subject:(Method of Manufactured Solutions)

Stellenbosch University

1. Marchand, Renier Gustav. The method of manufactured solutions for the verification of computational electromagnetic codes.

Degree: PhD, Electrical and Electronic Engineering, 2013, Stellenbosch University

URL: http://hdl.handle.net/10019.1/80210

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ENGLISH ABSTRACT: In this work the Method of Manufactured Solutions (MMS) is introduced for the code veri cation of full-wave frequency dependent electromagnetic computational software.… (more)

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ENGLISH ABSTRACT: In this work the Method of Manufactured Solutions (MMS) is introduced for the code veri cation of full-wave frequency dependent electromagnetic computational software. At rst the method is sketched in the context of the veri cation and validation process and the need for proper code veri cation is highlighted. Subsequently, the MMS is investigated in its natural context: the Finite Element Method, speci cally for the E- eld Vector Wave Equation. The usefulness of the method to detect error in a computational code is demonstrated. The selection of Manufactured Solutions is discussed and it is demonstrated how it can be used to nd the probable cause of bugs. Mutation testing is introduced and used to show the ability to detect errors present in code. The MMS is nally applied in a novel manner to a Method of Moments (MoM) code. The challenges of numerical integration associated with the application of the operator is discussed and correct integration is successfully demonstrated. Subsequently the MMS is demonstrated to be successfully applied to the MoM and mutation testing is used to demonstrate the practical e cacy of the method. The application of the MMS to the MoM is the main contribution of this work.

AFRIKAANSE OPSOMMING: Die Metode van Vervaardigde Oplossings (MVO) word hier bekend gestel vir die veri kasie van numeriese volgolf frekwensie-afhanklike elektromagnetise kode. Die metode word eerstens in die bre e konteks van algemene veri kasie en validasie geplaas en gevolglik word die noodsaaklikheid van kode veri kasie beklemtoon. Daarna, word die toets-metode in die konteks van die Eindige Element Metode vir die E-veld vektorgolf vergelyking bestudeer. Die MVO is oorspronklik ontwikkel in die di erentiaalvergelyking omgewing. Die bruikbaarheid van die metode vir elektromagnetiese simulasies word prakties gedemonstreer deur die opsporing van werklike foute. Die metode word ook verder ondersoek vir die oorsprong van foute. Mutasietoetsing word bekendgestel en word gebruik om die metode verder prakties te veri eer. Die MVO word laastens in 'n nuwe manier gebruik om 'n Moment Metode kode te veri eer. Die praktiese probleme betrokke by numeriese integrasie word ondersoek en die korrekte toepassing van die integraal operator word prakties gedemonstreer. Daarna, word die MVO in hierdie konteks gedemonstreer deur verskeie voorbeelde te ondersoek. Mutasietoetsing word weereens gebruik om na die e ektiewiteit van die MVO te kyk om 'n Moment Metode kode te toets. Die toepassing van die MVO op 'n Moment Metode kode is die hoof bydrae van hierdie werk.

Advisors/Committee Members: Davidson, D. B., Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering..

Subjects/Keywords: Electronic engineering; Electromagnetic fields; Computational electromagnetics; Method of manufactured solutions (MMS)

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APA (6^th Edition):

Marchand, R. G. (2013). The method of manufactured solutions for the verification of computational electromagnetic codes. (Doctoral Dissertation). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/80210

Chicago Manual of Style (16^th Edition):

Marchand, Renier Gustav. “The method of manufactured solutions for the verification of computational electromagnetic codes.” 2013. Doctoral Dissertation, Stellenbosch University. Accessed January 19, 2021. http://hdl.handle.net/10019.1/80210.

MLA Handbook (7^th Edition):

Marchand, Renier Gustav. “The method of manufactured solutions for the verification of computational electromagnetic codes.” 2013. Web. 19 Jan 2021.

Vancouver:

Marchand RG. The method of manufactured solutions for the verification of computational electromagnetic codes. [Internet] [Doctoral dissertation]. Stellenbosch University; 2013. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/10019.1/80210.

Council of Science Editors:

Marchand RG. The method of manufactured solutions for the verification of computational electromagnetic codes. [Doctoral Dissertation]. Stellenbosch University; 2013. Available from: http://hdl.handle.net/10019.1/80210

Penn State University

2. Elsworth, Cooper W. Verification of an Overset-grid Enabled Fluid-structure Interaction Solver.

Degree: 2014, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/22622

► Coupled systems occur when two domains governed by dissimilar physics interact dynamically, resulting in strong two-way coupling between the domains. Research into these systems has… (more)

▼ Coupled systems occur when two domains governed by dissimilar physics interact dynamically, resulting in strong two-way coupling between the domains. Research into these systems has become increasingly prevalent due to the wide variety of physical examples that exhibit these characteristics, as well as recent advancements in computational capability and parallelism. A notable example of coupled systems occurs in fluid-structure interaction (FSI), in which a deformable solid is surrounded by and/or immersed in a fluid. These systems exhibit strong, two-way coupling between the fluid and solid domains that require the development of expanded computational methods to solve. While current methods have provided the basis for the solution of these types of problems, optimizations are needed to solve realistic FSI problems. Existing overset mesh technology has been incorporated into an ALE based Fluid-Structure Interaction (FSI) code, producing a novel approach for investigating fully-coupled FSI phenomena. In particular, the Suggar++/DiRTlib overset mesh technology has been implemented into a partitioned FSI solver based on OpenFOAM and an in-house structural code. The impetus of this solver has been to address some of the problems that occur in complex FSI simulations, most notably concerns with the mesh motion experienced in large deformation cases. The overset solver intends to simplify mesh generation, maintain mesh quality throughout the simulation, and provide similar performance to current approaches. This thesis provides verification of the overset FSI solver and presents the effects of overset methods on FSI simulations. Verification is presented through the method of manufactured solutions on the disparate solver components and mesh refinement studies are performed on the coupled code. The method of manufactured solutions provides rigorous code verification, with error magnitudes and solver convergence rates determined for the separate solver components. Discussion of the challenges experienced in the establishment of a unified manufactured solution for partitioned FSI algorithms is also presented. The disparate solvers used in this work are found to exhibit the expected orders of convergence, verifying the correct implementation of the governing equations in these domains. A mesh refinement study with Richardson extrapolation further confirms the monotonic convergence of the FSI solution, and provides insight into the order of accuracy of the coupled solver. Use of the Turek and Hron benchmark case facilitates a consistent comparison of the proposed solver to current FSI methods and performance. Simulation data is presented, while investigations into the benefits of overset methods for FSI simulations is discussed. In addition, the relative performance of the solver is presented, in order to address the viability of the proposed solver's application. Advisors/Committee Members: Jonathan S Pitt, Thesis Advisor/Co-Advisor, Scott Miller, Thesis Advisor/Co-Advisor.

Subjects/Keywords: Fluid-Structure Interaction; Verification; Method of Manufactured Solutions; Overset; Finite Volume; Finite Element

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

APA (6^th Edition):

Elsworth, C. W. (2014). Verification of an Overset-grid Enabled Fluid-structure Interaction Solver. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/22622

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):

Elsworth, Cooper W. “Verification of an Overset-grid Enabled Fluid-structure Interaction Solver.” 2014. Thesis, Penn State University. Accessed January 19, 2021. https://submit-etda.libraries.psu.edu/catalog/22622.

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

MLA Handbook (7^th Edition):

Elsworth, Cooper W. “Verification of an Overset-grid Enabled Fluid-structure Interaction Solver.” 2014. Web. 19 Jan 2021.

Vancouver:

Elsworth CW. Verification of an Overset-grid Enabled Fluid-structure Interaction Solver. [Internet] [Thesis]. Penn State University; 2014. [cited 2021 Jan 19]. Available from: https://submit-etda.libraries.psu.edu/catalog/22622.

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

Council of Science Editors:

Elsworth CW. Verification of an Overset-grid Enabled Fluid-structure Interaction Solver. [Thesis]. Penn State University; 2014. Available from: https://submit-etda.libraries.psu.edu/catalog/22622

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

Virginia Tech

3. Choudhary, Aniruddha. Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation.

Degree: PhD, Aerospace Engineering, 2015, Virginia Tech

URL: http://hdl.handle.net/10919/51169

► Code verification is the process of ensuring, to the degree possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a scientific computing… (more)

▼ Code verification is the process of ensuring, to the degree possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a scientific computing simulation. In this work, techniques are presented for performing code verification of boundary conditions commonly used in compressible and incompressible Computational Fluid Dynamics (CFD) codes. Using a compressible CFD code, this study assesses the subsonic inflow (isentropic and fixed-mass), subsonic outflow, supersonic outflow, no-slip wall (adiabatic and isothermal), and inviscid slip-wall. The use of simplified curved surfaces is proposed for easier generation of manufactured solutions during the verification of certain boundary conditions involving many constraints. To perform rigorous code verification, general grids with mixed cell types at the verified boundary are used. A novel approach is introduced to determine manufactured solutions for boundary condition verification when the velocity-field is constrained to be divergence-free during the simulation in an incompressible CFD code. Order of accuracy testing using the Method of Manufactured Solutions (MMS) is employed here for code verification of the major components of an open-source, multiphase flow code - MFIX. The presence of two-phase governing equations and a modified SIMPLE-based algorithm requiring divergence-free flows makes the selection of manufactured solutions more involved than for single-phase, compressible flows. Code verification is performed here on 2D and 3D, uniform and stretched meshes for incompressible, steady and unsteady, single-phase and two-phase flows using the two-fluid model of MFIX. In a CFD simulation, truncation error (TE) is the difference between the continuous governing equation and its discrete approximation. Since TE can be shown to be the local source term for the discretization error, TE is proposed as the criterion for determining which regions of the computational mesh should be refined/coarsened. For mesh modification, an error equidistribution strategy to perform r-refinement (i.e., mesh node relocation) is employed. This technique is applied to 1D and 2D inviscid flow problems where the exact (i.e., analytic) solution is available. For mesh adaptation based upon TE, about an order of magnitude improvement in discretization error levels is observed when compared with the uniform mesh. Advisors/Committee Members: Roy, Christopher John (committeechair), Xiao, Heng (committee member), Neu, Wayne L. (committee member), Tafti, Danesh K. (committee member).

Subjects/Keywords: Code verification; Order of accuracy; Method of manufactured solutions; Boundary conditions; Multiphase flows; Mesh adaptation; Truncation error

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

APA (6^th Edition):

Choudhary, A. (2015). Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/51169

Chicago Manual of Style (16^th Edition):

Choudhary, Aniruddha. “Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation.” 2015. Doctoral Dissertation, Virginia Tech. Accessed January 19, 2021. http://hdl.handle.net/10919/51169.

MLA Handbook (7^th Edition):

Choudhary, Aniruddha. “Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation.” 2015. Web. 19 Jan 2021.

Vancouver:

Choudhary A. Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation. [Internet] [Doctoral dissertation]. Virginia Tech; 2015. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/10919/51169.

