Parallel multigrid waveform relaxation for parabolic problems

Inhaltsverzeichnis1 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.