Parallel Multigrid Waveform Relaxation for Parabolic Problems - Info and Reading Options

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1 Introduction -- 1.1 Numerical simulation and parallel processing -- 1.2 The simulation of time-dependent processes -- 1.3 Outline -- 2 Waveform Relaxation Methods -- 2.1 Introduction -- 2.2 Waveform relaxation: basic ideas -- 2.3 A classification of waveform methods -- 2.4 General convergence results -- 2.5 Convergence analysis for linear systems -- 2.6 Waveform relaxation acceleration techniques -- 2.7 Some concluding remarks -- 3 Waveform Relaxation Methods for Initial Boundary Value Problems -- 3.1 Introduction and notations -- 3.2 Standard waveform relaxation -- 3.3 Linear multigrid acceleration -- 3.4 Convergence analysis -- 3.5 Experimental results -- 3.6 Nonlinear multigrid waveform relaxation -- 3.7 A multigrid method on a space-time grid -- 3.8 Concluding remarks -- 4 Waveform Relaxation for Solving Time-Periodic Problems -- 4.1 Introduction -- 4.2 Standard time-periodic PDE solvers -- 4.3 Time-periodic waveform relaxation -- 4.4 Analysis of the continuous-time iteration -- 4.5 Analysis of the discrete-time iteration -- 4.6 Multigrid acceleration -- 4.7 Autonomous time-periodic problems -- 5 A Short Introduction to Parallel Computers and Parallel Computing -- 5.1 Introduction -- 5.2 Classification of parallel computers -- 5.3 The hypercube topology -- 5.4 The Intel iPSC/2 hypercube multiprocessor -- 5.5 Parallel performance parameters -- 6 Parallel Implementation of Standard Parabolic Marching Schemes -- 6.1 Introduction -- 6.2 Problem class and discretization -- 6.3 Parallel implementation: preliminaries -- 6.4 The explicit update step -- 6.5 The multigrid solver -- 6.6 The tridiagonal systems solver -- 6.7 Timing results on the Intel hypercube -- 6.8 Numerical examples -- 6.9 Concluding remarks -- 7 Computational Complexity of Multigrid Waveform Relaxation -- 7.1 Introduction -- 7.2 Arithmetic complexity -- 7.3 Parallel implementation -- 7.4 Vectorization -- 7.5 Concluding remarks -- 8 Case Studies -- 8.1 Introduction -- 8.2 Programming considerations -- 8.3 Representation of the results -- 8.4 Linear initial boundary value problems -- 8.5 Nonlinear initial boundary value problems -- 8.6 Linear time-periodic problems -- 8.7 Example 7: a nonlinear periodic system -- 8.8 Further remarks, limits of applicability -- 9 Concluding Remarks and Suggestions for Future Research -- A Discretization and Stencils

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