Council of Science Editors:

Choudhary A. Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation. [Doctoral Dissertation]. Virginia Tech; 2015. Available from: http://hdl.handle.net/10919/51169

Mississippi State University

4. Murali, Vasanth Kumar. Code Verification using The Method of Manufactured Solutions.

Degree: MS, Computational Engineering, 2002, Mississippi State University

URL: http://sun.library.msstate.edu/ETD-db/theses/available/etd-11112002-121649/ ;

► Implementations of numerical simulations for solving systems of partial differential equations are often not verified and are falsely assumed to work correctly. As a result,… (more)

▼ Implementations of numerical simulations for solving systems of partial differential equations are often not verified and are falsely assumed to work correctly. As a result, the implementations are prone to coding errors that could degrade the accuracy of the solution. In order to ensure that a code is written correctly, rigorous verification of all parts of the code is necessary. Code verification is the task of ascertaining whether a numerical algorithm is solving the governing equations of the problem correctly. If an exact solution existed for the governing equations then verification would be easier but these solutions are rare because of the non-linearity of common Computational Fluid Dynamics (CFD) problems. In the absence of exact solutions, grid refinement studies are the most commonly used methods to verify codes using simulations on a sequence of grids but even these studies have limitations. The Method of Manufactured Solutions (MMS) is a novel and a recently developed technique that verifies the observed order-of-accuracy of the implementation of a numerical algorithm. The method is more general and overcomes many of the limitations of the method of exact solutions and grid refinement studies. The central idea is to modify the governing equations and the boundary conditions by adding forcing functions or source terms in order to drive the discrete solution to a prescribed or ``manufactured' solution chosen a priori. A grid convergence study is performed subsequently to determine the observed orders. Two methods of accuracy assessment are presented here - solution accuracy analysis and residual error analysis. The method based on the error in the spatial residual is computationally less expensive and proved to be a valuable debugging tool. In the present work, the Method of Manufactured Solutions (MMS) is implemented on a compressible flow solver that solves the two-dimensional Euler equations on structured grids and an incompressible code that solves the two-dimensional Navier-Stokes equations on unstructured meshes. Exponential functions are used to ``manufacture' steady solutions to the governing equations. Solution and residual error analyses are presented. The influence of grid non-uniformity on the numerical accuracy is studied. Advisors/Committee Members: Dr. Clarence O.E. Burg (chair), Dr. Kidambi Sreenivas (committee member), Dr. James C. Newman III (committee member).

Subjects/Keywords: Method of Manufactured Solutions; Grid Refinement Studies; Code Verification

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

APA (6^th Edition):

Murali, V. K. (2002). Code Verification using The Method of Manufactured Solutions. (Masters Thesis). Mississippi State University. Retrieved from http://sun.library.msstate.edu/ETD-db/theses/available/etd-11112002-121649/ ;

Chicago Manual of Style (16^th Edition):

Murali, Vasanth Kumar. “Code Verification using The Method of Manufactured Solutions.” 2002. Masters Thesis, Mississippi State University. Accessed January 19, 2021. http://sun.library.msstate.edu/ETD-db/theses/available/etd-11112002-121649/ ;.

MLA Handbook (7^th Edition):

Murali, Vasanth Kumar. “Code Verification using The Method of Manufactured Solutions.” 2002. Web. 19 Jan 2021.

Vancouver:

Murali VK. Code Verification using The Method of Manufactured Solutions. [Internet] [Masters thesis]. Mississippi State University; 2002. [cited 2021 Jan 19]. Available from: http://sun.library.msstate.edu/ETD-db/theses/available/etd-11112002-121649/ ;.

Council of Science Editors:

Murali VK. Code Verification using The Method of Manufactured Solutions. [Masters Thesis]. Mississippi State University; 2002. Available from: http://sun.library.msstate.edu/ETD-db/theses/available/etd-11112002-121649/ ;

University of Michigan

5. Wang, Jipu. Application of the Method of Manufactured Solutions to Verify the Method of Characteristics for Reactor Analysis.

Degree: PhD, Nuclear Engineering & Radiological Sciences, 2019, University of Michigan

URL: http://hdl.handle.net/2027.42/151621

► The purpose of this study is to theoretically analyze the error of the method of characteristics (MOC) with respect to different independent variables and to… (more)

▼ The purpose of this study is to theoretically analyze the error of the method of characteristics (MOC) with respect to different independent variables and to develop the methodology to apply the method of manufactured solutions (MMS) to verify an MOC-based code system for reactor analysis. The MMS methodology has been applied to fixed-source problems, criticality eigenvalue problems, and multiphysics problems coupling neutronics with other physics essential to reactor analysis. Theoretical predictions for the order of accuracy as a function of mesh spacing (spatial and angular meshes) are compared with numerical results with MMS. The coupling of spatial and angular errors obscured the convergence with the spatial mesh, and a method for removing the angular error from the numerical solution was developed, resulting in excellent agreement between theory and numerical results for the spatial order of accuracy. The application of MMS to the criticality eigenvalue problem yields an “inhomogeneous eigenvalue” problem, which does not have a unique solution. This was addressed by adding a constraint to the application code eigenvalue solver. An alternative method for applying MMS to the criticality eigenvalue problem was developed, based on modifying the fission cross section, and this avoids the inhomogeneous eigenvalue problem. Both methods yielded numerical results for the order of accuracy that were in excellent agreement with theory. The MMS methodology was also applied to the C5G7 benchmark problem, a seven-group small core with realistic geometry, and the numerical solution reproduced the assumed MMS solution everywhere to within negligible error. The findings and conclusions are that MMS is a powerful, flexible and rigorous tool for reactor code verification, which is an essential step in developing a complex scientific computing code. This study contributes to reactor analysis by quantifying and removing errors associated with certain numerical approximations, revealing the rate of convergence with respect to the refined variable, and providing a verification methodology for both reactor physics and coupled multiphysics applications. Advisors/Committee Members: Collins, Benjamin Steven (committee member), Martin, William R (committee member), Garikipati, Krishnakumar R (committee member), Downar, Thomas J (committee member), Larsen, Edward W (committee member).

Subjects/Keywords: method of manufactured solutions; method of characteristics; reactor analysis; code verification; angular error removal; multiphysics; Nuclear Engineering and Radiological Sciences; Engineering; Science

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

APA (6^th Edition):

Wang, J. (2019). Application of the Method of Manufactured Solutions to Verify the Method of Characteristics for Reactor Analysis. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/151621

Chicago Manual of Style (16^th Edition):

Wang, Jipu. “Application of the Method of Manufactured Solutions to Verify the Method of Characteristics for Reactor Analysis.” 2019. Doctoral Dissertation, University of Michigan. Accessed January 19, 2021. http://hdl.handle.net/2027.42/151621.

MLA Handbook (7^th Edition):

Wang, Jipu. “Application of the Method of Manufactured Solutions to Verify the Method of Characteristics for Reactor Analysis.” 2019. Web. 19 Jan 2021.

Vancouver:

Wang J. Application of the Method of Manufactured Solutions to Verify the Method of Characteristics for Reactor Analysis. [Internet] [Doctoral dissertation]. University of Michigan; 2019. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/2027.42/151621.

Council of Science Editors:

Wang J. Application of the Method of Manufactured Solutions to Verify the Method of Characteristics for Reactor Analysis. [Doctoral Dissertation]. University of Michigan; 2019. Available from: http://hdl.handle.net/2027.42/151621

Penn State University

6. Awadelkarim, Amel Osama. FINITE-ELEMENT IMPLEMENTATION AND VERIFICATION OF COMPLEX FLUID MODELS BASED ON EVOLVING NATURAL CONFIGURATIONS, MOTIVATED BY STUDIES OF BLOOD.

Degree: 2017, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/14506aoa122

► The ability to model the flow of blood along with its concurrent capacity for clotting and lysis can greatly accelerate the development and deployment of… (more)

Subjects/Keywords: blood; fluid mechanics; COMSOL Multiphysics; continuum mechanics; arbitrary-Lagrangian-Eulerian; Method of Manufactured Solutions; clotting; lysis; modeling; viscoelastic fluids; finite element; complex fluids; verification; thermodynamics; natural configuration; Oldroyd-B fluid

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

APA (6^th Edition):

Awadelkarim, A. O. (2017). FINITE-ELEMENT IMPLEMENTATION AND VERIFICATION OF COMPLEX FLUID MODELS BASED ON EVOLVING NATURAL CONFIGURATIONS, MOTIVATED BY STUDIES OF BLOOD. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/14506aoa122

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):

Awadelkarim, Amel Osama. “FINITE-ELEMENT IMPLEMENTATION AND VERIFICATION OF COMPLEX FLUID MODELS BASED ON EVOLVING NATURAL CONFIGURATIONS, MOTIVATED BY STUDIES OF BLOOD.” 2017. Thesis, Penn State University. Accessed January 19, 2021. https://submit-etda.libraries.psu.edu/catalog/14506aoa122.

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

MLA Handbook (7^th Edition):

Awadelkarim, Amel Osama. “FINITE-ELEMENT IMPLEMENTATION AND VERIFICATION OF COMPLEX FLUID MODELS BASED ON EVOLVING NATURAL CONFIGURATIONS, MOTIVATED BY STUDIES OF BLOOD.” 2017. Web. 19 Jan 2021.

Vancouver:

Awadelkarim AO. FINITE-ELEMENT IMPLEMENTATION AND VERIFICATION OF COMPLEX FLUID MODELS BASED ON EVOLVING NATURAL CONFIGURATIONS, MOTIVATED BY STUDIES OF BLOOD. [Internet] [Thesis]. Penn State University; 2017. [cited 2021 Jan 19]. Available from: https://submit-etda.libraries.psu.edu/catalog/14506aoa122.

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

Council of Science Editors:

Awadelkarim AO. FINITE-ELEMENT IMPLEMENTATION AND VERIFICATION OF COMPLEX FLUID MODELS BASED ON EVOLVING NATURAL CONFIGURATIONS, MOTIVATED BY STUDIES OF BLOOD. [Thesis]. Penn State University; 2017. Available from: https://submit-etda.libraries.psu.edu/catalog/14506aoa122

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

Virginia Tech

7. Kurzen, Matthew James. Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems.

Degree: MS, Aerospace and Ocean Engineering, 2010, Virginia Tech

URL: http://hdl.handle.net/10919/31239

► This work examines the Method of Nearby Problems as a way to generate analytical exact solutions to problems governed by partial differential equations (PDEs). The… (more)

Subjects/Keywords: Discretization Error; Method of Manufactured Solutions; Computational Fluid Dynamics; Method of Nearby Problems; MNP

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

APA (6^th Edition):

Kurzen, M. J. (2010). Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/31239

Chicago Manual of Style (16^th Edition):

Kurzen, Matthew James. “Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems.” 2010. Masters Thesis, Virginia Tech. Accessed January 19, 2021. http://hdl.handle.net/10919/31239.

MLA Handbook (7^th Edition):

Kurzen, Matthew James. “Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems.” 2010. Web. 19 Jan 2021.

Vancouver:

Kurzen MJ. Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems. [Internet] [Masters thesis]. Virginia Tech; 2010. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/10919/31239.

