a paralelização de um modelo global de previsão do tempo em diferenças finitas com refinamento local. Este é baseado nas equações primitivas, e faz uso de uma discretização semi-Lagrangiana e semi-implícita em três níveis no tempo em uma malha de Lorenz na vertical e uma malha do tipo C de Arakawa na horizontal. A discretização horizontal é feita através de diferenças finitas de segunda ordem. A equação escalar elíptica tridimensional resultante é desacoplada em um sistema de equações bidimensionais do tipo Helmholtz, o qual é resolvido por meio de um método multigrid. O modelo de paralelização foi desenvolvido para máquinas com memória distribuída, fazendo uso de MPI para passagens de mensagens e baseado em técnicas de decomposição de domínio. O acoplamento apenas local dos operadores de diferenças finitas viabiliza a decomposição em duas direções horizontais. Evitamos a decomposição vertical, tendo em vista o
forte acoplamento nesta direção das parametrizações de fenômenos físicos. A estratégia de paralelização foi elaborada visando o uso eficiente de centenas ou alguns milhares de processadores, dependendo da resolução do modelo. Para tal, a malha localmente refinada é separada em três regiões: uma grossa, uma de transição e uma fina, onde cada uma delas é dividida de forma independente entre um número de processadores proporcional ao número de pontos que cada uma armazena, garantindo assim um balanceamento de carga adequado. Não obstante, para resolver o sistema de equações bidimensionais do tipo Helmholtz foi necessário mudar a estratégia de paralelização, dividindo o domínio unicamente nas direções vertical e latitudinal. Ambas partes do modelo com paralelizações diferentes estão conectadas por meio da estratégia de transposição de dados. Testamos nosso modelo utilizando até 1024 processadores e os resultados ainda mostraram uma boa escalabilidade.
The main goal of this work is
the parallelization of a weather prediction model employing finite differences on locally refined meshes. The model is based on the primitive equations and uses a three-time-level semi-implicit semi-Lagrangian temporal discretization on a Lorenz-type vertical grid combined with a horizontal Arakawa C-grid. The horizontal discretization is performed by means of second order finite differences. The resulting three-dimensional scalar elliptic equation is decoupled into a set of Helmholtz-type two-dimensional equations, solved by a multigrid method. The parallelization has been written for distributed-memory machines, employing the MPI message passing standard and was based on domain decomposition techniques. The local coupling of the finite difference operators was exploited in a two-dimensional horizontal decomposition. We avoid a vertical decomposition due to the strong coupling of physical parameterization routines. The parallelization strategy has been designed in order to allow the
efficient use of hundreds to a few thousand processors, depending on the model resolution. In order to…
Advisors/Committee Members: Saulo Rabello Maciel de Barros, Pedro Leite da Silva Dias, Claudia Inés Garcia, Jairo Panetta, Alexandre Megiorin Roma.
Subjects/Keywords: Computação paralela; Multigrid; Refinamento local; Simulação numérica do tempo; Local refinement; Multigrid; Numerical weather simulation; Parallel computing
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APA ·
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APA (6th Edition):
Navarrete, N. L. V. (2014). Paralelização de um modelo global de previsão do tempo em malhas localmente refinadas. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/45/45132/tde-23032015-110916/
Chicago Manual of Style (16th Edition):
Navarrete, Nelson Leonardo Vidaurre. “Paralelização de um modelo global de previsão do tempo em malhas localmente refinadas.” 2014. Doctoral Dissertation, University of São Paulo. Accessed April 11, 2021.
http://www.teses.usp.br/teses/disponiveis/45/45132/tde-23032015-110916/.
MLA Handbook (7th Edition):
Navarrete, Nelson Leonardo Vidaurre. “Paralelização de um modelo global de previsão do tempo em malhas localmente refinadas.” 2014. Web. 11 Apr 2021.
Vancouver:
Navarrete NLV. Paralelização de um modelo global de previsão do tempo em malhas localmente refinadas. [Internet] [Doctoral dissertation]. University of São Paulo; 2014. [cited 2021 Apr 11].
Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-23032015-110916/.
Council of Science Editors:
Navarrete NLV. Paralelização de um modelo global de previsão do tempo em malhas localmente refinadas. [Doctoral Dissertation]. University of São Paulo; 2014. Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-23032015-110916/
27.
Hugo Marcial Checo Silva.
Models and methods for the direct simulation of rough and micropatterned surfaces.
