Solution of Elliptic Partial Differential Equations by an Optimization-Based Domain Decomposition Method

Max D. Gunzburger
Department of Mathematics
Iowa State University

Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University

Hyesuk Kwon Lee
Department of Mathematical Sciences
Clemson University

Applied Mathematics and Computation, Vol. 113, 2000, pp. 111-139.


Abstract

An optimization-based, non-overlapping domain decomposition method for the solution of elliptic partial differential equations is presented. The crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between subdomains; the constraints are the partial differential equations. The method is reformulated as a linear least-squares problem. The latter is examined and a conjugate gradient method for its solution is presented and analyzed. The results of some numerical experiments are then given.

Keywords

Domain decomposition, linear least-squares

AMS subject classification

65N30