subject:(Fast solvers)

Indian Institute of Science

1. Das, Arkaprovo. Fast Solvers for Integtral-Equation based Electromagnetic Simulations.

Degree: PhD, Faculty of Engineering, 2018, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2998

► With the rapid increase in available compute power and memory, and bolstered by the advent of efficient formulations and algorithms, the role of 3D full-wave… (more)

▼ With the rapid increase in available compute power and memory, and bolstered by the advent of efficient formulations and algorithms, the role of 3D full-wave computational methods for accurate modelling of complex electromagnetic (EM) structures has gained in significance. The range of problems includes Radar Cross Section (RCS) computation, analysis and design of antennas and passive microwave circuits, bio-medical non-invasive detection and therapeutics, energy harvesting etc. Further, with the rapid advances in technology trends like System-in-Package (SiP) and System-on-Chip (SoC), the fidelity of chip-to-chip communication and package-board electrical performance parameters like signal integrity (SI), power integrity (PI), electromagnetic interference (EMI) are becoming increasingly critical. Rising pin-counts to satisfy functionality requirements and decreasing layer-counts to maintain cost-effectiveness necessitates 3D full wave electromagnetic solution for accurate system modelling. Method of Moments (MoM) is one such widely used computational technique to solve a 3D electromagnetic problem with full-wave accuracy. Due to lesser number of mesh elements or discretization on the geometry, MoM has an advantage of a smaller matrix size. However, due to Green's Function interactions, the MoM matrix is dense and its solution presents a time and memory challenge. The thesis focuses on formulation and development of novel techniques that aid in fast MoM based electromagnetic solutions. With the recent paradigm shift in computer hardware architectures transitioning from single-core microprocessors to multi-core systems, it is of prime importance to parallelize the serial electromagnetic formulations in order to leverage maximum computational benefits. Therefore, the thesis explores the possibilities to expedite an electromagnetic simulation by scalable parallelization of near-linear complexity algorithms like Fast Multipole Method (FMM) on a multi-core platform. Secondly, with the best of parallelization strategies in place and near-linear complexity algorithms in use, the solution time of a complex EM problem can still be exceedingly large due to over-meshing of the geometry to achieve a desired level of accuracy. Hence, the thesis focuses on judicious placement of mesh elements on the geometry to capture the physics of the problem without compromising on accuracy- a technique called Adaptive Mesh Refinement. This facilitates a reduction in the number of solution variables or degrees of freedom in the system and hence the solution time. For multi-scale structures as encountered in chip-package-board systems, the MoM formulation breaks down for parts of the geometry having dimensions much smaller as compared to the operating wavelength. This phenomenon is popularly known as low-frequency breakdown or low-frequency instability. It results in an ill-conditioned MoM system matrix, and hence higher iteration count to converge when solved using an iterative solver framework. This consequently increases the solution time… Advisors/Committee Members: Gope, Dipanjan (advisor).

Subjects/Keywords: Electromagnetic Solvers; Method of Moments (MOM); Electromagnetic Simulations; Computational Electromagnetics; Electromagnetics; Fast Multiple Method; Adaptive Mesh Refinement; Integral Equation Electromagnetic Solvers; Electromagnetic Refinement Indicators; Electric Field Integral Equation; Electrical Communication Engineering

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APA (6^th Edition):

Das, A. (2018). Fast Solvers for Integtral-Equation based Electromagnetic Simulations. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2998

Chicago Manual of Style (16^th Edition):

Das, Arkaprovo. “Fast Solvers for Integtral-Equation based Electromagnetic Simulations.” 2018. Doctoral Dissertation, Indian Institute of Science. Accessed April 10, 2021. http://etd.iisc.ac.in/handle/2005/2998.

MLA Handbook (7^th Edition):

Das, Arkaprovo. “Fast Solvers for Integtral-Equation based Electromagnetic Simulations.” 2018. Web. 10 Apr 2021.

Vancouver:

Das A. Fast Solvers for Integtral-Equation based Electromagnetic Simulations. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2018. [cited 2021 Apr 10]. Available from: http://etd.iisc.ac.in/handle/2005/2998.