Council of Science Editors:

Kurzen MJ. Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems. [Masters Thesis]. Virginia Tech; 2010. Available from: http://hdl.handle.net/10919/31239

Virginia Tech

8. Veluri, Subrahmanya Pavan Kumar. Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes.

Degree: PhD, Aerospace and Ocean Engineering, 2010, Virginia Tech

URL: http://hdl.handle.net/10919/28715

► A detailed code verification study of an unstructured finite volume Computational Fluid Dynamics (CFD) code is performed. The Method of Manufactured Solutions is used to… (more)

▼ A detailed code verification study of an unstructured finite volume Computational Fluid Dynamics (CFD) code is performed. The Method of Manufactured Solutions is used to generate exact solutions for the Euler and Navier-Stokes equations to verify the correctness of the code through order of accuracy testing. The verification testing is performed on different mesh types which include triangular and quadrilateral elements in 2D and tetrahedral, prismatic, and hexahedral elements in 3D. The requirements of systematic mesh refinement are discussed, particularly in regards to unstructured meshes. Different code options verified include the baseline steady state governing equations, transport models, turbulence models, boundary conditions and unsteady flows. Coding mistakes, algorithm inconsistencies, and mesh quality sensitivities uncovered during the code verification are presented. In recent years, there has been significant work on the development of algorithms for the compressible Navier-Stokes equations on unstructured grids. One of the challenging tasks during the development of these algorithms is the formulation of consistent and accurate diffusion operators. The robustness and accuracy of diffusion operators depends on mesh quality. A survey of diffusion operators for compressible CFD solvers is conducted to understand different formulation procedures for diffusion fluxes. A patch-wise version of the Method of Manufactured Solutions is used to test the accuracy of selected diffusion operators. This testing of diffusion operators is limited to cell-centered finite volume methods which are formally second order accurate. These diffusion operators are tested and compared on different 2D mesh topologies to study the effect of mesh quality (stretching, aspect ratio, skewness, and curvature) on their numerical accuracy. Quantities examined include the numerical approximation errors and order of accuracy associated with face gradient reconstruction. From the analysis, defects in some of the numerical formulations are identified along with some robust and accurate diffusion operators. Advisors/Committee Members: Roy, Christopher John (committeechair), Mason, William H. (committee member), McCue-Weil, Leigh S. (committee member), Tafti, Danesh K. (committee member).

Subjects/Keywords: Order of Accuracy; Computational Fluid Dynamics; Discretization Error; Method of Manufactured Solutions; Code Verification

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

APA (6^th Edition):

Veluri, S. P. K. (2010). Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/28715

Chicago Manual of Style (16^th Edition):

Veluri, Subrahmanya Pavan Kumar. “Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes.” 2010. Doctoral Dissertation, Virginia Tech. Accessed January 19, 2021. http://hdl.handle.net/10919/28715.

MLA Handbook (7^th Edition):

Veluri, Subrahmanya Pavan Kumar. “Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes.” 2010. Web. 19 Jan 2021.

Vancouver:

Veluri SPK. Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes. [Internet] [Doctoral dissertation]. Virginia Tech; 2010. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/10919/28715.

Council of Science Editors:

Veluri SPK. Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes. [Doctoral Dissertation]. Virginia Tech; 2010. Available from: http://hdl.handle.net/10919/28715

9. Silva, Homero Ghioti da. Regime não-linear de trens de ondas modulados na direção transversal em um escoamento de Poiseuille plano.

Degree: PhD, Engenharia Mecânica, 2008, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/18/18135/tde-12062008-145838/ ;

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A presente tese se refere a três principais objetivos. Um objetivo foi desenvolver um código de simulação numérica direta para simulação de ondas de instabilidade… (more)

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A presente tese se refere a três principais objetivos. Um objetivo foi desenvolver um código de simulação numérica direta para simulação de ondas de instabilidade em um escoamento de Poiseuille plano. O outro objetivo foi analisá-Io através do Método das Soluções Manufaturadas (MMS), e por fim, um terceiro objetivo foi estudar o regime não-linear da evolução de trens de ondas modulados em um escoamento de Poiseuille plano. O código resolve numericamente, com diferenças finitas de ordem de precisão alta e métodos pseudo espectrais, as equações de Navier-Stokes tri-dimensionais e incompressíveis numa formulação vorticidade-velocidade. O MMS é um método de verificação de código mais completo que os normalmente usados, por exemplo, comparação com teoria de estabilidade linear. O código usa diferenças finitas de ordem alta de precisão, mas com diferentes ordens em diferentes regiões do domínio. O MMS é pouco utilizado neste tipo de código. Concluiu-se que estes códigos em geral não operam na chamada faixa assintótica de erro. Na faixa de trabalho, a ordem do erro varia no domínio computacional de forma consistente com os métodos numéricos empregados. Isto permite, entre outras coisas, a otimização do esquema numérico. Após os testes de verifição, simulações numéricas dos trens de ondas foram realizadas. A análise dos resultados foi feita através das teorias de instabilidade primária e secundária e teoria fracamente não-linear. Foi estudado um trem de ondas modulado numa região do diagrama de instabilidade onde vários estudos para ondas mono cromáticas foram realizados. Os resultados sugeriram que nesta região o regime não-linear de transição dos trens de ondas modulados é governado pela instabilidade tipo-K. Com a redução da amplitude inicial de perturbação um cenário mais complexo, que pode estar envolvendo outros mecanismos, foi observado. Casos mais próximos ao primeiro ramo do diagrama também foram estudados. Nesta região a teoria linear prevê ondas tri-dimensionais sendo as mais instáveis, fato que poderia favorecer a ocorrência da chamada transição oblíqua. Os resultados indicaram que o trem de ondas modulado se divide em duas regiões que tendem-se afastar uma da outra. Apesar de estar associado com a instabilidade linear, este comportamento não havia sido antecipado na literatura. Neste cenário, para trens de ondas modulados isolados, o regime não-linear não pode ser correlacionado claramente com nenhum dos cenários clássicos de transição. Neste contexto transição oblíqua pode estar restrito a situações que envolvem a interação entre trens de ondas modulados.

The current thesis had three objectives. The first objective was to develop a code of direct numerical simulation (DNS) to simulation of waves of instability in a plane Poiseuille flow. The other main objective was to analyze it through the method of manufactured solutions (MMS). Finally, a third objective was to study the nonlinear regime of spanwise modulated wavetrains in a plane Poiseuille flow. Using high-order finite differences and pseudo-spectral…

Advisors/Committee Members: Medeiros, Marcello Augusto Faraco de.

Subjects/Keywords: Code verification; Escoamentos de Poiseuille plano; Method of manufactured solutions; Método das soluções manufaturadas; Natural transition; Plane Poiseuille flow; Spanwise modulated wavetrains; Transição natural; Trens de ondas modulados; Verificação de código

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APA (6^th Edition):

Silva, H. G. d. (2008). Regime não-linear de trens de ondas modulados na direção transversal em um escoamento de Poiseuille plano. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/18/18135/tde-12062008-145838/ ;

Chicago Manual of Style (16^th Edition):

Silva, Homero Ghioti da. “Regime não-linear de trens de ondas modulados na direção transversal em um escoamento de Poiseuille plano.” 2008. Doctoral Dissertation, University of São Paulo. Accessed January 19, 2021. http://www.teses.usp.br/teses/disponiveis/18/18135/tde-12062008-145838/ ;.

MLA Handbook (7^th Edition):

Silva, Homero Ghioti da. “Regime não-linear de trens de ondas modulados na direção transversal em um escoamento de Poiseuille plano.” 2008. Web. 19 Jan 2021.

Vancouver:

Silva HGd. Regime não-linear de trens de ondas modulados na direção transversal em um escoamento de Poiseuille plano. [Internet] [Doctoral dissertation]. University of São Paulo; 2008. [cited 2021 Jan 19]. Available from: http://www.teses.usp.br/teses/disponiveis/18/18135/tde-12062008-145838/ ;.

Council of Science Editors:

Silva HGd. Regime não-linear de trens de ondas modulados na direção transversal em um escoamento de Poiseuille plano. [Doctoral Dissertation]. University of São Paulo; 2008. Available from: http://www.teses.usp.br/teses/disponiveis/18/18135/tde-12062008-145838/ ;

University of Gothenburg / Göteborgs Universitet

10. Ahlberg Helgee, Ernst. Improving Drug Discovery Decision Making using Machine Learning and Graph Theory in QSAR Modeling.

Degree: 2010, University of Gothenburg / Göteborgs Universitet

URL: http://hdl.handle.net/2077/21838

► During the last decade non-linear machine-learning methods have gained popularity among QSAR modelers. The machine-learning algorithms generate highly accurate models at a cost of increased… (more)

▼ During the last decade non-linear machine-learning methods have gained popularity among QSAR modelers. The machine-learning algorithms generate highly accurate models at a cost of increased model complexity where simple interpretations, valid in the entire model domain, are rare. This thesis focuses on maximizing the amount of extracted knowledge from predictive QSAR models and data. This has been achieved by the development of a descriptor importance measure, a method for automated local optimization of compounds and a method for automated extraction of substructural alerts. Furthermore diﬀerent QSAR modeling strategies have been evaluated with respect to predictivity, risks and information content. To test hypotheses and theories large scale simulations of known relations between activities and de- scriptors have been conducted. With the simulations it has been possible to study properties of methods, risks, implementations and errors in a controlled manner since the correct answer has been known. Sim- ulation studies have been used in the development of the generally applicable descriptor importance measure and in the analysis of QSAR modeling strategies. The use of simulations is spread in many areas, but not that common in the computational chemistry community. The descriptor importance mea- sure developed can be applied to any machine-learning method and validations using both real data and simulated data show that the descriptor importance measure is very accurate for non-linear methods. An automated method for local optimization of compounds was developed to partly replace manual searches made to optimize compounds. The local optimization of compounds make use of the informa- tion in available data and deterministically enumerates new compounds in a space spanned close to the compound of interest. This can be used as a starting point for further compound optimization and aids the chemist in ﬁnding new compounds. An other approach to guide chemists in the process of optimiz- ing compounds is through substructural warnings. A fast method for signiﬁcant substructure extraction has been developed that extracts signiﬁcant substructures from data with respect to the activity of the compound. The method is at least on par with existing methods in terms of accuracy but is signiﬁcantly less time consuming. Non-linear machine-learning methods have opened up new possibilities for QSAR modeling that changes the way chemical data can be handled by model algorithms. Therefore properties of Local and Global QSAR modeling strategies have been studied. The results show that Local models come with high risks and are less accurate compared to Global models. In summary this thesis shows that Global QSAR modeling strategies should be applied preferably using methods that are able to handle non-linear relationships. The developed methods can be interpreted easily and an extensive amount of information can be retrieved. For the methods to become easily available to a broader group of users packaging with an open-source chemical…

Subjects/Keywords: machine learning; drug design; QSAR; descriptor importance; local and global models; method of manufactured solutions; automated compound optimization

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APA (6^th Edition):

Ahlberg Helgee, E. (2010). Improving Drug Discovery Decision Making using Machine Learning and Graph Theory in QSAR Modeling. (Thesis). University of Gothenburg / Göteborgs Universitet. Retrieved from http://hdl.handle.net/2077/21838

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):

Ahlberg Helgee, Ernst. “Improving Drug Discovery Decision Making using Machine Learning and Graph Theory in QSAR Modeling.” 2010. Thesis, University of Gothenburg / Göteborgs Universitet. Accessed January 19, 2021. http://hdl.handle.net/2077/21838.

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

MLA Handbook (7^th Edition):

Ahlberg Helgee, Ernst. “Improving Drug Discovery Decision Making using Machine Learning and Graph Theory in QSAR Modeling.” 2010. Web. 19 Jan 2021.

Vancouver:

Ahlberg Helgee E. Improving Drug Discovery Decision Making using Machine Learning and Graph Theory in QSAR Modeling. [Internet] [Thesis]. University of Gothenburg / Göteborgs Universitet; 2010. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/2077/21838.

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

Council of Science Editors:

Ahlberg Helgee E. Improving Drug Discovery Decision Making using Machine Learning and Graph Theory in QSAR Modeling. [Thesis]. University of Gothenburg / Göteborgs Universitet; 2010. Available from: http://hdl.handle.net/2077/21838

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

11. Grier, Benjamin. A verification of steady state discontinuous solutions using the method of manufactured solutions for finite volume computational fluid dynamic codes.

