Parallel Solution of Partial Differential Equations

This volume contains papers on the development and assessment of new approximation and solution techniques that can take advantage of parallel computers. It will be of interest to applied mathematicians, computer scientists, and engineers concerned with investigating the state of the art and future directions in numerical computing. Topics include domain decomposition methods, parallel multi-grid methods, front tracking methods, sparse matrix techniques, adaptive methods, fictitious domain methods, and novel time and space discretizations. Applications discussed include fluid dynamics, radiative transfer, solid mechanics, and semiconductor simulation.

Contents

Foreword
Preface

Iterative substructuring methods for spectral element discretizations of elliptic systems in three dimensions 1
Parallel linear stationary iterative methods 31
Adaptive finite element methods for domain decomposition on nonmatching grids 57
Solution of multi-dimensional radiative transfer problems on parallel computers 85
A Lagrange multiplier/fictitious domain/collocation method for solid-liquid flows 97
Multidimensional parallel spectral solver for Navier-Stokes equations 123
An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows 159
Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions 181
Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations 209
Scalable Poisson and VLSI biharmonic solvers 229
Prospects for CFD on petaflops systems 247
Additive Schwarz for anisotropic elliptic problems 279

List of participants