A Schwarz splitting variant of cubic spline collocation methods for elliptic PDEs

Authors:
E. N. Houstis;J. R. Rice;E. A. Vavalis
Affiliations:
Department of Computer Science, Purdue University, West Lafayette, IN;Department of Computer Science, Purdue University, West Lafayette, IN;Department of Computer Science, Purdue University, West Lafayette, IN
Venue:
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
Year:
1989

Citing 6
Cited 3

Solving elliptic problems using ELLPACK

Solving elliptic problems using ELLPACK
Two parallel SOR variants of the Schwarz alternating procedure

Parallel Computing
The Numerical Schwarz alternating procedure and SOR

SIAM Journal on Scientific and Statistical Computing
Iterative methods for the solution of elliptic problems on regions partitioned into substructures

SIAM Journal on Numerical Analysis
A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation

SIAM Journal on Scientific and Statistical Computing
Convergence of O(h4) cubic spline collocation methods for elliptic partial differential equations

SIAM Journal on Numerical Analysis

What have we learnt from using real parallel machines to solve real problems?

C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
Schur complement preconditioned conjugate gradient methods for spline collocation equations

ICS '90 Proceedings of the 4th international conference on Supercomputing
Semi-iterative methods on distributed memory multiprocessor architectures

ICS '89 Proceedings of the 3rd international conference on Supercomputing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the formulation of the Schwarz alternating method for a new class of elliptic cubic spline collocation discretization schemes. The convergence of the method is studied using Jacobi and Gauss-Seidel iterative methods for implementing the interaction among subdomains. The Schwarz Cubic Spline Collocation (SCSC) method is formulated for hypercube architectures and implemented on the NCUBE (128 processors) machine. The performance and convergence of the hypercube SCSC algorithm is studied with respect to domain partition and subdomain overlapping area. The numerical results indicate that the partition and mapping of the SCSC on the NCUBE is almost optimal while the speedup obtained is similar to other domain decomposition techniques.