Degree: PhD, Mechanical Engineering, 2014, Clemson University

URL: https://tigerprints.clemson.edu/all_dissertations/1381

► When applying the method of manufactured solutions (MMS) on computational fluid dynamic (CFD) software, it is traditionally a requirement that all solutions be continuous… (more)

▼ When applying the method of manufactured solutions (MMS) on computational fluid dynamic (CFD) software, it is traditionally a requirement that all solutions be continuous on the computational domain. This stipulation is limiting for the verification and validation of CFD solutions where discontinuities are frequent. This work details the development of a discontinuous MMS method for finite volume codes. The CFD code used throughout this research is a cell centered, finite volume, 1st order, Eulerian scheme within the software AVUS (Air Vehicles Unstructured Solver) which is combined with uniform structured grids. This code is used as a representative testing platform with the convenience of accessible source code. A piecewise technique is used for defining manufactured solutions which simulate discontinuities. Since source terms which allow arbitrary solutions in continuous MMS do not exist within Riemann solvers, conditions at the shock boundary are physically constrained by the Rankine-Hugoniot jump conditions. Upwind manufactured solutions are first initialized and a regression technique is then used to solve for solutions downwind of the discontinuity. It is shown that a change in regression error of four order of magnitude has no significant effect on an order of convergence test. When applying MMS on finite volume CFD codes, determining the exact solutions and source terms when the stored value is the integrated average over the control volume is a non-trivial and frequently ignored problem. MMS with discontinuities further complicates the problem of determining these values. To obtain low error and high convergence rates, linearly and quadratically exact transformations are proposed for cells split by discontinuities. These transformations are combined with a nine point Gauss quadrature method to achieve 4th order accuracy for fully general solutions and shock shapes. To begin testing, continuous MMS is first performed to ensure a verified code. AVUS is verified for 1st order solutions but retains lower order boundary conditions when solving 2nd order. The error is verified using a second academic CFD solver but is left unchanged for shock solutions which are inherently 1st order. Constant primitive, oblique shock solutions are then used to demonstrate a solution's error dependence on grid alignment. Grid alignment is shown to play a vital role in the error surrounding a shock. Constant oblique solutions with a grid aligned shock result in no discretization error while a shock that passed through the interior of cells yields error upwards of 4% for the u-component velocity. A semi one-dimensional problem combined with a grid aligned shock is then used to demonstrate the error magnitude (< 1%) due to the cell averaging on both sides of the discontinuity. Fully generic primitives and discontinuities are then introduced and grid convergence studies yielding 1st order results typically associated with shocks are used to verify the correctness of the code. Despite high errors near the region of the shock,… Advisors/Committee Members: Dr. Richard Figliola, Dr. Edward Alyanak, Dr. Richard Miller, Dr. Chenning Tong.

Subjects/Keywords: Method of Manufactured Solutions; MMS; Uncertainty Quantification; Validation; Verification; Mechanical Engineering

…called the method of manufactured solutions (MMS) and is discussed in detail in the… …following section. 1.1 Method of Manufactured Solutions A general method for developing exact… …solutions to difficult partial differential equations is called the method of manufactured… …of a normal, cell aligned shock combined with quasi-one dimensional manufactured solutions… …rigor than the ones presented so far, is the method of exact solutions (MES)…

14 more images…

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APA (6^th Edition):

Grier, B. (2014). A verification of steady state discontinuous solutions using the method of manufactured solutions for finite volume computational fluid dynamic codes. (Doctoral Dissertation). Clemson University. Retrieved from https://tigerprints.clemson.edu/all_dissertations/1381

Chicago Manual of Style (16^th Edition):

Grier, Benjamin. “A verification of steady state discontinuous solutions using the method of manufactured solutions for finite volume computational fluid dynamic codes.” 2014. Doctoral Dissertation, Clemson University. Accessed January 19, 2021. https://tigerprints.clemson.edu/all_dissertations/1381.

MLA Handbook (7^th Edition):

Grier, Benjamin. “A verification of steady state discontinuous solutions using the method of manufactured solutions for finite volume computational fluid dynamic codes.” 2014. Web. 19 Jan 2021.

Vancouver:

Grier B. A verification of steady state discontinuous solutions using the method of manufactured solutions for finite volume computational fluid dynamic codes. [Internet] [Doctoral dissertation]. Clemson University; 2014. [cited 2021 Jan 19]. Available from: https://tigerprints.clemson.edu/all_dissertations/1381.

Council of Science Editors:

Grier B. A verification of steady state discontinuous solutions using the method of manufactured solutions for finite volume computational fluid dynamic codes. [Doctoral Dissertation]. Clemson University; 2014. Available from: https://tigerprints.clemson.edu/all_dissertations/1381

University of Akron

12. Brubaker, Lauren P. Completely Residual Based Code Verification.

Degree: MS, Applied Mathematics, 2006, University of Akron

URL: http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325

► Mathematical models of physical processes often include partial differential equations (PDEs). Oftentimes solving PDEs analytically is not feasible and a numerical method is implemented to… (more)

Subjects/Keywords: Mathematics; Code verification; Partial Differential Equations; Numerical Methods; Method of Manufactured Exact Solutions; Frontal Polymerization; Heat Equation; Residual

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APA (6^th Edition):

Brubaker, L. P. (2006). Completely Residual Based Code Verification. (Masters Thesis). University of Akron. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325

Chicago Manual of Style (16^th Edition):

Brubaker, Lauren P. “Completely Residual Based Code Verification.” 2006. Masters Thesis, University of Akron. Accessed January 19, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325.

MLA Handbook (7^th Edition):

Brubaker, Lauren P. “Completely Residual Based Code Verification.” 2006. Web. 19 Jan 2021.

Vancouver:

Brubaker LP. Completely Residual Based Code Verification. [Internet] [Masters thesis]. University of Akron; 2006. [cited 2021 Jan 19]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325.

Council of Science Editors:

Brubaker LP. Completely Residual Based Code Verification. [Masters Thesis]. University of Akron; 2006. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325

University of Toledo

13. Ingraham, Daniel. Verification of a Computational Aeroacoustics Code Using External Verification Analysis (EVA).

Degree: MSin Mechanical Engineering, College of Engineering, 2010, University of Toledo

URL: http://rave.ohiolink.edu/etdc/view?acc_num=toledo1271271426

► As Computational Aeroacoustics (CAA) codes become more complex andwidely used, robust Verification of such codes becomes more and moreimportant. Recently, Hixon et al. proposed a… (more)

Subjects/Keywords: Acoustics; Mechanical Engineering; Computational Aeroacoustics; Computational Fluid Dynamics; Code Verification; External Verification Analysis; Method of Manufactured Solutions; CAA; CFD; EVA; MMS

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APA (6^th Edition):

Ingraham, D. (2010). Verification of a Computational Aeroacoustics Code Using External Verification Analysis (EVA). (Masters Thesis). University of Toledo. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=toledo1271271426

Chicago Manual of Style (16^th Edition):

Ingraham, Daniel. “Verification of a Computational Aeroacoustics Code Using External Verification Analysis (EVA).” 2010. Masters Thesis, University of Toledo. Accessed January 19, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1271271426.

MLA Handbook (7^th Edition):

Ingraham, Daniel. “Verification of a Computational Aeroacoustics Code Using External Verification Analysis (EVA).” 2010. Web. 19 Jan 2021.

Vancouver:

Ingraham D. Verification of a Computational Aeroacoustics Code Using External Verification Analysis (EVA). [Internet] [Masters thesis]. University of Toledo; 2010. [cited 2021 Jan 19]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=toledo1271271426.

Council of Science Editors:

Ingraham D. Verification of a Computational Aeroacoustics Code Using External Verification Analysis (EVA). [Masters Thesis]. University of Toledo; 2010. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=toledo1271271426

NSYSU

14. Lin, Wei-ling. The Trefftz Method using Fundamental Solutions and Particular Solutions for Exterior and Annular Problems of Laplace's Equation.

Degree: Master, Applied Mathematics, 2008, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143445

► Most of reports deal with bounded simply-connected domains; only a few involve in exterior and annular problems (Chen et al. [3], Katsuroda[10] and Ushijima and… (more)

Subjects/Keywords: error analysis; annular problems; Method of fundamental solutions; fundamental solutions; exterior problems; particular solutions; Method of particular solutions

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APA (6^th Edition):

Lin, W. (2008). The Trefftz Method using Fundamental Solutions and Particular Solutions for Exterior and Annular Problems of Laplace's Equation. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143445

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):

Lin, Wei-ling. “The Trefftz Method using Fundamental Solutions and Particular Solutions for Exterior and Annular Problems of Laplace's Equation.” 2008. Thesis, NSYSU. Accessed January 19, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143445.

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

MLA Handbook (7^th Edition):

Lin, Wei-ling. “The Trefftz Method using Fundamental Solutions and Particular Solutions for Exterior and Annular Problems of Laplace's Equation.” 2008. Web. 19 Jan 2021.

Vancouver:

Lin W. The Trefftz Method using Fundamental Solutions and Particular Solutions for Exterior and Annular Problems of Laplace's Equation. [Internet] [Thesis]. NSYSU; 2008. [cited 2021 Jan 19]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143445.

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

Council of Science Editors:

Lin W. The Trefftz Method using Fundamental Solutions and Particular Solutions for Exterior and Annular Problems of Laplace's Equation. [Thesis]. NSYSU; 2008. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143445

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

University of Michigan

15. Martin, William R. The Application of the Finite Element Method to the Neutron Transport Equation.

Degree: 1976, University of Michigan

URL: http://hdl.handle.net/2027.42/85376

► This paper examines the theoretical and practical application of the finite element method to the neutron transport equation. The theoretical examination which is applicable to… (more)

▼ This paper examines the theoretical and practical application of the finite element method to the neutron transport equation. The theoretical examination which is applicable to the general transport equation in arbitrary geometry includes a derivation of the equivalent integral law (or weak form) of the first order neutron transport equation, to which the finite element method (Galerkin approach) is applied, resulting in a system of algebraic equations. We show that in principle the system of equations can be solved with certain physical restrictions concerning the criticality of the medium. The convergence of this approximate solution to the exact solution with mesh refinement is examined, and a non-optimal estimate of the convergence rate is obtained analytically. It is noted that the numerical results indicate a faster convergence rate and several approaches to obtain this result analytically are outlined. The practical application of the finite element method involved the development of a computer code capable of solving the neutron transport equation in l-D plane geometry. Vacuum, reflecting, or specified incoming boundary conditions may be analyzed, and all are treated as natural boundary conditions. The incorporation of the reflecting boundary conditions is seen to result in an ambiguity, which must be resolved by consideration of the direction in which neutrons travel. Discontinuous phase space finite elements are introduced, and it is seen that discontinuous angular elements effectively match the analytical discontinuities in the angular flux at mu = 0 for plane geometry. In addition, the use of discontinuous spatial elements is shown to result in treating continuity of the angular flux at an interface as-a natural interface condition in the direction of neutron travel. The time-dependent transport. equation is also examined and it is shown that the application of the finite element method in conjunction . with the Crank-Nicholson time discretization method results in a system of algebraic equations which is readily solved. Numerical results are given for several critical slab eigenvalue problems, including anisotropic scattering, and the results compare extremely well with benchmark results. It is seen that the finite element code is more efficient than a standard discrete ordinates code for certain problems. Precise numerical tests are made on the convergence rate of the approximate solution (L2 norm) with mesh refinement and also with the eigenvalue error. These results indicate O[h^(k+l )] solution error in the L2 norm and O(h 2k+l ) error in the eigenvalue, where h is the mesh spacing and k the degree of the finite element. A problem with severe heterogeneities is considered and it is shown that the use of discontinuous spatial and angular elements results in a marked improvement in the results. Finally, time-dependent problems are examined and it is seen that the phenomenon of angular mode separation makes the numerical treatment of the transport equation "in slab geometry a considerable challenge,… Advisors/Committee Members: (advisor), Nuclear Engineering and Radiological Sciences (affiliationum), Ann Arbor (affiliationumcampus).

