Find this at http://www.npac.syr.edu/users/gcf/cps713nasiii96/

Further PDE Solvers for the NAS Benchmarks

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

001 CPS713 Case Study (II) CFD and Numerical Relativity
    Benchmarks -- Part III
    Further PDE Solvers
002 Abstract of CPS713NAS- Part III --NAS Benchmarks -- Further PDE 
    Solvers
003 General Analysis of Parallel ADI Performance -- the Pipeline 
    start-up
004 General Analysis of Parallel ADI Performance -- Dependence of 
    Computation and Communication
005 SP -- The Second NAS Benchmark -- Diagonalized ADI
006 LU or SSOR -- The Third NAS Benchmark -- Roughly Gauss Seidel
007 Symmetric Successive Overrelaxation Structure
008 The Relaxation in Symmetric Successive Overrelaxation
009 Parallelization of LU NAS Benchmark and Gauss Seidel Iteration
010 Ideas behind Wavefront or Hyperplane Parallelization of LU NAS 
    Benchmark
011 Basic Formulae for Hyperplane Parallelization of LU NAS Benchmark
012 Cyclic -- Decomposition I for Hyperplane Method for LU NAS 
    Benchmark
013 Block Cyclic -- Decomposition II for Hyperplane Method for LU NAS 
    Benchmark
014 Block -- Decomposition III for Hyperplane Method for LU NAS 
    Benchmark
015 ill Chosen Scattered -- Decomposition IV for Hyperplane Method for
     LU NAS Benchmark
016 Comments on Three NAS Benchmarks
017 Overview of Iterative Solvers for Partial Differential Equations
018 Iterative Methods for Solving Partial Differential Equations
019 SLOR or Successive Line Over Relaxation Exemplified for Laplace's 
    Equation
020 Solution of SLOR -- Successive Line Over Relaxation
021 Red-Black Point Iteration Schemes 
022 Red-Black Line or Zebra Schemes
023 Preconditioners and Other Partial Differential Equation Solution 
    Schemes
024 Incomplete Cholesky Factorization or ILU -- Incomplete LU 
    Decomposition
025 Physical Picture of Domain Decomposition
026 Mathematical Formulation of Domain Decomposition Preconditioning
027 Multigrid Method
028 Physical Picture of the Multigrid Algorithm on a 16 by 16 Grid
029 Mathematical Structure of Exemplar 16 by 16 Multigrid Solution

Northeast Parallel Architectures Center, Syracuse University, npac@npac.syr.edu