Degree: 2016, University of São Paulo
URL: http://www.teses.usp.br/teses/disponiveis/55/55134/tde-08072016-165025/
► Friction in hydrodynamic bearings are a major source of losses in car engines ([69]). The extreme loading conditions in those bearings lead to contact between…
(more)
▼ Friction in hydrodynamic bearings are a major source of losses in car engines ([69]). The extreme loading conditions in those bearings lead to contact between the matching surfaces. In such conditions not only the overall geometry of the bearing is relevant, but also the small-scale topography of the surface determines the bearing performance. The possibility of shaping the surface of lubricated bearings down to the micrometer ([57]) opened the question of whether friction can be reduced by mean of micro-textures, with mixed results. This work focuses in the development of efficient numerical methods to solve thin film (lubrication) problems down to the roughness scale of measured surfaces. Due to the high velocities and the convergent-divergent geometries of hydrodynamic bearings, cavitation takes place. To treat cavitation in the lubrication problem the Elrod- Adams model is used, a mass-conserving model which has proven in careful numerical
([12]) and experimental ([119]) tests to be essential to obtain physically meaningful results. Another relevant aspect of the modeling is that the bearing inertial effects are considered, which is necessary to correctly simulate moving textures. As an application, the effects of micro-texturing the moving surface of the bearing were studied. Realistic values are assumed for the physical parameters defining the problems. Extensive fundamental studies were carried out in the hydrodynamic lubrication regime. Mesh-converged simulations considering the topography of real measured surfaces were also run, and the validity of the lubrication approximation was assessed for such rough surfaces.
O atrito em mancais hidrodinâmicos é uma fonte importante de perdas em motores de combustão ([69]). As condições extremas de carga induzem contato entre as superfícies dos mancais. Em tais condições não somente a macro-geometria do mancal é relevante, mas também são as escalas menores da superfície
as que determinam o desempenho do mancal. A possibilidade de fabricar superfícies com detalhes na escala do micrometro ([57]) deixou em aberto a questão de se o atrito pode ser reduzido por meio de micro-texturas, até agora com resultados mistos. Este trabalho centra-se no desenvolvimento de métodos numéricos eficientes para resolver problemas de lubrificação na escala da rugosidade das superfícies. Devido às altas velocidades e a forma convergente-divergente dos mancais hidrodinâmicos o fluido cavita. Para tratar o fenômeno de cavitação empregamos o modelo de Elrod-Adams, um modelo conservativo que tem demonstrado em cuidadosos testes numéricos ([12]) e experimentais ([119]) ser essencial para obter resultados físicos significativos. Outro aspecto revelante do modelado é que os efeitos inerciais do mancal são considerados, o que é necessário para simular corretamente texturas em movimento. Como aplicação, os efeitos de micro-texturizar a superfície móvel do mancal foram estudados.
Valores realistas são assumidos nos parâmetros físicos que definem o problema. Foram realizados extensivos…
Advisors/Committee Members: Gustavo Carlos Buscaglia, Enzo Alberto Dari, Luis Felipe Feres Pereira, Fabrício Simeoni de Sousa, Antonio Eduardo Meirelles Tomanik.
Subjects/Keywords: Cavitação; Modelo de Elrod-Adams; Multigrid; Simulação numérica; Superfícies texturizadas; Cavitation; Elrod-Adams model; Measured surfaces; Multigrid; Numerical simulation
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APA ·
Chicago ·
MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Silva, H. M. C. (2016). Models and methods for the direct simulation of rough and micropatterned surfaces. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/55/55134/tde-08072016-165025/
Chicago Manual of Style (16th Edition):
Silva, Hugo Marcial Checo. “Models and methods for the direct simulation of rough and micropatterned surfaces.” 2016. Doctoral Dissertation, University of São Paulo. Accessed April 11, 2021.
http://www.teses.usp.br/teses/disponiveis/55/55134/tde-08072016-165025/.
MLA Handbook (7th Edition):
Silva, Hugo Marcial Checo. “Models and methods for the direct simulation of rough and micropatterned surfaces.” 2016. Web. 11 Apr 2021.
Vancouver:
Silva HMC. Models and methods for the direct simulation of rough and micropatterned surfaces. [Internet] [Doctoral dissertation]. University of São Paulo; 2016. [cited 2021 Apr 11].
Available from: http://www.teses.usp.br/teses/disponiveis/55/55134/tde-08072016-165025/.
Council of Science Editors:
Silva HMC. Models and methods for the direct simulation of rough and micropatterned surfaces. [Doctoral Dissertation]. University of São Paulo; 2016. Available from: http://www.teses.usp.br/teses/disponiveis/55/55134/tde-08072016-165025/
28.
Juan Eduardo Casavilca Silva.
p-Multigrid explícito para um método de volumes finitos de alta-ordem não estruturado.