Subjects/Keywords: Neutron Transport; Finite Element Method; Manufactured Solutions; Nuclear Engineering and Radiological Sciences; Engineering

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APA (6^th Edition):

Martin, W. R. (1976). The Application of the Finite Element Method to the Neutron Transport Equation. (Thesis). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/85376

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):

Martin, William R. “The Application of the Finite Element Method to the Neutron Transport Equation.” 1976. Thesis, University of Michigan. Accessed January 19, 2021. http://hdl.handle.net/2027.42/85376.

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

MLA Handbook (7^th Edition):

Martin, William R. “The Application of the Finite Element Method to the Neutron Transport Equation.” 1976. Web. 19 Jan 2021.

Vancouver:

Martin WR. The Application of the Finite Element Method to the Neutron Transport Equation. [Internet] [Thesis]. University of Michigan; 1976. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/2027.42/85376.

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

Council of Science Editors:

Martin WR. The Application of the Finite Element Method to the Neutron Transport Equation. [Thesis]. University of Michigan; 1976. Available from: http://hdl.handle.net/2027.42/85376

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

University of Nairobi

16. Ayieko, Benard O. Competitiveness Of Kenya’S Manufactured Exports To The East African Community .

Degree: 2011, University of Nairobi

URL: http://hdl.handle.net/11295/97008

► Despite policy efforts to diversify exports, Kenya’s export base is still largely dominated by primary products from the agricultural sector. Trade and commodity concentration has… (more)

▼ Despite policy efforts to diversify exports, Kenya’s export base is still largely dominated by primary products from the agricultural sector. Trade and commodity concentration has led to export earnings fluctuations which eventually leads to the problem of balance of payments, budgets deficits and does not permit future systematic economic planning. With dwindling fortunes in the agricultural sector due to vagaries of weather among others, it is imperative for policy makers to deal with the issue of diversification of the country’s exports. This will help cushion the country against shocks arising from the instability in the foreign exchange markets especially for the primary products. This strategy will contribute to the development of new export markets for manufactured goods destined for the EAC. By using panel data this paper investigated factors influencing competitiveness of Kenya’s manufactured exports to the EAC. The primary concern of policy makers and macroeconomic analysts is what factors promote or inhibit the flow of Kenya’s manufactured exports to the EAC. The findings indicate that trade policy, captured by openness and nominal exchange has a large effect on export competitiveness, their coefficients are large. However, fixed capital formation which is a proxy for trade facilitation has a small effect on export competitiveness. Infrastructural development is not playing the rightful role in releasing export potential of the trading bloc; hence is a bottle neck on the export supply side. The national government should have a policy of infrastructural investment like construction of corridors and upgrading of railway system to increase accessibility and ease the movement of manufactured exports. Unit labour cost has a negative effect on export competiveness. EAC member countries are labour abundant and therefore productivity of labour is more important than numbers. The member countries should invest in research and development, health care, education and capital equipment to increase labour productivity that lower unit labour cost thereby increasing competitiveness of manufactured goods. Therefore, manufactured exports are important for Kenya’s export matrix. It is therefore critical for the GOK and policy makers to work towards accelerating policies that will improve the volume of exports of manufactured goods to the EAC while drawing lessons from Asian tigers.

Subjects/Keywords: Competitiveness Of Kenya’S Manufactured Exports

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APA (6^th Edition):

Ayieko, B. O. (2011). Competitiveness Of Kenya’S Manufactured Exports To The East African Community . (Thesis). University of Nairobi. Retrieved from http://hdl.handle.net/11295/97008

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):

Ayieko, Benard O. “Competitiveness Of Kenya’S Manufactured Exports To The East African Community .” 2011. Thesis, University of Nairobi. Accessed January 19, 2021. http://hdl.handle.net/11295/97008.

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

MLA Handbook (7^th Edition):

Ayieko, Benard O. “Competitiveness Of Kenya’S Manufactured Exports To The East African Community .” 2011. Web. 19 Jan 2021.

Vancouver:

Ayieko BO. Competitiveness Of Kenya’S Manufactured Exports To The East African Community . [Internet] [Thesis]. University of Nairobi; 2011. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/11295/97008.

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

Council of Science Editors:

Ayieko BO. Competitiveness Of Kenya’S Manufactured Exports To The East African Community . [Thesis]. University of Nairobi; 2011. Available from: http://hdl.handle.net/11295/97008

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

University of Colorado

17. Woods, Charles Nathan. Enabling Design-Oriented Fluid Simulations: Verification with Discontinuous Manufactured Solutions and Automatic Grid Generation with Moving Coordinates.

Degree: PhD, Aerospace Engineering Sciences, 2015, University of Colorado

URL: https://scholar.colorado.edu/asen_gradetds/98

► Computer simulations of complex mathematical models are a powerful tool for design, but they introduce uncertainties which can lead to poor design choices when… (more)

Subjects/Keywords: Discontinuous Integration; Discontinuous Manufactured Solutions; Manufactured Solutions; Quadrature; Unified Coordinate System; Verification; Applied Mathematics; Systems Engineering and Multidisciplinary Design Optimization

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

APA (6^th Edition):

Woods, C. N. (2015). Enabling Design-Oriented Fluid Simulations: Verification with Discontinuous Manufactured Solutions and Automatic Grid Generation with Moving Coordinates. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/98

Chicago Manual of Style (16^th Edition):

Woods, Charles Nathan. “Enabling Design-Oriented Fluid Simulations: Verification with Discontinuous Manufactured Solutions and Automatic Grid Generation with Moving Coordinates.” 2015. Doctoral Dissertation, University of Colorado. Accessed January 19, 2021. https://scholar.colorado.edu/asen_gradetds/98.

MLA Handbook (7^th Edition):

Woods, Charles Nathan. “Enabling Design-Oriented Fluid Simulations: Verification with Discontinuous Manufactured Solutions and Automatic Grid Generation with Moving Coordinates.” 2015. Web. 19 Jan 2021.

Vancouver:

Woods CN. Enabling Design-Oriented Fluid Simulations: Verification with Discontinuous Manufactured Solutions and Automatic Grid Generation with Moving Coordinates. [Internet] [Doctoral dissertation]. University of Colorado; 2015. [cited 2021 Jan 19]. Available from: https://scholar.colorado.edu/asen_gradetds/98.

Council of Science Editors:

Woods CN. Enabling Design-Oriented Fluid Simulations: Verification with Discontinuous Manufactured Solutions and Automatic Grid Generation with Moving Coordinates. [Doctoral Dissertation]. University of Colorado; 2015. Available from: https://scholar.colorado.edu/asen_gradetds/98

Utah State University

18. Folkner, David E. Improvement in Computational Fluid Dynamics Through Boundary Verification and Preconditioning.

Degree: MS, Mechanical and Aerospace Engineering, 2013, Utah State University

URL: https://digitalcommons.usu.edu/etd/1738

► This thesis provides improvements to computational fluid dynamics accuracy and ef- ficiency through two main methods: a new boundary condition verification procedure and preconditioning… (more)

Subjects/Keywords: Artificial Dissipation; Boundaries; Cusp; Manufactured Solutions; Preconditioning; Verification; Engineering

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APA (6^th Edition):

Folkner, D. E. (2013). Improvement in Computational Fluid Dynamics Through Boundary Verification and Preconditioning. (Masters Thesis). Utah State University. Retrieved from https://digitalcommons.usu.edu/etd/1738

Chicago Manual of Style (16^th Edition):

Folkner, David E. “Improvement in Computational Fluid Dynamics Through Boundary Verification and Preconditioning.” 2013. Masters Thesis, Utah State University. Accessed January 19, 2021. https://digitalcommons.usu.edu/etd/1738.

MLA Handbook (7^th Edition):

Folkner, David E. “Improvement in Computational Fluid Dynamics Through Boundary Verification and Preconditioning.” 2013. Web. 19 Jan 2021.

Vancouver:

Folkner DE. Improvement in Computational Fluid Dynamics Through Boundary Verification and Preconditioning. [Internet] [Masters thesis]. Utah State University; 2013. [cited 2021 Jan 19]. Available from: https://digitalcommons.usu.edu/etd/1738.

Council of Science Editors:

Folkner DE. Improvement in Computational Fluid Dynamics Through Boundary Verification and Preconditioning. [Masters Thesis]. Utah State University; 2013. Available from: https://digitalcommons.usu.edu/etd/1738

NSYSU

19. Lo, Lin-Feng. The Method of Fundamental Solutions for 2D Helmholtz Equation.

Degree: Master, Applied Mathematics, 2008, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143959

► In the thesis, the error and stability analysis is made for the 2D Helmholtz equation by the method of fundamental solutions (MFS) using both Bessel… (more)

Subjects/Keywords: the method of fundamental solutions; Bessel functions; Helmholtz equation; error analysis; the method of particular solutions; stability analysis; Neumann functions

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APA (6^th Edition):

Lo, L. (2008). The Method of Fundamental Solutions for 2D Helmholtz Equation. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143959

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):

Lo, Lin-Feng. “The Method of Fundamental Solutions for 2D Helmholtz Equation.” 2008. Thesis, NSYSU. Accessed January 19, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143959.

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

MLA Handbook (7^th Edition):

Lo, Lin-Feng. “The Method of Fundamental Solutions for 2D Helmholtz Equation.” 2008. Web. 19 Jan 2021.

Vancouver:

Lo L. The Method of Fundamental Solutions for 2D Helmholtz Equation. [Internet] [Thesis]. NSYSU; 2008. [cited 2021 Jan 19]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143959.

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

Council of Science Editors:

Lo L. The Method of Fundamental Solutions for 2D Helmholtz Equation. [Thesis]. NSYSU; 2008. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143959

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

NSYSU

20. Chu, Po-chun. Models of Corner and Crack Singularity of Linear Elastostatics and their Numerical Solutions.

Degree: Master, Applied Mathematics, 2010, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0823110-173542

► The singular solutions for linear elastostatics at corners are essential in both theory and computation. In this thesis, we seek new singular solutions for corners… (more)

▼ The singular solutions for linear elastostatics at corners are essential in both theory and computation. In this thesis, we seek new singular solutions for corners with the fixed (displacement), the free stress (traction) boundary conditions, and their mixed types, and to explore their corner singularity and provide the algorithms and error estimates in detail. The singular solutions of linear elastostatics are derived, and a number of new models of corner and crack singularity are proposed. Effective numerical methods, such as the collocation Trefftz methods (CTM), the method of fundamental solutions (MFS), the method of particular solutions (MPS) and their combinations: the so called combined method, are developed. Such solutions are useful to examine other numerical methods for singularity problems in linear elastostatics. This thesis consists of three parts, Part I: Basic approaches, Part II: Advanced topics, and Part III: Mixed types of displacement and traction conditions. Contents of Parts I and II have been published in [47,82]. In Part I, the collocation Trefftz methods are used to obtain highly accurate solutions, where the leading coefficient has 14 (or 13) significant digits by the computation with double precision. In part II, two more new models (symmetric and anti-symmetric) of interior crack singularities are proposed, for the corner and crack singularity problems, the combined methods by using many fundamental solutions, but by adding a few singular solutions are proposed. Such a kind of combined methods is significant for linear elastostatics with corners (i.e., the L-shaped domain), because the singular solutions can only be obtained by seeking the power Î½k of rÎ½k numerically. Hence, only a few singular solutions used may greatly simplify the numerical algorithms; Part III is a continued study of Parts I and II, to explore mixed type of displacement and free traction boundary conditions. To our best knowledge, this is the first time to provide the particular solutions near the corner with mixed types of boundary conditions and to report their numerical computation with different boundary conditions on the same corner edge in linear elastostatics. This thesis explores corner singularity and its numerical methods, to form a systematic study of basic theory and advanced computation for linear elastostatics. Advisors/Committee Members: Tzon-Tzer Lu (chair), Hung-Tsai Huang (chair), Ming-Gong Lee (chair), Zi-Cai Li (committee member), Chien-Sen Huang (chair).