Council of Science Editors:

Das A. Fast Solvers for Integtral-Equation based Electromagnetic Simulations. [Doctoral Dissertation]. Indian Institute of Science; 2018. Available from: http://etd.iisc.ac.in/handle/2005/2998

King Abdullah University of Science and Technology

2. Chavez Chavez, Gustavo Ivan. Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2017, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/625172

► This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic… (more)

▼ This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST's Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption. Advisors/Committee Members: Keyes, David E. (advisor), Moshkov, Mikhail (committee member), Ketcheson, David I. (committee member), Turkiyyah, George (committee member), Huang, Jingfang (committee member).

Subjects/Keywords: hierarchical matrices; cyclic reduction; fast solvers; Direct solvers; preconditioning; Parallel Computing

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APA (6^th Edition):

Chavez Chavez, G. I. (2017). Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/625172

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chavez Chavez, Gustavo Ivan. “Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations.” 2017. Thesis, King Abdullah University of Science and Technology. Accessed April 10, 2021. http://hdl.handle.net/10754/625172.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chavez Chavez, Gustavo Ivan. “Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations.” 2017. Web. 10 Apr 2021.

Vancouver:

Chavez Chavez GI. Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2017. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/10754/625172.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chavez Chavez GI. Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations. [Thesis]. King Abdullah University of Science and Technology; 2017. Available from: http://hdl.handle.net/10754/625172

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

3. Alharthi, Noha. Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2019, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/660105

► Acoustic and electromagnetic scattering from arbitrarily shaped structures can be numerically characterized by solving various surface integral equations (SIEs). One of the most effective techniques… (more)

▼ Acoustic and electromagnetic scattering from arbitrarily shaped structures can be numerically characterized by solving various surface integral equations (SIEs). One of the most effective techniques to solve SIEs is the Nyström method. Compared to other existing methods,the Nyström method is easier to implement especially when the geometrical discretization is non-conforming and higher-order representations of the geometry and unknowns are desired. However,singularities of the Green’s function are more difﬁcult to”manage”since they are not ”smoothened” through the use of a testing function. This dissertation describes purely numerical schemes to account for different orders of singularities that appear in acoustic and electromagnetic SIEs when they are solved by a high-order Nyström method utilizing a mesh of curved discretization elements. These schemes make use of two sets of basis functions to smoothen singular integrals: the grid robust high-order Lagrange and the high-order Silvester-Lagrange interpolation basis functions. Numerical results comparing the convergence of two schemes are presented. Moreover, an extremely scalable implementation of fast multipole method (FMM) is developed to efﬁciently (and iteratively) solve the linear system resulting from the discretization of the acoustic SIEs by the Nyström method. The implementation results in O(N log N) complexity for high-frequency scattering problems. This FMM-accelerated solver can handle N =2 billion on a 200,000-core Cray XC40 with 85% strong scaling efﬁciency. Iterative solvers are often ineffective for ill-conditioned problems. Thus, a fast direct (LU)solver,which makes use of low-rank matrix approximations,is also developed. This solver relies on tile low rank (TLR) data compression format, as implemented in the hierarchical computations on many corearchitectures (HiCMA) library. This requires to taskify the underlying SIE kernels to expose ﬁne-grained computations. The resulting asynchronous execution permit to weaken the artifactual synchronization points,while mitigating the overhead of data motion. We compare the obtained performance results of our TLRLU factorization against the state-of-the-art dense factorizations on shared memory systems. We achieve up to a fourfold performance speedup on a 3D acoustic problem with up to 150 K unknowns in double complex precision arithmetics. Advisors/Committee Members: Keyes, David E. (advisor), Hadwiger, Markus (committee member), Bagci, Hakan (committee member), Kressner, Daniel (committee member).

Subjects/Keywords: Boundary Integral Equation; Acoustic Scattering; LU-Based Solver; Fast Solvers; Fast Multipole Solvers; Tile Low-Rank Approximations

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APA (6^th Edition):

Alharthi, N. (2019). Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/660105

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Alharthi, Noha. “Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems.” 2019. Thesis, King Abdullah University of Science and Technology. Accessed April 10, 2021. http://hdl.handle.net/10754/660105.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Alharthi, Noha. “Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems.” 2019. Web. 10 Apr 2021.

