Fine tuning interface relaxation methods for elliptic differential equations

Authors:
J. R. Rice;P. Tsompanopoulou;E. Vavalis
Affiliations:
Purdue University, Computer Science Department, West Lafayette, IN;Purdue University, Computer Science Department, West Lafayette, IN;Purdue University, Computer Science Department, West Lafayette, IN and University of Crete, Mathematics Department, 714 09 Heraklion, Greece and IACM, FORTH, 711 10 Heraklion, Greece
Venue:
Applied Numerical Mathematics
Year:
2002

Citing 11
Cited 7

Solving elliptic problems using ELLPACK

Solving elliptic problems using ELLPACK
An iterative method for elliptic problems on regions partitioned into substructures

Mathematics of Computation
Iterative methods for the solution of elliptic problems on regions partitioned into substructures

SIAM Journal on Numerical Analysis
Domain decomposition methods for large linearly elliptic three-dimensional problems

Journal of Computational and Applied Mathematics
Geometry related convergence results for domain decomposition algorithms

SIAM Journal on Numerical Analysis
Multi-parameterized Schwarz alternating methods for elliptic boundary value problems

Mathematics and Computers in Simulation
Timely Communicaton: An Analysis for a Nonoverlapping Domain Decomposition Iterative Procedure

SIAM Journal on Scientific Computing
A Parallel Grid Modification and Domain Decomposition Algorithm for Local Phenomena Capturing and Load Balancing

Journal of Scientific Computing
Analysis of a nonoverlapping domain decomposition method for elliptic partial differential equations

Journal of Computational and Applied Mathematics
Solving Composite Problems with Interface Relaxation

SIAM Journal on Scientific Computing
Nonoverlapping domain decomposition: a linear algebra viewpoint

Mathematics and Computers in Simulation

Runtime support for collaborative air pollution models

Systems Analysis Modelling Simulation - Special issue: Applications of information systems in environmental modelling
Novel runtime systems support for adaptive compositional modeling in PSEs

Future Generation Computer Systems - Special section: Complex problem-solving environments for grid computing
On a data-driven environment for multiphysics applications

Future Generation Computer Systems - Special section: Complex problem-solving environments for grid computing
Analysis of an interface relaxation method for composite elliptic differential equations

Journal of Computational and Applied Mathematics
A composite grid solver for conjugate heat transfer in fluid-structure systems

Journal of Computational Physics
Row scaling as a preconditioner for some nonsymmetric linear systems with discontinuous coefficients

Journal of Computational and Applied Mathematics
Finite element simulations of window Josephson junctions

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.01

Visualization

Abstract

Two simple interface relaxation techniques for solving elliptic differential equations are considered. A theoretical analysis is carried out at the differential level and "optimal" relaxation parameters are obtained for model problems. A comprehensive experimental numerical study for 1- and 2-dimensional problems is also presented. We present a complete analysis of convergence and optimum parameters for two 1-dimensional methods applied to Helmholtz equations: the averaging method AVE and the Robin-type method ROB. We then present experimental studies for 1- and 2-dimensional methods and more general equations. These studies confirm the theoretical results and suggest they are valid in these more general cases.