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Further PDE Solvers for the NAS Benchmarks

Given by Geoffrey C. Fox at CPSP713 Case studies in Computational Science on Spring Semester 1996. Foils prepared 15 March 1996

This is third of three foilsets on CFD and NAS Benchmarks
This completes analysis of parallel ADI from first BT application benchmark
Second (SP) and third(LU) benchmarks with diagonalized ADI and SSOR methods and their parallelization
Details of SSOR and its parallelization with different decompositions
Relation of SSOR to related iterative solvers -- SLOR, red-black, zebra
Brief remarks on other more sophisticated modern solvers
  • ILU and Incomplete Cholesky
  • Domain Decomposition
  • Multigrid

Table of Contents for Further PDE Solvers for the NAS Benchmarks

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1 CPS713 Case Study (II) CFD and Numerical Relativity
Benchmarks -- Part III
Further PDE Solvers
2 Abstract of CPS713NAS- Part III --NAS Benchmarks -- Further PDE Solvers
3 General Analysis of Parallel ADI Performance -- the Pipeline start-up
4 General Analysis of Parallel ADI Performance -- Dependence of Computation and Communication
5 SP -- The Second NAS Benchmark -- Diagonalized ADI
6 LU or SSOR -- The Third NAS Benchmark -- Roughly Gauss Seidel
7 Symmetric Successive Overrelaxation Structure
8 The Relaxation in Symmetric Successive Overrelaxation
9 Parallelization of LU NAS Benchmark and Gauss Seidel Iteration
10 Ideas behind Wavefront or Hyperplane Parallelization of LU NAS Benchmark
11 Basic Formulae for Hyperplane Parallelization of LU NAS Benchmark
12 Cyclic -- Decomposition I for Hyperplane Method for LU NAS Benchmark
13 Block Cyclic -- Decomposition II for Hyperplane Method for LU NAS Benchmark
14 Block -- Decomposition III for Hyperplane Method for LU NAS Benchmark
15 ill Chosen Scattered -- Decomposition IV for Hyperplane Method for LU NAS Benchmark
16 Comments on Three NAS Benchmarks
17 Overview of Iterative Solvers for Partial Differential Equations
18 Iterative Methods for Solving Partial Differential Equations
19 SLOR or Successive Line Over Relaxation Exemplified for Laplace's Equation
20 Solution of SLOR -- Successive Line Over Relaxation
21 Red-Black Point Iteration Schemes
22 Red-Black Line or Zebra Schemes
23 Preconditioners and Other Partial Differential Equation Solution Schemes
24 Incomplete Cholesky Factorization or ILU -- Incomplete LU Decomposition
25 Physical Picture of Domain Decomposition
26 Mathematical Formulation of Domain Decomposition Preconditioning
27 Multigrid Method
28 Physical Picture of the Multigrid Algorithm on a 16 by 16 Grid
29 Mathematical Structure of Exemplar 16 by 16 Multigrid Solution
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