Vancouver:

Alharthi N. Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2019. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/10754/660105.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Alharthi N. Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems. [Thesis]. King Abdullah University of Science and Technology; 2019. Available from: http://hdl.handle.net/10754/660105

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Rice University

4. Geldermans, Peter. Accelerated PDE Constrained Optimization using Direct Solvers.

Degree: MA, Engineering, 2018, Rice University

URL: http://hdl.handle.net/1911/105485

► In this thesis, I propose a method to reduce the cost of computing solutions to optimization problems governed by partial differential equations (PDEs). Standard second… (more)

Subjects/Keywords: PDE constrained optimization; direct solvers; fast solvers

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APA (6^th Edition):

Geldermans, P. (2018). Accelerated PDE Constrained Optimization using Direct Solvers. (Masters Thesis). Rice University. Retrieved from http://hdl.handle.net/1911/105485

Chicago Manual of Style (16^th Edition):

Geldermans, Peter. “Accelerated PDE Constrained Optimization using Direct Solvers.” 2018. Masters Thesis, Rice University. Accessed April 10, 2021. http://hdl.handle.net/1911/105485.

MLA Handbook (7^th Edition):

Geldermans, Peter. “Accelerated PDE Constrained Optimization using Direct Solvers.” 2018. Web. 10 Apr 2021.

Vancouver:

Geldermans P. Accelerated PDE Constrained Optimization using Direct Solvers. [Internet] [Masters thesis]. Rice University; 2018. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/1911/105485.

Council of Science Editors:

Geldermans P. Accelerated PDE Constrained Optimization using Direct Solvers. [Masters Thesis]. Rice University; 2018. Available from: http://hdl.handle.net/1911/105485

5. Zhang, Yabin. A fast direct solver for boundary value problems with locally-perturbed geometries.

Degree: MA, Engineering, 2017, Rice University

URL: http://hdl.handle.net/1911/105467

► Many problems in science and engineering can be formulated as integral equations with elliptic kernels. In particular, in optimal control and design problems, the domain… (more)

Subjects/Keywords: fast direct solvers; boundary integral equations; local perturbation

…system as well as a more detailed discussion of one of the fast direct solvers, specifically… …the HBS solver. 6 Chapter 2 Fast Direct Solvers for BIEs The solver proposed in this… …wider range of problems. In the last fifteen years, new fast direct solvers, such as HSS, HBS… …area in current research. 10 2.2 Outline of Fast Direct Solvers The previous section… …lists several recently-developed fast direct solvers for BIEs: HSS, HBS, and HODLR [20…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zhang, Y. (2017). A fast direct solver for boundary value problems with locally-perturbed geometries. (Masters Thesis). Rice University. Retrieved from http://hdl.handle.net/1911/105467

Chicago Manual of Style (16^th Edition):

Zhang, Yabin. “A fast direct solver for boundary value problems with locally-perturbed geometries.” 2017. Masters Thesis, Rice University. Accessed April 10, 2021. http://hdl.handle.net/1911/105467.

MLA Handbook (7^th Edition):

Zhang, Yabin. “A fast direct solver for boundary value problems with locally-perturbed geometries.” 2017. Web. 10 Apr 2021.

Vancouver:

Zhang Y. A fast direct solver for boundary value problems with locally-perturbed geometries. [Internet] [Masters thesis]. Rice University; 2017. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/1911/105467.

Council of Science Editors:

Zhang Y. A fast direct solver for boundary value problems with locally-perturbed geometries. [Masters Thesis]. Rice University; 2017. Available from: http://hdl.handle.net/1911/105467

Stellenbosch University

6. Jackman, Kyle. Fast multi-core CEM solvers and flux trapping analysis for superconducting structures.

Degree: PhD, Electrical and Electronic Engineering, 2018, Stellenbosch University

URL: http://hdl.handle.net/10019.1/103747

►

ENGLISH ABSTRACT: The dissertation presents the development of a numerical field solver, called TetraHenry (TTH), for inductance extraction and flux trapping analysis of superconducting integrated… (more)