Subjects/Keywords: collocation Trefftz method; method of fundamental solutions; Trefftz method; corner singularity; crack singularity; singular particular solutions; crack models; combined method; crack tip; Elastostatics

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

APA (6^th Edition):

Chu, P. (2010). Models of Corner and Crack Singularity of Linear Elastostatics and their Numerical Solutions. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0823110-173542

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):

Chu, Po-chun. “Models of Corner and Crack Singularity of Linear Elastostatics and their Numerical Solutions.” 2010. Thesis, NSYSU. Accessed January 19, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0823110-173542.

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

MLA Handbook (7^th Edition):

Chu, Po-chun. “Models of Corner and Crack Singularity of Linear Elastostatics and their Numerical Solutions.” 2010. Web. 19 Jan 2021.

Vancouver:

Chu P. Models of Corner and Crack Singularity of Linear Elastostatics and their Numerical Solutions. [Internet] [Thesis]. NSYSU; 2010. [cited 2021 Jan 19]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0823110-173542.

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

Council of Science Editors:

Chu P. Models of Corner and Crack Singularity of Linear Elastostatics and their Numerical Solutions. [Thesis]. NSYSU; 2010. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0823110-173542

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

Mississippi State University

21. Collins, Eric Michael. ON MESH QUALITY CONSIDERATIONS FOR THE DISCONTINUOUS GALERKIN METHOD.

Degree: PhD, Computational Engineering, 2009, Mississippi State University

URL: http://sun.library.msstate.edu/ETD-db/theses/available/etd-07102009-153131/ ;

► It is widely accepted that the accuracy and efficiency of computational fluid dynamics (CFD) simulations is heavily influenced by the quality of the mesh… (more)

▼ It is widely accepted that the accuracy and efficiency of computational fluid dynamics (CFD) simulations is heavily influenced by the quality of the mesh upon which the solution is computed. Unfortunately, the computational tools available for assessing mesh quality remain rather limited. This report describes a methodology for rigorously investigating the interaction between a flow solver and a variety of mesh configurations for the purposes of deducing which mesh properties produce the best results from the solver. The techniques described herein permit a more detailed exploration of what constitutes a quality mesh in the context of a given solver and a desired flow regime. In the present work, these newly developed tools are used to investigate mesh quality as it pertains to a high-order accurate discontinuous Galerkin solver when it is used to compute inviscid and high-Reynolds number flows in domains possessing smoothly curving boundaries. For this purpose, two flow models have been generated and used to conduct parametric studies of mesh configurations involving curved elements. The results of these studies allow us to make some observations regarding mesh quality when the discontinuous Galerkin method is used to solve these types of problems. Briefly, we have found that for inviscid problems, the mesh elements used to resolve curved boundaries should be at least third order accurate. For viscous problems, the domain boundaries must be approximated by mesh elements that are of the same order as the polynomial approximation of the solution if the theoretical order of accuracy of the scheme is to be maintained. Increasing the accuracy of the boundary elements to at least one order higher than the solution approximation typically results in a noticeable improvement in the computed error norms. It is also noted that C¹-continuity of the mesh is not required at element interfaces along the boundary. Advisors/Committee Members: Edward A. Luke (chair), David S. Thompson (committee member), Pasquale Cinnella (committee member), Seth Oppenheimer (committee member), J. Mark Janus (committee member).

Subjects/Keywords: manufactured solutions; mesh generation; solver verification

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APA (6^th Edition):

Collins, E. M. (2009). ON MESH QUALITY CONSIDERATIONS FOR THE DISCONTINUOUS GALERKIN METHOD. (Doctoral Dissertation). Mississippi State University. Retrieved from http://sun.library.msstate.edu/ETD-db/theses/available/etd-07102009-153131/ ;

Chicago Manual of Style (16^th Edition):

Collins, Eric Michael. “ON MESH QUALITY CONSIDERATIONS FOR THE DISCONTINUOUS GALERKIN METHOD.” 2009. Doctoral Dissertation, Mississippi State University. Accessed January 19, 2021. http://sun.library.msstate.edu/ETD-db/theses/available/etd-07102009-153131/ ;.

MLA Handbook (7^th Edition):

Collins, Eric Michael. “ON MESH QUALITY CONSIDERATIONS FOR THE DISCONTINUOUS GALERKIN METHOD.” 2009. Web. 19 Jan 2021.

Vancouver:

Collins EM. ON MESH QUALITY CONSIDERATIONS FOR THE DISCONTINUOUS GALERKIN METHOD. [Internet] [Doctoral dissertation]. Mississippi State University; 2009. [cited 2021 Jan 19]. Available from: http://sun.library.msstate.edu/ETD-db/theses/available/etd-07102009-153131/ ;.

Council of Science Editors:

Collins EM. ON MESH QUALITY CONSIDERATIONS FOR THE DISCONTINUOUS GALERKIN METHOD. [Doctoral Dissertation]. Mississippi State University; 2009. Available from: http://sun.library.msstate.edu/ETD-db/theses/available/etd-07102009-153131/ ;

Texas A&M University

22. Edwards, Jarrod Douglas. Second-Order Accurate Method for Solving Radiation-Hydrodynamics.

Degree: PhD, Nuclear Engineering, 2013, Texas A&M University

URL: http://hdl.handle.net/1969.1/151848

► Second-order discretization for radiation-hydrodynamics is currently an area of great interest. Second-order methods used to solve the respective single-physics problems often differ fundamentally, making it… (more)

Subjects/Keywords: Radiation-Hydrodynamics; Multi-Physics Methods; Second-Order Accuracy; Radiative Shocks; Manufactured Solutions

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APA (6^th Edition):

Edwards, J. D. (2013). Second-Order Accurate Method for Solving Radiation-Hydrodynamics. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/151848

Chicago Manual of Style (16^th Edition):

Edwards, Jarrod Douglas. “Second-Order Accurate Method for Solving Radiation-Hydrodynamics.” 2013. Doctoral Dissertation, Texas A&M University. Accessed January 19, 2021. http://hdl.handle.net/1969.1/151848.

MLA Handbook (7^th Edition):

Edwards, Jarrod Douglas. “Second-Order Accurate Method for Solving Radiation-Hydrodynamics.” 2013. Web. 19 Jan 2021.

Vancouver:

Edwards JD. Second-Order Accurate Method for Solving Radiation-Hydrodynamics. [Internet] [Doctoral dissertation]. Texas A&M University; 2013. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/1969.1/151848.

Council of Science Editors:

Edwards JD. Second-Order Accurate Method for Solving Radiation-Hydrodynamics. [Doctoral Dissertation]. Texas A&M University; 2013. Available from: http://hdl.handle.net/1969.1/151848

University of Windsor

23. Esmaeilzadeh, Mohammadali. A Cartesian Cut‐Stencil Method for the Finite Difference Solution of PDEs in Complex Domains.

Degree: PhD, Mechanical, Automotive, and Materials Engineering, 2016, University of Windsor

URL: https://scholar.uwindsor.ca/etd/5788

► A new finite difference formulation, referred to as the Cartesian cut-stencil finite difference method (FDM), for discretization of partial differential equations (PDEs) in any… (more)

▼ A new finite difference formulation, referred to as the Cartesian cut-stencil finite difference method (FDM), for discretization of partial differential equations (PDEs) in any complex physical domain is proposed in this dissertation. The method employs unique localized 1-D quadratic transformation functions to map non-uniform (uncut or cut) physical stencils to a uniform computational stencil. The transformation functions are uniquely determined by the coordinates of the points on the physical stencil. In its basic formulation, 2nd-order central differencing is used to approximate derivatives in the transformed PDEs. The resulting finite difference equations can be solved by classical iterative methods. In the case of a boundary node with a Dirichlet boundary condition, the prescribed value can be used directly in the calculations on the corresponding stencil adjacent to the boundary. However, for Neumann boundary nodes, discretization of the normal derivative in the Neumann condition is accomplished using one-sided approximations, producing an approximate value for the solution variable at the boundary. Then, the cut-stencil method allows stencils adjacent to boundaries to be treated in the same way as interior stencils, thus enabling finite difference calculations on arbitrarily complex domains. This new formulation can be combined with the higher-order compact Padé-Hermitian method to produce higher-order cut-stencil schemes. Three different Cartesian cut-stencil formulations based on local 4th-order approximations are proposed and analyzed. It has been shown that global 4th-order accuracy can be achieved when the same order of accuracy is implemented at Neumann boundaries. Comparison of numerical results for some manufactured problems with the exact solution verifies the capability of the cut-stencil method to deal with PDEs in regular and irregular shaped domains. Cartesian cut-stencil FDM solutions are also obtained for some classical engineering benchmark problems, including Prandtl’s stress function, steady or unsteady heat conduction and flow in a lid-driven cavity. This dissertation demonstrates that the Cartesian cut-stencil finite difference method has many desirable features of a high-end numerical simulation code including simplicity in formulation, meshing and coding, higher-order accuracy, high-fidelity solutions, reliable error estimator, applicable in different science and engineering fields, and can solve complicated nonlinear PDEs in complex geometries. Advisors/Committee Members: Ronald M Barron, Ram Balachandar.

Subjects/Keywords: Boundart condition implementation; Convection-diffusion equation; Cut-stencil finite difference; Higher-order accurate approximation; Method of manufactured problem; Prandtl’s stress function & lid-driven cavity flow

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

APA (6^th Edition):

Esmaeilzadeh, M. (2016). A Cartesian Cut‐Stencil Method for the Finite Difference Solution of PDEs in Complex Domains. (Doctoral Dissertation). University of Windsor. Retrieved from https://scholar.uwindsor.ca/etd/5788

Chicago Manual of Style (16^th Edition):

Esmaeilzadeh, Mohammadali. “A Cartesian Cut‐Stencil Method for the Finite Difference Solution of PDEs in Complex Domains.” 2016. Doctoral Dissertation, University of Windsor. Accessed January 19, 2021. https://scholar.uwindsor.ca/etd/5788.

MLA Handbook (7^th Edition):

Esmaeilzadeh, Mohammadali. “A Cartesian Cut‐Stencil Method for the Finite Difference Solution of PDEs in Complex Domains.” 2016. Web. 19 Jan 2021.

Vancouver:

Esmaeilzadeh M. A Cartesian Cut‐Stencil Method for the Finite Difference Solution of PDEs in Complex Domains. [Internet] [Doctoral dissertation]. University of Windsor; 2016. [cited 2021 Jan 19]. Available from: https://scholar.uwindsor.ca/etd/5788.

Council of Science Editors:

Esmaeilzadeh M. A Cartesian Cut‐Stencil Method for the Finite Difference Solution of PDEs in Complex Domains. [Doctoral Dissertation]. University of Windsor; 2016. Available from: https://scholar.uwindsor.ca/etd/5788

NSYSU

24. Chi, Ya-Ting. The method of fundamental solution for Laplace's equation in 3D.

Degree: Master, Applied Mathematics, 2009, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0709109-015029

► For the method of fundamental solutions(MFS), many reports deal with 2D problems. Since the MFS is more advantageous for 3D problems, this thesis is devoted… (more)

Subjects/Keywords: Laplace's equation; method of fundamental solutions; sources points; collocation points; cylinder; spheres; 3D problems

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

APA (6^th Edition):

Chi, Y. (2009). The method of fundamental solution for Laplace's equation in 3D. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0709109-015029

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):

Chi, Ya-Ting. “The method of fundamental solution for Laplace's equation in 3D.” 2009. Thesis, NSYSU. Accessed January 19, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0709109-015029.

