The papers in this volume are based on lectures given at the IMA workshop on the Parallel Solution of PDE during June 9-13, 1997. The numerical solution of partial differential equations has been of major importance to the development of many technologies and has been the target of much of the development of parallel computer hardware and software. Parallel computer offers the promise of greatly increased performance and the routine calculation of previously intractable problems.
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.

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