▼

ENGLISH ABSTRACT: The dissertation presents the development of a numerical field solver, called TetraHenry (TTH), for inductance extraction and flux trapping analysis of superconducting integrated circuits. The solver uses tetrahedral elements to model multidirectional current flow in complex three-dimensional superconducting volumes; whereas two dimensional triangular elements are used for sheet currents in thin superconducting films. Triangular meshing significantly reduces the number of unknowns and provides the capability to analyse chipscale superconducting layouts. Support for piecewise homogenous dielectric materials are implemented, which enables frequency-depended impedance extraction. The Fast Multipole Method for the Biot-Savart law, which enables the simulation of magnetic materials, is derived. The effects of external magnetic fields on the performance of superconducting circuits are analysed. The amount of flux through each hole or moat can be specified using the Volume Loop basis function; enabling flux trapping analysis and inductance extraction around holes. The full derivation of the integral equations for volume and sheet currents are discussed. The Method of Moments is used to obtain a system of linear equations, which is solved with a preconditioned GMRES solver. Matrix-vector multiplication is accelerated with the Fast Multipole method. The accuracy and performance of the numerical solver are evaluated, by comparing simulated results to existing software.

AFRIKAANSE OPSOMMING: Die dissertasie bied aan die ontwikkeling van ’n numeriese veldoplosser, genaamd TetraHenry (TTH), vir induktansie onttrekking en vloed-vasvang analise van supergeleier geïntegreerde stroombane. Die veldoplosser gebruik tetrahedraal elemente om stroomvloei binne komplekse driedimensionele supergeleidende volumes te modelleer; terwyl tweedimensionele driehoekige elemente gebruik word vir stroomvloei in dun supergeleier filamente. Driehoekige elemente verminder die aantal onbekendes aansienlik en bied die vermoë om supergeleier uitlegte op groot skaal te analiseer. Ondersteuning vir stuksgewyse homogene diëlektriese materiale word geïmplementeer, wat frekwensie-afhanklike impedansie onttrekking moontlik maak. Die “Fast Multipole” metode vir die Biot Savart wet, wat die simulering van magnetiese materiale moontlik maak, word afgelei. Die effekte van eksterne magnetiese velde op supergeleier stroombane word ontleed. Vloed-vasvang analise en induktansie onttrekking rondom gate word uitgevoer met behulp van Volume Lus funksies. Die volledige afleiding van die integraalvergelykings vir volume en oppervlakstrome word bespreek. Die Metode van Momente word gebruik om ’n stelsel van lineêre vergelykings te verkry, wat opgelos word met ’n voorafbepaalde GMRES iteratiewe oplosser. Matriks-vektor vermenigvuldiging word versnel met die “Fast Multipole” metode. Die akkuraatheid en spoed van die numeriese enjin word geëvalueer deur gesimuleerde resultate te vergelyk met bestaande sagteware.

Advisors/Committee Members: Fourie, Coenrad J., Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering..

Subjects/Keywords: Fast Multi-Core CEM Solvers; CEM (Air quality); Integrated circuits; Heat flux; UCTD

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APA (6^th Edition):

Jackman, K. (2018). Fast multi-core CEM solvers and flux trapping analysis for superconducting structures. (Doctoral Dissertation). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/103747

Chicago Manual of Style (16^th Edition):

Jackman, Kyle. “Fast multi-core CEM solvers and flux trapping analysis for superconducting structures.” 2018. Doctoral Dissertation, Stellenbosch University. Accessed April 10, 2021. http://hdl.handle.net/10019.1/103747.

MLA Handbook (7^th Edition):

Jackman, Kyle. “Fast multi-core CEM solvers and flux trapping analysis for superconducting structures.” 2018. Web. 10 Apr 2021.

Vancouver:

Jackman K. Fast multi-core CEM solvers and flux trapping analysis for superconducting structures. [Internet] [Doctoral dissertation]. Stellenbosch University; 2018. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/10019.1/103747.