Degree: 2016, University of São Paulo
URL: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-24082016-174037/
► Desde o importante trabalho de Barth e Frederickson (1990), um certo número de pesquisadores têm estudado o método de Volumes Finitos de alta-ordem k-exato, por…
(more)
▼ Desde o importante trabalho de Barth e Frederickson (1990), um certo número de pesquisadores têm estudado o método de Volumes Finitos de alta-ordem k-exato, por exemplo o grupo do Prof. Ollivier-Gooch: Ollivier-Gooch e van Altena (2002), Nejat (2007), Michalak (2009), etc. Outras discretizações espaciais de alta-ordem bastante populares são o método Galerkin Descontínuo e o método de Diferença Espectral; processos iterativos que involucram estes esquemas tem sido acelerados, nos últimos anos, por métodos p-multigrid. Porém, esta aceleração não tem sido aplicada no contexto do método de Volumes Finitos de alta-ordem, pelo menos para conhecimento do autor desta tese. Por isso, o objetivo desta pesquisa é adaptar o p-multigrid desenvolvido por Liang et al. (2009b) no contexto da Diferença Espectral, para o ambiente dos Volumes Finitos estudado pelo Prof. Ollivier-Gooch. A pesquisa começa implementando o solver VF-RK, de Volumes Finitos com avanço
Runge-Kutta, para resolver as equações de advecção-difusão e de Euler aplicados a problemas estacionários, por exemplo, o escoamento transônico ao redor do NACA 0012. Depois, estuda-se o método p-multigrid no contexto da Diferença Espectral; o p-multigrid acelera o processo iterativo comutando níveis polinomiais de alta e de baixa-ordem. Após esse estudo, a adaptação ao âmbito dos Volumes Finitos é realizada resultando num p-multigrid relativamente mais simples porque, em contraposição com o p-multigrid para Diferença Espectral, não precisa de operadores de restrição e prolongação para a comunicação entre diferentes níveis polinomiais. A pesquisa conclui com uma comparação com o método de Volumes Finitos de 4a ordem sem p-multigrid (solver VF-RK). Nesse sentido, implementa-se o solver pMG, baseado no p-multigrid proposto, para resolver os problemas estacionários considerados na primeira parte do trabalho; o smoother do p-multigrid é o esquema Runge-Kutta do código VF-RK, e cada
problema estacionário é resolvido utilizando diferentes Vciclos procurando sempre soluções de 4a ordem. Os resultados indicam que o método p-multigrid proposto é mais eficiente que o método de Volumes Finitos de 4a ordem sem p-multigrid, isto é, os dois métodos oferecem a mesma precisão mas o primeiro pode levar menos de 50% do tempo de CPU do segundo.
Since Barth and Frederickson\'s important work (Barth e Frederickson, 1990), a number of researchers have studied high-order k-exact Finite Volume method, for example Prof. Ollivier-Gooch\'s group: Ollivier-Gooch e van Altena (2002), Nejat (2007), Michalak (2009), etc. Other quite popular high-order spatial discretizations are the Discontinuous Galerkin methods and the Spectral Difference methods; the iterative processes involving these schemes have been accelerated in recent years by p-multigrid methods. However, this acceleration has not been applied in the context of the high-order Finite Volume method, at least for the
knowledge of the author of this thesis. Therefore, the objective of this research is to adapt the p-multigrid developed by…
Advisors/Committee Members: Luis Carlos de Castro Santos, Cláudia Regina de Andrade, Antonio Castelo Filho, Nelson Mugayar Kuhl, Ernani Vitillo Volpe.
Subjects/Keywords: Advecção-difusão; Alta-ordem; Euler; p-multigrid; Volumes finitos; Advection-diffusion; Euler; Finite volume; High-order; p-multigrid
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APA ·
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Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Silva, J. E. C. (2016). p-Multigrid explícito para um método de volumes finitos de alta-ordem não estruturado. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/45/45132/tde-24082016-174037/
Chicago Manual of Style (16th Edition):
Silva, Juan Eduardo Casavilca. “p-Multigrid explícito para um método de volumes finitos de alta-ordem não estruturado.” 2016. Doctoral Dissertation, University of São Paulo. Accessed April 11, 2021.
http://www.teses.usp.br/teses/disponiveis/45/45132/tde-24082016-174037/.
MLA Handbook (7th Edition):
Silva, Juan Eduardo Casavilca. “p-Multigrid explícito para um método de volumes finitos de alta-ordem não estruturado.” 2016. Web. 11 Apr 2021.
