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.
This IMA Volume in Mathematics and its Applications PARALLEL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS is based on the proceedings of a workshop with the same title. The work shop was an integral part of the 1996-97IMA program on "MATHEMAT ICS IN HIGH-PERFORMANCE COMPUTING." I would like to thank Petter Bj0rstad of the Institutt for Informatikk, University of Bergen and Mitchell Luskin of the School of Mathematics, University of Minnesota for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE 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 computers offer the promise of greatly increased perfor mance and the routine calculation of previously intractable problems. The papers in this volume were presented at the IMA workshop on the Paral lel Solution of PDE held during June 9-13, 1997. The workshop brought together leading numerical analysts, computer scientists, and engineers to assess the state-of-the-art and to consider future directions.
This volume contains papers on the development and assessment of new approximation and solution techniques that can take advantage of parallel computers. Parallel computers offers the promise of greatly increased performance and the routine calculation of previously intractable problems. The work 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.