Council of Science Editors:

Jackman K. Fast multi-core CEM solvers and flux trapping analysis for superconducting structures. [Doctoral Dissertation]. Stellenbosch University; 2018. Available from: http://hdl.handle.net/10019.1/103747

Universitat Politècnica de Catalunya

7. Tamayo Palau, José María. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.

Degree: Departament de Teoria del Senyal i Comunicacions, 2011, Universitat Politècnica de Catalunya

URL: http://hdl.handle.net/10803/6952

► The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in… (more)

▼ The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in several electromagnetic antenna and scattering problems. The most utilized of these formulations are the Electric Field Integral Equation (EFIE), the Magnetic Field Integral Equation (MFIE) and the Combined Field Integral Equation (CFIE), which is a linear combination of the other two. The MFIE and CFIE formulations are only valid for closed objects and need to deal with the integration of singular kernels with singularities of higher order than the EFIE. The lack of efficient and accurate techniques for the computation of these singular integrals has led to inaccuracies in the results. Consequently, their use has been mainly restricted to academic purposes, even having a much better convergence rate when solved iteratively, due to their excellent conditioning number. In general, the main drawback of the MoM is the costly construction, storage and solution considering the unavoidable dense linear system, which grows with the electrical size of the object to analyze. Consequently, a wide range of fast methods have been developed for its compression and solution. Most of them, though, are absolutely dependent on the kernel of the integral equation, claiming for a complete re-formulation, if possible, for each new kernel. This thesis dissertation presents new approaches to accelerate or increase the accuracy of integral equations discretized by the Method of Moments (MoM) in computational electromagnetics. Firstly, a novel fast iterative solver, the Multilevel Adaptive Cross Approximation (MLACA), has been developed for accelerating the solution of the MoM linear system. In the quest for a general-purpose scheme, the MLACA is a method independent of the kernel of the integral equation and is purely algebraic. It improves both efficiency and compression rate with respect to the previously existing single-level version, the ACA. Therefore, it represents an excellent alternative for the solution of the MoM system of large-scale electromagnetic problems. Secondly, the direct evaluation method, which has proved to be the main reference in terms of efficiency and accuracy, is extended to overcome the computation of the challenging 4-D hyper-singular integrals arising in the Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE) formulations. The maximum affordable accuracy – machine precision – is obtained in a more than reasonable computation time, surpassing any other existing technique in the literature. Thirdly, the aforementioned hyper-singular integrals become near-singular when the discretized elements are very closely placed but not touching. It is shown how traditional integration rules fail to converge also in this case, and a possible solution based on more sophisticated integration rules, like the Double Exponential and the Gauss-Laguerre, is proposed. Finally, an effort to facilitate the… Advisors/Committee Members: [email protected] (authoremail), false (authoremailshow), Rius Casals, Juan Manuel (director).

Subjects/Keywords: vertex adjacent integration; edge adjacent integration; adaptive cross approximation; impedance matrix compression; electromagnetism; numerical simulation; singular integrals; surface integral equations; fast solvers; method of moments (MOM); 517; 621.3

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APA (6^th Edition):

Tamayo Palau, J. M. (2011). Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. (Thesis). Universitat Politècnica de Catalunya. Retrieved from http://hdl.handle.net/10803/6952

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Tamayo Palau, José María. “Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.” 2011. Thesis, Universitat Politècnica de Catalunya. Accessed April 10, 2021. http://hdl.handle.net/10803/6952.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Tamayo Palau, José María. “Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.” 2011. Web. 10 Apr 2021.

Vancouver:

Tamayo Palau JM. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. [Internet] [Thesis]. Universitat Politècnica de Catalunya; 2011. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/10803/6952.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Tamayo Palau JM. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. [Thesis]. Universitat Politècnica de Catalunya; 2011. Available from: http://hdl.handle.net/10803/6952

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Southern California

8. Chaudhari, Abhijit J. Fast solvers in hyperspectral optical bioluminescence tomography for small animal imaging.

Degree: MS, Electrical Engineering, 2007, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/156808/rec/2772

► Hyperspectral Optical Bioluminescence Tomography (HOBT) yields fairly accurate 3D reconstructed source distributions in small animal studies. The diffusion equation models the light propagation in tissue… (more)

Subjects/Keywords: hyperspectral optical bioluminescence tomography; fast solvers

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APA (6^th Edition):

Chaudhari, A. J. (2007). Fast solvers in hyperspectral optical bioluminescence tomography for small animal imaging. (Masters Thesis). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/156808/rec/2772

Chicago Manual of Style (16^th Edition):

Chaudhari, Abhijit J. “Fast solvers in hyperspectral optical bioluminescence tomography for small animal imaging.” 2007. Masters Thesis, University of Southern California. Accessed April 10, 2021. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/156808/rec/2772.