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

MLA Handbook (7^th Edition):

Chi, Ya-Ting. “The method of fundamental solution for Laplace's equation in 3D.” 2009. Web. 19 Jan 2021.

Vancouver:

Chi Y. The method of fundamental solution for Laplace's equation in 3D. [Internet] [Thesis]. NSYSU; 2009. [cited 2021 Jan 19]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0709109-015029.

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

Council of Science Editors:

Chi Y. The method of fundamental solution for Laplace's equation in 3D. [Thesis]. NSYSU; 2009. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0709109-015029

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

25. Caille, Laetitia. Méthodes de régularisation évanescente pour la complétion de données : Fading regularization methods for data completion.

Degree: Docteur es, Mécanique des solides, génie mecanique, productique, transport et génie civil, 2018, Normandie

URL: http://www.theses.fr/2018NORMC231

►

Les problèmes de complétion de données interviennent dans divers domaines de la physique, tels que la mécanique, l'acoustique ou la thermique. La mesure directe des… (more)

▼

Les problèmes de complétion de données interviennent dans divers domaines de la physique, tels que la mécanique, l'acoustique ou la thermique. La mesure directe des conditions aux limites se heurte souvent à l'impossibilité de placer l'instrumentation adéquate. La détermination de ces données n'est alors possible que grâce à des informations complémentaires. Des mesures surabondantes sur une partie accessible de la frontière mènent à la résolution d'un problème inverse de type Cauchy. Cependant, dans certains cas, des mesures directes sur la frontière sont irréalisables, des mesures de champs plus facilement accessibles permettent de pallier ce problème. Cette thèse présente des méthodes de régularisation évanescente qui permettent de trouver, parmi toutes les solutions de l'équation d'équilibre, la solution du problème de complétion de données qui s'approche au mieux des données de type Cauchy ou de champs partiels. Ces processus itératifs ne dépendent pas d'un coefficient de régularisation et sont robustes vis à vis du bruit sur les données, qui sont recalculées et de ce fait débruitées. Nous nous intéressons, dans un premier temps, à la résolution de problèmes de Cauchy associés à l'équation d'Helmholtz. Une étude numérique complète est menée, en utilisant la méthode des solutions fondamentales en tant que méthode numérique pour discrétiser l'espace des solutions de l'équation d'Helmholtz. Des reconstructions précises attestent de l'efficacité et de la robustesse de la méthode. Nous présentons, dans un second temps, la généralisation de la méthode de régularisation évanescente aux problèmes de complétion de données à partir de mesures de champs partielles. Des simulations numériques, pour l'opérateur de Lamé, dans le cadre des éléments finis et des solutions fondamentales, montrent la capacité de la méthode à compléter et débruiter des données partielles de champs de déplacements et à identifier les conditions aux limites en tout point de la frontière. Nous retrouvons des reconstructions précises et un débruitage efficace des données lorsque l'algorithme est appliqué à des mesures réelles issues de corrélation d'images numériques. Un éventuel changement de comportement du matériau est détecté grâce à l'analyse des résidus de déplacements.

Data completion problems occur in many engineering fields, such as mechanical, acoustical and thermal sciences. Direct measurement of boundary conditions is often confronting with the impossibility of placing the appropriate instrumentation. The determination of these data is then possible only through additional informations. Overprescribed measurements on an accessible part of the boundary lead to the resolution of an inverse Cauchy problem. However, in some cases, direct measurements on the boundary are inaccessible, to overcome this problem field measurements are more easily accessible. This thesis presents fading regularization methods that allow to find, among all the solutions of the equilibrium equation, the solution of the data completion problem which fits at best…

Advisors/Committee Members: Delvare, Franck (thesis director).

Subjects/Keywords: Problèmes de complétion de donnée; Régularisation; Méthode des solutions fondamentales; Inverse problems; Cauchy problems; Data completion problems; Regularization, Method of fundamental solutions; Finite element method; Digital Image Correlation

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

APA (6^th Edition):

Caille, L. (2018). Méthodes de régularisation évanescente pour la complétion de données : Fading regularization methods for data completion. (Doctoral Dissertation). Normandie. Retrieved from http://www.theses.fr/2018NORMC231

Chicago Manual of Style (16^th Edition):

Caille, Laetitia. “Méthodes de régularisation évanescente pour la complétion de données : Fading regularization methods for data completion.” 2018. Doctoral Dissertation, Normandie. Accessed January 19, 2021. http://www.theses.fr/2018NORMC231.

MLA Handbook (7^th Edition):

Caille, Laetitia. “Méthodes de régularisation évanescente pour la complétion de données : Fading regularization methods for data completion.” 2018. Web. 19 Jan 2021.

Vancouver:

Caille L. Méthodes de régularisation évanescente pour la complétion de données : Fading regularization methods for data completion. [Internet] [Doctoral dissertation]. Normandie; 2018. [cited 2021 Jan 19]. Available from: http://www.theses.fr/2018NORMC231.

Council of Science Editors:

Caille L. Méthodes de régularisation évanescente pour la complétion de données : Fading regularization methods for data completion. [Doctoral Dissertation]. Normandie; 2018. Available from: http://www.theses.fr/2018NORMC231

Virginia Tech

26. Wu, Wan. Analytical and Numerical Methods Applied to Nonlinear Vessel Dynamics and Code Verification for Chaotic Systems.

Degree: PhD, Aerospace and Ocean Engineering, 2009, Virginia Tech

URL: http://hdl.handle.net/10919/30099

► In this dissertation, the extended Melnikov's method has been applied to several nonlinear ship dynamics models, which are related to the new generation of stability… (more)

▼ In this dissertation, the extended Melnikov's method has been applied to several nonlinear ship dynamics models, which are related to the new generation of stability criteria in the International Maritime Organization (IMO). The advantage of this extended Melnikov's method is it overcomes the limitation of small damping that is intrinsic to the implementation of the standard Melnikov's method. The extended Melnikv's method is first applied to two published roll motion models. One is a simple roll model with nonlinear damping and cubic restoring moment. The other is a model with a biased restoring moment. Numerical simulations are investigated for both models. The effectiveness and accuracy of the extended Melnikov's method is demonstrated. Then this method is used to predict more accurately the threshold of global surf-riding for a ship operating in steep following seas. A reference ITTC ship is used here by way of example and the result is compared to that obtained from previously published standard analysis as well as numerical simulations. Because the primary drawback of the extended Melnikov's method is the inability to arrive at a closed form equation, a 'best fit'approximation is given for the extended Melnikov numerically predicted result. The extended Melnikov's method for slowly varying system is applied to a roll-heave-sway coupled ship model. The Melnikov's functions are calculated based on a fishing boat model. And the results are compared with those from standard Melnikov's method. This work is a preliminary research on the application of Melnikov's method to multi-degree-of-freedom ship dynamics. In the last part of the dissertation, the method of manufactured solution is applied to systems with chaotic behavior. The purpose is to identify points with potential numerical discrepancies, and to improve computational efficiency. The numerical discrepancies may be due to the selection of error tolerances, precisions, etc. Two classical chaotic models and two ship capsize models are examined. The current approach overlaps entrainment in chaotic control theory. Here entrainment means two dynamical systems have the same period, phase and amplitude. The convergent region from control theory is used to give a rough guideline on identifying numerical discrepancies for the classical chaotic models. The effectiveness of this method in improving computational efficiency is demonstrated for the ship capsize models. Advisors/Committee Members: McCue-Weil, Leigh S. (committeechair), Woolsey, Craig A. (committee member), Brown, Alan J. (committee member), Spyrou, Kostas J. (committee member).

Subjects/Keywords: Chaotic control; Method of Manufactured Solution; non-Hamiltonian; Broaching-to; Surf-riding; Capsize; Ship stability; Melnikov's method

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

APA (6^th Edition):

Wu, W. (2009). Analytical and Numerical Methods Applied to Nonlinear Vessel Dynamics and Code Verification for Chaotic Systems. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/30099

Chicago Manual of Style (16^th Edition):

Wu, Wan. “Analytical and Numerical Methods Applied to Nonlinear Vessel Dynamics and Code Verification for Chaotic Systems.” 2009. Doctoral Dissertation, Virginia Tech. Accessed January 19, 2021. http://hdl.handle.net/10919/30099.

MLA Handbook (7^th Edition):

Wu, Wan. “Analytical and Numerical Methods Applied to Nonlinear Vessel Dynamics and Code Verification for Chaotic Systems.” 2009. Web. 19 Jan 2021.

Vancouver:

Wu W. Analytical and Numerical Methods Applied to Nonlinear Vessel Dynamics and Code Verification for Chaotic Systems. [Internet] [Doctoral dissertation]. Virginia Tech; 2009. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/10919/30099.

Council of Science Editors:

Wu W. Analytical and Numerical Methods Applied to Nonlinear Vessel Dynamics and Code Verification for Chaotic Systems. [Doctoral Dissertation]. Virginia Tech; 2009. Available from: http://hdl.handle.net/10919/30099

University of Notre Dame

27. Jessica H. Schiltz. Additive Manufacturing of Orthopedic Ceramics</h1>.

Degree: Bioengineering, 2019, University of Notre Dame

URL: https://curate.nd.edu/show/bn999596z18

► Annually, hundreds of thousands elect for a total hip replacement (THR), a surgical operation meant to address the complications associated with severe osteoarthrosis. The… (more)

▼ Annually, hundreds of thousands elect for a total hip replacement (THR), a surgical operation meant to address the complications associated with severe osteoarthrosis. The forecasted rise in THR utilization has heightened the demand for implant materials optimized for survivorship. Consequently, a critical factor in THR longevity is wear resistance. Oxide ceramics like zirconia (ZrO₂), have consistently surpassed metal and polymer variants and been long accepted constituents in hip implants. However, ceramics are damage intolerant, requiring costly processing steps to mitigate microstructural defects that could initiate catastrophic failure in vivo. As a result, premium pricing of ceramic-on-ceramic THR has limited their widespread use, a problem further compounded by clinician concern over brittle fracture despite generational improvements in manufacturing. As such, additive manufacturing (AM) has emerged as a platform positioned to revitalize the ceramic market. AM presents a cost-reduction opportunity for orthopedics because upfront tooling is eliminated, and the process remains competitive for moderate production runs. Though the AM market has observed significant growth, developments around dense structural ceramics have lagged behind metals and polymers. Consequently, factors that produce AM ceramics that favorably compete with traditional bulk-forming methods are largely unknown. Layered manufacturing strategies could potentially accelerate the next generation of ceramics with improved THR utilization. The primary objective of this work was to advance material processing of AM orthopedic ceramics through tribological and mechanical evaluation. Zirconia specimens produced with photo-polymerization and material-jetting AM, tested in pin-on-disk configurations, were found to have wear coefficients equivalent to reported literature and experimental controls. Investigations into the effect of build direction for stereolithography (SLA) ZrO₂ coupons were performed with respect to thermal aging and accelerated wear outcomes. Results from a modest data set revealed that wear behavior of self-mated SLA ZrO₂ was isotropic when build direction was varied. In addition to wear-resistance, mechanical competence is a crucial metric for orthopedic bearing applications. Certain AM technologies demonstrated that bend strengths of photopolymerized ZrO₂ can meet the minimum standard. Subsequent fractography showcased defect populations introduced by layered manufacturing, including air bubbles and incomplete laminar consolidation. Preliminary experiments then established a size-strength dependency for SLA ZrO₂ which supports that predictive strategies employed for brittle materials can be extended to the development and advancement of AM ceramics. Advisors/Committee Members: Steven R. Schmid, Research Director, Ryan Roeder, Committee Member, Paul McGinn, Committee Member.

