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Spatial Differencing and ADI Solution of the NAS Benchmarks

This is second of three foilsets on CFD and NAS Benchmarks

We describe spatial differencing including numerical dissipation for stability

General analysis of resultant sparse matrix structure and iterative solvers

Role of preconditioning and artificial time formulations

focus on NAS ADI solution and its parallel solution with various distributions and their consequent communication cost

Table of Contents for Spatial Differencing and ADI Solution of the NAS Benchmarks

001 CPS713 Case Study II) CFD and Numerical Relativity
    Module  on NAS Benchmarks --- Part II
    Spatial Differencing and ADI
002 Abstract of CPS713NAS-II: ADI and Spatial Differencing Module
003 Spatial Differencing in NAS Benchmarks
004 Numerical Dissipation in NAS Benchmarks
005 Matrix Formalism for NAS Benchmarks
006 Structure of Sparse Matrices in NAS Benchmarks
007 Three Types of Iteration needed in Solution of NAS Benchmarks
008 Comparison of Structure of Elliptic(steady state) and Hyperbolic 
    Equations
009 Relation between Discretized time in Hyperbolic/Parabolic 
    Equations and Iteration Index for Solution of Steady State Equs
010 Richardson's Method and General Preconditioning Formalism in 
    Artificial Time Framework
011 Analysis of Richardson's Method for Laplace or Poisson Equation 
012 Preconditioning in the Artificial Time Approach to Iteration 
    Methods
013 Relation of Artificial Time and Matrix Preconditioning
014 Alternating Direction Iteration -- ADI
015 ADI for NAS Benchmarks -- The first BT or Block Tridiagonal 
    Benchmark
016 Explicit Equations for ADI with NAS Benchmarks
017 Computational Complexity of Solution of ADI Equations
018 Solution of Tridiagonal Equations
019 Parallelization of ADI
020 Communication Cost for Parallel ADI in NAS Benchmarks
021 Examples of Possible Distributions in Two Dimension for Parallel 
    ADI
    Distribute over j(h) with all values of i(x) in each node 
022 Examples of Possible Distributions in Two Dimension for Parallel 
    ADI Distribute both i and j ( x and h) in square subdomains
023 Basis of Estimates for Communication Costs for ADI
024 Examples of Different Distributions for Parallel ADI Solvers
025 Comparisons of Different Distributions for Parallel ADI Solvers

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