MLA Handbook (7^th Edition):

Chaudhari, Abhijit J. “Fast solvers in hyperspectral optical bioluminescence tomography for small animal imaging.” 2007. Web. 10 Apr 2021.

Vancouver:

Chaudhari AJ. Fast solvers in hyperspectral optical bioluminescence tomography for small animal imaging. [Internet] [Masters thesis]. University of Southern California; 2007. [cited 2021 Apr 10]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/156808/rec/2772.

Council of Science Editors:

Chaudhari AJ. Fast solvers in hyperspectral optical bioluminescence tomography for small animal imaging. [Masters Thesis]. University of Southern California; 2007. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/156808/rec/2772

University of Texas – Austin

9. -5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.

Degree: PhD, Aerospace Engineering, 2019, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/5474

► The hybridized discontinuous Galerkin methods (HDG) introduced a decade ago is a promising candidate for high-order spatial discretization combined with implicit/implicit-explicit time stepping. Roughly speaking,… (more)

▼ The hybridized discontinuous Galerkin methods (HDG) introduced a decade ago is a promising candidate for high-order spatial discretization combined with implicit/implicit-explicit time stepping. Roughly speaking, HDG methods combines the advantages of both discontinuous Galerkin (DG) methods and hybridized methods. In particular, it enjoys the benefits of equal order spaces, upwinding and ability to handle large gradients of DG methods as well as the smaller globally coupled linear system, adaptivity, and multinumeric capabilities of hybridized methods. However, the main bottleneck in HDG methods, limiting its use to small to moderate sized problems, is the lack of scalable linear solvers. In this thesis we develop fast and scalable solvers for HDG methods consisting of domain decomposition, multigrid and multilevel solvers/preconditioners with an ultimate focus on simulating large scale problems in fluid dynamics and magnetohydrodynamics (MHD). First, we propose a domain decomposition based solver namely iterative HDG for partial differential equations (PDEs). It is a fixed point iterative scheme, with each iteration consisting only of element-by-element and face-by-face embarrassingly parallel solves. Using energy analysis we prove the convergence of the schemes for scalar and system of hyperbolic PDEs and verify the results numerically. We then propose a novel geometric multigrid approach for HDG methods based on fine scale Dirichlet-to-Neumann maps. The algorithm combines the robustness of algebraic multigrid methods due to operator dependent intergrid transfer operators and at the same time has fixed coarse grid construction costs due to its geometric nature. For diffusion dominated PDEs such as the Poisson and the Stokes equations the algorithm gives almost perfect hp – scalability. Next, we propose a multilevel algorithm by combining the concepts of nested dissection, a fill-in reducing ordering strategy, variational structure and high-order properties of HDG, and domain decomposition. Thanks to its root in direct solver strategy the performance of the solver is almost independent of the nature of the PDEs and mostly depends on the smoothness of the solution. We demonstrate this numerically with several prototypical PDEs. Finally, we propose a block preconditioning strategy for HDG applied to incompressible visco-resistive MHD. We use a least squares commutator approximation for the inverse of the Schur complement and algebraic multigrid or the multilevel preconditioner for the approximate inverse of the nodal block. With several 2D and 3D transient examples we demonstrate the robustness and parallel scalability of the block preconditioner Advisors/Committee Members: Bui-Thanh, Tan (advisor), Demkowicz, Leszek F (committee member), Ghattas, Omar (committee member), Raja, Laxminarayan L (committee member), Shadid, John N (committee member), Waelbroeck, Francois L (committee member), Wheeler, Mary F (committee member).

Subjects/Keywords: Hybridized discontinuous Galerkin; Fast solvers; Multigrid; Multilevel; MHD; Domain decomposition

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APA (6^th Edition):

-5494-1880. (2019). Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/5474

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Chicago Manual of Style (16^th Edition):

-5494-1880. “Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed April 10, 2021. http://dx.doi.org/10.26153/tsw/5474.

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MLA Handbook (7^th Edition):

-5494-1880. “Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.” 2019. Web. 10 Apr 2021.

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Vancouver:

-5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Apr 10]. Available from: http://dx.doi.org/10.26153/tsw/5474.

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Council of Science Editors:

-5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/5474

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