Subjects/Keywords: wear and strength characterization of additive manufactured oxide ceramics

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

APA (6^th Edition):

Schiltz, J. H. (2019). Additive Manufacturing of Orthopedic Ceramics</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/bn999596z18

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):

Schiltz, Jessica H.. “Additive Manufacturing of Orthopedic Ceramics</h1>.” 2019. Thesis, University of Notre Dame. Accessed January 19, 2021. https://curate.nd.edu/show/bn999596z18.

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

MLA Handbook (7^th Edition):

Schiltz, Jessica H.. “Additive Manufacturing of Orthopedic Ceramics</h1>.” 2019. Web. 19 Jan 2021.

Vancouver:

Schiltz JH. Additive Manufacturing of Orthopedic Ceramics</h1>. [Internet] [Thesis]. University of Notre Dame; 2019. [cited 2021 Jan 19]. Available from: https://curate.nd.edu/show/bn999596z18.

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

Council of Science Editors:

Schiltz JH. Additive Manufacturing of Orthopedic Ceramics</h1>. [Thesis]. University of Notre Dame; 2019. Available from: https://curate.nd.edu/show/bn999596z18

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

Delft University of Technology

28. Min, Anne-wil (author). New perspective on the [food] landscapes in MRA 2050: Developing a new perspective & design for resilient and attractive agricultural landscapes in the metropolitan region of Amsterdam in 2050.

Degree: 2019, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:2c2f2860-646f-45b0-9d1a-f558257753ab

►

The purpose of this graduation report is to give an overview and inspiration on the route towards a resilient & attractive metropolitan [food] landscape of… (more)

▼

The purpose of this graduation report is to give an overview and inspiration on the route towards a resilient & attractive metropolitan [food] landscape of Amsterdam in 2050. The topic of research is the impact of climate change, unsustainable agriculture and urbanisation towards 2050, on the agricultural landscapes in the metropolitan region of Amsterdam, in the Netherlands. With the challenges and the problems that arise from these, it becomes inevitable to design a transition of the [food] landscapes in the region. Therefore the following research question is defined: ‘‘How to design a new perspective on the food landscapes in the metropolitan region of Amsterdam towards 2050 for a landscape that is resilient to the effects of climate change, to restore the ecosystem (in the freshwater) of the landscape and create opportunities for new activities to start that will strengthen the connection between cities and landscapes, for a resilient & attractive region?’’ A new method is used to find solutions for the three challenges in an integrative way, as there is a lot of potential in the synergy of the solutions. The maximization method provides an overview of individual solutions for the problems in the region, which can be used if the challenges change over time. Subsequently, in the optimization phase, the solutions with the most potential to be combined are given (water storage, new food types, a circular water system, purifying nature & greenhouses). In the final integration phase, the solutions are integrated into the landscapes of the region. An innovative element in this research is the addition of scenarios for the future transition of agricultural landscapes to the maximization method to create climate resilient, purifying agriculture or recreational [food] landscapes. This, together with interviews, results in a new perspective on the [food] landscapes in the region, that is a design for the landscapes created by the synergy between the solutions for the challenges (with a focus on the purifying & climate resilient scenarios). With a new perspective, pilot projects are designed to give an example of the new perspective solutions through the scales and by using the unique characteristics of the agricultural landscapes in the region (in Waterland, Haarlemmermeer, Zaanstreek & the Beemster). In the conclusion, the new perspective combined with pilot projects will create solutions for the challenges in the metropolitan region of Amsterdam towards 2050.

Architecture, Urbanism and Building Sciences | Urbanism

Advisors/Committee Members: Aalbers, Kristel (mentor), Tilie, Nico (graduation committee), Delft University of Technology (degree granting institution).

Subjects/Keywords: Agricultural landscapes; Climate change; Ecosystem pollution; Urbanisation; Metropolitan region of Amsterdam; Maximization method; Synergy solutions; Scenarios; Pilot projects

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

APA (6^th Edition):

Min, A. (. (2019). New perspective on the [food] landscapes in MRA 2050: Developing a new perspective & design for resilient and attractive agricultural landscapes in the metropolitan region of Amsterdam in 2050. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:2c2f2860-646f-45b0-9d1a-f558257753ab

Chicago Manual of Style (16^th Edition):

Min, Anne-wil (author). “New perspective on the [food] landscapes in MRA 2050: Developing a new perspective & design for resilient and attractive agricultural landscapes in the metropolitan region of Amsterdam in 2050.” 2019. Masters Thesis, Delft University of Technology. Accessed January 19, 2021. http://resolver.tudelft.nl/uuid:2c2f2860-646f-45b0-9d1a-f558257753ab.

MLA Handbook (7^th Edition):

Min, Anne-wil (author). “New perspective on the [food] landscapes in MRA 2050: Developing a new perspective & design for resilient and attractive agricultural landscapes in the metropolitan region of Amsterdam in 2050.” 2019. Web. 19 Jan 2021.

Vancouver:

Min A(. New perspective on the [food] landscapes in MRA 2050: Developing a new perspective & design for resilient and attractive agricultural landscapes in the metropolitan region of Amsterdam in 2050. [Internet] [Masters thesis]. Delft University of Technology; 2019. [cited 2021 Jan 19]. Available from: http://resolver.tudelft.nl/uuid:2c2f2860-646f-45b0-9d1a-f558257753ab.

Council of Science Editors:

Min A(. New perspective on the [food] landscapes in MRA 2050: Developing a new perspective & design for resilient and attractive agricultural landscapes in the metropolitan region of Amsterdam in 2050. [Masters Thesis]. Delft University of Technology; 2019. Available from: http://resolver.tudelft.nl/uuid:2c2f2860-646f-45b0-9d1a-f558257753ab

Australian National University

29. Lee, Cheuk Yu. Fundamental solution based numerical methods for three dimensional problems: efficient treatments of inhomogeneous terms and hypersingular integrals .

Degree: 2016, Australian National University

URL: http://hdl.handle.net/1885/117204

► In recent years, fundamental solution based numerical methods including the meshless method of fundamental solutions (MFS), the boundary element method (BEM) and the hybrid fundamental… (more)

▼ In recent years, fundamental solution based numerical methods including the meshless method of fundamental solutions (MFS), the boundary element method (BEM) and the hybrid fundamental solution based finite element method (HFS-FEM) have become popular for solving complex engineering problems. The application of such fundamental solutions is capable of reducing computation requirements by simplifying the domain integral to the boundary integral for the homogeneous partial differential equations. The resulting weak formulations, which are of lower dimensions, are often more computationally competitive than conventional domain-type numerical methods such as the finite element method (FEM) and the finite difference method (FDM). In the case of inhomogeneous partial differential equations arising from transient problems or problems involving body forces, the domain integral related to the inhomogeneous solutions term will need to be integrated over the interior domain, which risks losing the competitive edge over the FEM or FDM. To overcome this, a particular treatment to the inhomogeneous term is needed in the solution procedure so that the integral equation can be defined for the boundary. In practice, particular solutions in approximated form are usually applied rather than the closed form solutions, due to their robustness and readiness. Moreover, special numerical treatment may be required when evaluating stress directly on the domain surface which may give rise to hypersingular integral formulation. This thesis will discuss how the MFS and the BEM can be applied to the three-dimensional elastic problems subjected to body forces by introducing the compactly supported radial basis functions in addition to the efficient treatment of hypersingular surface integrals. The present meshless approach with the MFS and the compactly supported radial basis functions is later extended to solve transient and coupled problems for three-dimensional porous media simulation.

Subjects/Keywords: Three-dimensional linear elasticity; method of fundamental solutions; particular solutions; compactly supported radial basis functions; dual reciprocity method; boundary element method; Hypersingular integral; Hadamard finite part integral; Cauchy principal value integral; complex-step derivative

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

APA (6^th Edition):

Lee, C. Y. (2016). Fundamental solution based numerical methods for three dimensional problems: efficient treatments of inhomogeneous terms and hypersingular integrals . (Thesis). Australian National University. Retrieved from http://hdl.handle.net/1885/117204

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):

Lee, Cheuk Yu. “Fundamental solution based numerical methods for three dimensional problems: efficient treatments of inhomogeneous terms and hypersingular integrals .” 2016. Thesis, Australian National University. Accessed January 19, 2021. http://hdl.handle.net/1885/117204.

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

MLA Handbook (7^th Edition):

Lee, Cheuk Yu. “Fundamental solution based numerical methods for three dimensional problems: efficient treatments of inhomogeneous terms and hypersingular integrals .” 2016. Web. 19 Jan 2021.

Vancouver:

Lee CY. Fundamental solution based numerical methods for three dimensional problems: efficient treatments of inhomogeneous terms and hypersingular integrals . [Internet] [Thesis]. Australian National University; 2016. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/1885/117204.

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

Council of Science Editors:

Lee CY. Fundamental solution based numerical methods for three dimensional problems: efficient treatments of inhomogeneous terms and hypersingular integrals . [Thesis]. Australian National University; 2016. Available from: http://hdl.handle.net/1885/117204

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

30. Kuusi, Tuomo. Harnack Estimates for Supersolutions to a Nonlinear Degenerate Parabolic Equation.

Degree: 2008, Helsinki University of Technology

URL: http://lib.tkk.fi/Diss/2007/isbn9789512289752/

►

In this work, we prove both global and local weak Harnack estimates for supersolutions to a nonlinear degenerate parabolic partial differential equation using measure-theoretical arguments.… (more)

Subjects/Keywords: parabolic nonlinear partial differential equations; Harnack estimates; weak solutions; parabolic Moser's method; De Giorgi's estimates; intrinsic time scale; regularity of solutions; Hölder continuity of solutions; paraboliset epälineaariset osittaisdifferentiaaliyhtälöt; Harnackin estimaatit; heikot ratkaisut; parabolinen Moserin menetelmä; De Giorgin estimaatit; luontainen aikaskaala; ratkaisuiden säännöllisyys; ratkaisuiden Hölder-jatkuvuus

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

APA (6^th Edition):

Kuusi, T. (2008). Harnack Estimates for Supersolutions to a Nonlinear Degenerate Parabolic Equation. (Thesis). Helsinki University of Technology. Retrieved from http://lib.tkk.fi/Diss/2007/isbn9789512289752/

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):

Kuusi, Tuomo. “Harnack Estimates for Supersolutions to a Nonlinear Degenerate Parabolic Equation.” 2008. Thesis, Helsinki University of Technology. Accessed January 19, 2021. http://lib.tkk.fi/Diss/2007/isbn9789512289752/.

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

MLA Handbook (7^th Edition):

Kuusi, Tuomo. “Harnack Estimates for Supersolutions to a Nonlinear Degenerate Parabolic Equation.” 2008. Web. 19 Jan 2021.

Vancouver:

Kuusi T. Harnack Estimates for Supersolutions to a Nonlinear Degenerate Parabolic Equation. [Internet] [Thesis]. Helsinki University of Technology; 2008. [cited 2021 Jan 19]. Available from: http://lib.tkk.fi/Diss/2007/isbn9789512289752/.

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

Council of Science Editors:

Kuusi T. Harnack Estimates for Supersolutions to a Nonlinear Degenerate Parabolic Equation. [Thesis]. Helsinki University of Technology; 2008. Available from: http://lib.tkk.fi/Diss/2007/isbn9789512289752/

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

Open Access Theses and Dissertations