Vancouver:
Silva JEC. p-Multigrid explícito para um método de volumes finitos de alta-ordem não estruturado. [Internet] [Doctoral dissertation]. University of São Paulo; 2016. [cited 2021 Apr 11].
Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-24082016-174037/.
Council of Science Editors:
Silva JEC. p-Multigrid explícito para um método de volumes finitos de alta-ordem não estruturado. [Doctoral Dissertation]. University of São Paulo; 2016. Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-24082016-174037/
Universidade Estadual de Campinas
29.
Ramos, Leandro Ito, 1990-.
Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial.
Degree: Faculdade de Engenharia Mecânica; Programa de Pós-Graduação em Engenharia Mecânica, 2018, Universidade Estadual de Campinas
URL: RAMOS,
Leandro
Ito.
Modelagem
de
mancais
hidrodinâmicos
com
efeitos
de
texturização
superficial.
2018.
1
recurso
online
(119
p.).
Dissertação
(mestrado)
-
Universidade
Estadual
de
Campinas,
Faculdade
de
Engenharia
Mecânica,
Campinas,
SP.
Disponível
em:
<http://www.repositorio.unicamp.br/handle/REPOSIP/331142>.
Acesso
em:
3
set.
2018.
;
http://repositorio.unicamp.br/jspui/handle/REPOSIP/331142
► Orientador: Gregory Bregion Daniel
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
Made available in DSpace on 2018-09-03T09:22:52Z (GMT). No. of bitstreams:…
(more)
▼ Orientador: Gregory Bregion Daniel
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
Made available in DSpace on 2018-09-03T09:22:52Z (GMT). No. of bitstreams: 1 Ramos_LeandroIto_M.pdf: 6462078 bytes, checksum: bec1cda289b67bf3c4dbf72ad1a2dc0a (MD5) Previous issue date: 2018
Resumo: É crescente a demanda por máquinas e equipamentos mais eficientes quanto ao consumo energético, uma vez que as legislações ambiental e de eficiência energética têm pressionado de forma crescente os fabricantes das mesmas. Neste contexto, o mancal hidrodinâmico radial apresenta-se como um componente de máquinas rotativas com grandes oportunidades de melhoria de projeto para redução da energia dissipada em seu fluido lubrificante. Recentemente a texturização da superfície interna de mancais tem sido uma abordagem explorada no intuito de alcançar melhorias não somente nesta dissipação viscosa como também na sustentação
hidrodinâmica no componente. Assim, o objetivo do presente trabalho foi desenvolver códigos computacionais eficientes para investigação do efeito da inserção de texturas na superfície de mancais hidrodinâmicos sobre seu funcionamento, definindo ainda parâmetros adequados de texturização para as condições estática e dinâmica de carregamento do componente. Para tanto, a equação clássica de Reynolds com condição de fronteira de cavitação de Swift-Stieber foi adotada e sua discretização foi realizada pela aplicação do Método dos Volumes Finitos (MVF). O sistema de equações resultante é resolvido por um algoritmo Full Multigrid (FMG). Foram estudados os valores mais adequados para os parâmetros da técnica numérica de multiníveis para, em seguida, explorar os efeitos das texturizações parcial e total da superfície do mancal sobre suas principais características estáticas. Os resultados mostram a necessidade por uma seleção adequada principalmente do número de níveis utilizados na técnica
multiníveis de modo que mesmo o nível com a malha mais grosseira ainda seja capaz de detectar com nitidez as texturas na superfície do componente. As simulações com mancais texturizados em condição estática de carregamento mostraram que as condições de operação influenciam de forma significativa os efeitos dos parâmetros de texturas, para as texturizações completa e parcial, e que é possível obter ganho de sustentação e/ou redução da perda viscosa no componente através dos adequados posicionamento e especificação das características geométricas das texturas. Mancais com texturizações projetadas em condição estática de carregamento mantêm as melhorias atingidas na sustentação hidrodinâmica e/ou dissipação viscosa quando empregados em sistemas rotativos com pequeno desbalanceamento de massa
The demand for more efficient machines and equipment regarding energy consumption is growing since environmental and energy efficiency legislations have increasingly pressured their
manufacturers. In this context, the radial hydrodynamic bearing is a component of rotary machines with great opportunities for…
Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS, Daniel, Gregory Bregion, 1984-, Bittencourt, Marco Lúcio, Bavastri, Carlos Alberto.
