Multigrid methods: theory, applications, and supercomputing

✍ Scribed by McCormick, Stephen Fahrney

• Publisher: CRC Press
• Year: 2020
• Tongue: English
• Leaves: 665
• Series: Lecture notes in pure and applied mathematics 110
• Category: Library

✦ Synopsis

1. Multigrid Acceleration of a 2D Full Potential Flow Solver 2. Fast Pseudo-Inverse Algorithms on Hypercubes 3. Multilevel Computations: Review and Recent Developments 4. Multigrid Methods on a Hypercube 5. The Multigrid Method for Fermion Calculations in Quantum Chromodynamics 6. Design and Implementation of Parallel Multigrid Algorithms 7. The Fourier Analysis of a Multigrid Preconditioner 8. On the Role of Regularity in Multigrid Methods 9. A Multigrid Method for Steady Incompressible Navier-Stokes Equations Based on Flux-Vector Splitting 10. Some Nontelescoping Parallel Algorithms Based on Serial Multigrid/Aggregation/ Disaggregation Techniques 11. Spectral Multigrid Methods for the Solution of Homogeneous Turbulence Problems 12. Parallel Superconvergent Multigrid 13. Multiblock Multigrid Solution of the Implicit Time Advance Equations for Magnetic Resistive Diffusion in Geometrically Complex Regions 14. Multigrid Localization and Multigrid Grid Generation for the Computation of Vortex Structures and Dynamics of Flows in Cavities and About Airfoils 15. Applications of the Fast Adaptive Composite Grid Method 16. Multigrid Methods for the Two-Phase Stefan Problem 17. Experimental Results for Multigrid and Transport Problems 18. Solution of the Steady Euler Equations by a Multigrid Method 19. A Multigrid Finite Element Method for Solving the Two-Dimensional Euler Equations 20. Multigrid, Elliptic Grid Generation and the Fast Adaptive Composite Grid Method for Solving Transonic Potential Flow Equations 21. Fourier Estimates for a Multigrid Method for Three-Dimensional Elasticity 22. Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes 23. Multigrid Acceleration of the Isenthalpic Form of the Compressible Flow Equations 24. Parallelization of Multigrid Methods with Local Refinements for a Class of Nonshared Memory Systems 25. Analysis of a Multigrid Method for the Euler Equations of Gas Dynamics in Two Dimensions 26. On Multigrid Methods for the Navier-Stokes Computer 27. On the Accurate Computation of Singular Solutions of Laplace's and Poisson's Equation 28. A Multigrid Approach for Elasticity Problems on "Thin" Domains 29. A Multigrid-Relaxation Scheme for the Navier-Stokes Equations 30. The Simple Pressure-Correction Method as a Nonlinear Smoother 31. Multigrid Methods for Calculation of Electromagnets and Their Implementation on MIMD Computers 32. Application of a Multigrid Method to a Buoyancy-Induced Flow Problem 33. Cell-Centered Multigrid for Interface Problems;This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado.

✦ Table of Contents

Cover......Page 1
Half Title......Page 2
Series Page......Page 3
Title Page......Page 8
Copyright Page......Page 9
Preface......Page 12
Contents......Page 14
Contributors......Page 18
Multigrid Acceleration of a 2D Full Potential Flow Solver......Page 22
Fast Pseudo-Inverse Algorithms on Hypercubes......Page 44
Multilevel Computations: Review and Recent Developments......Page 56
Multigrid Methods on a Hypercube......Page 84
The Multigrid Method for Fermion Calculations in Quantum Chromodynamics......Page 106
Design and Implementation of Parallel Multigrid Algorithms......Page 122
The Fourier Analysis of a Multigrid Preconditioner......Page 138
On the Role of Regularity in Multigrid Methods......Page 164
A Multigrid Method for Steady Incompressible Navier-Stokes Equations Based on Flux-Vector Splitting......Page 178
Some Nontelescoping Parallel Algorithms Based on Serial Multigrid/ Aggregation/Disaggregation Techniques......Page 188
Spectral Multigrid Methods for the Solution of Homogeneous Turbulence Problems......Page 198
Parallel Superconvergent Multigrid......Page 216
Multiblock Multigdd Solution of the Implicit Time Advance Equations for Magnetic Resistive Diffusion in Geometrically Complex Regions......Page 232
Multigrid Localization and Multigrid Grid Generation for the Computation of Vortex Structures and Dynamics of Flows in Cavities and About Airfoils......Page 250
Applications of the Fast Adaptive Composite Grid Method......Page 272
Multigrid Methods for the Two-Phase Stefan Problem......Page 288
Experimental Results for Multigrid and Transport Problems......Page 320
Solution of the Steady Euler Equations by a Multigrid Method......Page 344
A Multigrid Finite Element Method for Solving the Two-Dimensional Euler Equations......Page 358
Multigrid, Elliptic Grid Generation and the Fast Adaptive Composite Grid Method for Solving Transonic Potential Flow Equations......Page 386
Fourier Estimates for a Multigrid Method for Three-Dimensional Elasticity......Page 410
Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes......Page 434
Multigrid Acceleration of the Isenthalpic Form of the Compressible Flow Equations......Page 452
Parallelization of Multigrid Methods with Local Refinements for a Class of Nonshared Memory Systems......Page 470
Analysis of a Multigrid Method for the Euler Equations of Gas Dynamics in Two Dimensions......Page 488
On Multigrid Methods for the Navier-Stokes Computer......Page 512
On the Accurate Computation of Singular Solutions of Laplace's and Poisson's Equation......Page 538
A Multigrid Approach for Elasticity Problems on "Thin" Domains......Page 562
A Multigrid-Relaxation Scheme for the Navier-Stokes Equations......Page 576
The Simple Pressure-Correction Method as a Nonlinear Smoother......Page 600
Multigrid Methods for Calculation of Electromagnets and Their Implementation on MIMD Computers......Page 618
Application of a Multigrid Method to a Buoyancy-Induced Flow Problem......Page 626
Cell-Centered Multigrid for Interface Problems......Page 652
Index......Page 664

✦ Subjects

Differential equations, Partial--Numerical solutions;MATHEMATICS / General;MATHEMATICS / Number Systems;Multigrid methods (Numerical analysis);Conference papers and proceedings;Conference publication;Electronic books;Differential equations, Partial -- Numerical solutions -- Congresses;Multigrid methods (Numerical analysis) -- Congresses