Stability and Accuracy Analysis of An Explicit-Implicit Finite Difference Algorithm for Solving Time Dependent PDEs
by
W. Rivera-Gallego
Mississippi State University
Coauthors: J. Zhu, D. H. Huddleston

Domain decomposition is a natural approach for solving PDEs when the equations are defined on geometrically complex domains, or when parallel computers are used. The ideal situation is to decompose the original domain into a set of smaller subdomains that can then be treated independently with a periodic exchange of boundary information. The advantages of this approach include the flexibility to deal with equations that exhibit different behaviors in different regions of the domain, a significantly reduced memory requirement for large problems, and a high level of parallelism for multiprocessor computers. However, in order to maintain stability and accuracy, the numerical boundary conditions imposed at subdomain interfaces must be handled very carefully.

A systematic stability and accuracy analysis of various schemes for imposing numerical boundary conditions at subdomain interfaces will be given in this presentation. A new scheme based on an explicit predictor and an implicit corrector will be discussed, in which numerical boundary conditions are first predicted explicitly and then updated by an implicit corrector step. Both theoretical analysis and numerical experiments demonstrate that this approach yields unconditional stability while retaining comparable accuracy to the single domain finite difference implementation.

Date received: April 8, 1999