Ebook: Parallel Solution of Partial Differential Equations

This IMA Volume in Mathematics and its Applications PARALLEL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS is based on the proceedings of a workshop with the same title. The work­ shop was an integral part of the 1996-97IMA program on "MATHEMAT­ ICS IN HIGH-PERFORMANCE COMPUTING." I would like to thank Petter Bj0rstad of the Institutt for Informatikk, University of Bergen and Mitchell Luskin of the School of Mathematics, University of Minnesota for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda­ tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE The numerical solution of partial differential equations has been of major importance to the development of many technologies and has been the target of much of the development of parallel computer hardware and software. Parallel computers offer the promise of greatly increased perfor­ mance and the routine calculation of previously intractable problems. The papers in this volume were presented at the IMA workshop on the Paral­ lel Solution of PDE held during June 9-13, 1997. The workshop brought together leading numerical analysts, computer scientists, and engineers to assess the state-of-the-art and to consider future directions.

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The papers in this volume are based on lectures given at the IMA workshop on the Parallel Solution of PDE during June 9-13, 1997. The numerical solution of partial differential equations has been of major importance to the development of many technologies and has been the target of much of the development of parallel computer hardware and software. Parallel computer offers the promise of greatly increased performance and the routine calculation of previously intractable problems.
This volume contains papers on the development and assessment of new approximation and solution techniques that can take advantage of parallel computers. It will be of interest to applied mathematicians, computer scientists, and engineers concerned with investigating the state of the art and future directions in numerical computing.
Topics include domain decomposition methods, parallel multi-grid methods, front tracking methods, sparse matrix techniques, adaptive methods, fictitious domain methods, and novel time and space discretizations. Applications discussed include fluid dynamics, radiative transfer, solid mechanics, and semiconductor simulation.

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The papers in this volume are based on lectures given at the IMA workshop on the Parallel Solution of PDE during June 9-13, 1997. The numerical solution of partial differential equations has been of major importance to the development of many technologies and has been the target of much of the development of parallel computer hardware and software. Parallel computer offers the promise of greatly increased performance and the routine calculation of previously intractable problems.
This volume contains papers on the development and assessment of new approximation and solution techniques that can take advantage of parallel computers. It will be of interest to applied mathematicians, computer scientists, and engineers concerned with investigating the state of the art and future directions in numerical computing.
Topics include domain decomposition methods, parallel multi-grid methods, front tracking methods, sparse matrix techniques, adaptive methods, fictitious domain methods, and novel time and space discretizations. Applications discussed include fluid dynamics, radiative transfer, solid mechanics, and semiconductor simulation.
Content:
Front Matter....Pages i-x
Iterative Substructuring Methods for Spectral Element Discretizations of Elliptic Systems in Three Dimensions....Pages 1-30
Parallel Linear Stationary Iterative Methods....Pages 31-55
Adaptive Finite Element Methods for Domain Decomposition on Nonmatching Grids....Pages 57-83
Solution of Multi-Dimensional Radiative Transfer Problems on Parallel Computers....Pages 85-96
A Lagrange Multiplier/Fictitious Domain/Collocation Method for Solid-Liquid Flows....Pages 97-121
Multidimensional Parallel Spectral Solver for Navier-Stokes Equations....Pages 123-158
An Overlapping Schwarz Method for Spectral Element Simulation of Three-Dimensional Incompressible Flows....Pages 159-180
Overlapping and Multilevel Schwarz Methods for Vector Valued Elliptic Problems in Three Dimensions....Pages 181-208
Front Tracking and Operator Splitting for Nonlinear Degenerate Convection-Diffusion Equations....Pages 209-227
Scalable Poisson and VLSI Biharmonic Solvers....Pages 229-246
Prospects for CFD on Petaflops Systems....Pages 247-277
Additive Schwarz for Anisotropic Elliptic Problems....Pages 279-293
Back Matter....Pages 295-306

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The papers in this volume are based on lectures given at the IMA workshop on the Parallel Solution of PDE during June 9-13, 1997. The numerical solution of partial differential equations has been of major importance to the development of many technologies and has been the target of much of the development of parallel computer hardware and software. Parallel computer offers the promise of greatly increased performance and the routine calculation of previously intractable problems.
This volume contains papers on the development and assessment of new approximation and solution techniques that can take advantage of parallel computers. It will be of interest to applied mathematicians, computer scientists, and engineers concerned with investigating the state of the art and future directions in numerical computing.
Topics include domain decomposition methods, parallel multi-grid methods, front tracking methods, sparse matrix techniques, adaptive methods, fictitious domain methods, and novel time and space discretizations. Applications discussed include fluid dynamics, radiative transfer, solid mechanics, and semiconductor simulation.
Content:
Front Matter....Pages i-x
Iterative Substructuring Methods for Spectral Element Discretizations of Elliptic Systems in Three Dimensions....Pages 1-30
Parallel Linear Stationary Iterative Methods....Pages 31-55
Adaptive Finite Element Methods for Domain Decomposition on Nonmatching Grids....Pages 57-83
Solution of Multi-Dimensional Radiative Transfer Problems on Parallel Computers....Pages 85-96
A Lagrange Multiplier/Fictitious Domain/Collocation Method for Solid-Liquid Flows....Pages 97-121
Multidimensional Parallel Spectral Solver for Navier-Stokes Equations....Pages 123-158
An Overlapping Schwarz Method for Spectral Element Simulation of Three-Dimensional Incompressible Flows....Pages 159-180
Overlapping and Multilevel Schwarz Methods for Vector Valued Elliptic Problems in Three Dimensions....Pages 181-208
Front Tracking and Operator Splitting for Nonlinear Degenerate Convection-Diffusion Equations....Pages 209-227
Scalable Poisson and VLSI Biharmonic Solvers....Pages 229-246
Prospects for CFD on Petaflops Systems....Pages 247-277
Additive Schwarz for Anisotropic Elliptic Problems....Pages 279-293
Back Matter....Pages 295-306
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