Parallel non-overlapping domain decomposition algorithms for elliptic partial differential equations

Daoqi Yang, Purdue University

Abstract

We propose iterative nonoverlapping domain decomposition algorithms for second order partial differential equations. For the first algorithm, at the interface of two subdomains, one subdomain problem requires that Dirichlet data be passed to it from the previous iteration level, while the other subdomain problem requires that Neumann data be passed to it. The second algorithm can be characterized as follows: the transmission conditions at the interfaces of subdomains are taken to be Dirichlet at odd iterations and Neumann at even iterations. These two algorithms lead to full parallelizable subdomain problems. The convergence of the iterative sequence of subdomain solutions is established for these two algorithms. Finite-dimensional discretization schemes, such as the finite element approximation, the finite element approximation with Lagrange multipliers, and the hybrid mixed finite element approximation, are considered and analyzed. Applications to parabolic and hyperbolic problems are indicated. Numerical examples are provided to confirm the fast convergence of the iterative procedures.

Degree

Ph.D.

Advisors

Douglas, Purdue University.

Subject Area

Mathematics

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