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Spatial Differencing and ADI Solution of 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 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

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1 CPS713 Case Study II) CFD and Numerical Relativity
Module on NAS Benchmarks --- Part II
Spatial Differencing and ADI
2 Abstract of CPS713NAS-II: ADI and Spatial Differencing Module
3 Spatial Differencing in NAS Benchmarks
4 Numerical Dissipation in NAS Benchmarks
5 Matrix Formalism for NAS Benchmarks
6 Structure of Sparse Matrices in NAS Benchmarks
7 Three Types of Iteration needed in Solution of NAS Benchmarks
8 Comparison of Structure of Elliptic(steady state) and Hyperbolic Equations
9 Relation between Discretized time in Hyperbolic/Parabolic Equations and Iteration Index for Solution of Steady State Equs
10 Richardson's Method and General Preconditioning Formalism in Artificial Time Framework
11 Analysis of Richardson's Method for Laplace or Poisson Equation
12 Preconditioning in the Artificial Time Approach to Iteration Methods
13 Relation of Artificial Time and Matrix Preconditioning
14 Alternating Direction Iteration -- ADI
15 ADI for NAS Benchmarks -- The first BT or Block Tridiagonal Benchmark
16 Explicit Equations for ADI with NAS Benchmarks
17 Computational Complexity of Solution of ADI Equations
18 Solution of Tridiagonal Equations
19 Parallelization of ADI
20 Communication Cost for Parallel ADI in NAS Benchmarks
21 Examples of Possible Distributions in Two Dimension for Parallel ADI
Distribute over j(h) with all values of i(x) in each node
22 Examples of Possible Distributions in Two Dimension for Parallel ADI Distribute both i and j ( x and h) in square subdomains
23 Basis of Estimates for Communication Costs for ADI
24 Examples of Different Distributions for Parallel ADI Solvers
25 Comparisons of Different Distributions for Parallel ADI Solvers
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