Subjects/Keywords: Mancais; Textura; Métodos multigrid (Análise numérica); Método dos volumes finitos; Bearings; Texture; Multigrid methods (Numerical analysis); Finite volume method
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APA ·
Chicago ·
MLA ·
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Export
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APA (6th Edition):
Ramos, Leandro Ito, 1. (2018). Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. (Masters Thesis). Universidade Estadual de Campinas. Retrieved from RAMOS, Leandro Ito. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. 2018. 1 recurso online (119 p.). Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/331142>. Acesso em: 3 set. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/331142
Chicago Manual of Style (16th Edition):
Ramos, Leandro Ito, 1990-. “Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial.” 2018. Masters Thesis, Universidade Estadual de Campinas. Accessed April 11, 2021.
RAMOS, Leandro Ito. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. 2018. 1 recurso online (119 p.). Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/331142>. Acesso em: 3 set. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/331142.
MLA Handbook (7th Edition):
Ramos, Leandro Ito, 1990-. “Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial.” 2018. Web. 11 Apr 2021.
Vancouver:
Ramos, Leandro Ito 1. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. [Internet] [Masters thesis]. Universidade Estadual de Campinas; 2018. [cited 2021 Apr 11].
Available from: RAMOS, Leandro Ito. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. 2018. 1 recurso online (119 p.). Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/331142>. Acesso em: 3 set. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/331142.
Council of Science Editors:
Ramos, Leandro Ito 1. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. [Masters Thesis]. Universidade Estadual de Campinas; 2018. Available from: RAMOS, Leandro Ito. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. 2018. 1 recurso online (119 p.). Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/331142>. Acesso em: 3 set. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/331142
University of Pretoria
30.
[No author].
An algebraic multigrid solution strategy for efficient
solution of free-surface flows
.
Degree: 2011, University of Pretoria
URL: http://upetd.up.ac.za/thesis/available/etd-09222011-093322/
► Free-surface modelling (FSM) is a highly relevant and computationally intensive area of study in modern computational fluid dynamics. The Elemental software suite currently under development…
(more)
▼ Free-surface modelling (FSM) is a highly relevant
and computationally intensive area of study in modern computational
fluid dynamics. The Elemental software suite currently under
development offers FSMcapability, and employs a preconditioned
GMRES solver in an attempt to effect fast solution times. In terms
of potential solver performance however,
multigrid methods can be
considered state-of-the-art. This work details the investigation
into the use of AlgebraicMultigrid (AMG) as a high performance
solver tool for use as black box plug-in for Elemental FSM. Special
attention was given to the development of novel and robust methods
of addressing AMG setup costs in addition to transcribing the
solver to efficient C++ object-oriented code. This led to the
development of the so-called Freeze extension of the basic
algebraic
multigrid method in an object-oriented C++ programming
environment. The newly developed Freeze method reduces setup costs
by periodically performing the setup procedure in an automatic and
robust manner. The developed technology was evaluated in terms of
robustness, stability and speed by applying it to benchmark FSM
problems on structured and unstructured meshes of various sizes.
This evaluation yielded a number of conclusive findings. First, the
developed Freeze method reduced setup times by an order of
magnitude. Second, the developed AMG solver offered substantial
performance increases over the preconditioned GMRES method. In this
way, it is proposed that this work has furthered the
state-of-the-art of algebraic
multigrid methods applied in the
context of free-surface modelling.
Advisors/Committee Members: Dr A G Malan (advisor), Dr D N Wilke (advisor).
Subjects/Keywords: Algebraic;
Multigrid solution strategy;
Free-surface flows;
UCTD
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APA (6th Edition):
author], [. (2011). An algebraic multigrid solution strategy for efficient
solution of free-surface flows
. (Masters Thesis). University of Pretoria. Retrieved from http://upetd.up.ac.za/thesis/available/etd-09222011-093322/
Chicago Manual of Style (16th Edition):
author], [No. “An algebraic multigrid solution strategy for efficient
solution of free-surface flows
.” 2011. Masters Thesis, University of Pretoria. Accessed April 11, 2021.
http://upetd.up.ac.za/thesis/available/etd-09222011-093322/.
MLA Handbook (7th Edition):
author], [No. “An algebraic multigrid solution strategy for efficient
solution of free-surface flows
.” 2011. Web. 11 Apr 2021.
Vancouver:
author] [. An algebraic multigrid solution strategy for efficient
solution of free-surface flows
. [Internet] [Masters thesis]. University of Pretoria; 2011. [cited 2021 Apr 11].
Available from: http://upetd.up.ac.za/thesis/available/etd-09222011-093322/.
Council of Science Editors:
author] [. An algebraic multigrid solution strategy for efficient
solution of free-surface flows
. [Masters Thesis]. University of Pretoria; 2011. Available from: http://upetd.up.ac.za/thesis/available/etd-09222011-093322/
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