COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics

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Mathematics Colloquium: Rigorously justified solvers for rough PDE coefficients

2009-04-29

4:10 p.m. Neill Hall 5W

Burak Aksoylu

Abstract: Roughness of PDE coefficients causes loss of robustness of preconditioners. The main goal is to recover robustness and obtain rigorous structural understanding of the involved process. A qualitative understanding of the PDE operators and their dependence on the coefficients is essential for designing preconditioners. Controlling the infinite dimensional problem provides a basis for the construction of preconditioners. We use tools from operator theory for this. On the other hand, we control the discretized problem using singular perturbation analysis (SPA) which provides valuable insight to the asymptotic behavior of the solution of the underlying PDE. We construct a preconditioner based on this feedback and justify its effectiveness rigorously. As a result, we present a new preconditioning strategy which is computationally comparable to algebraic multigrid, but with rigorous justification. (The speaker is a candidate for Applied Mathematics or Statistics on WSU-Vancouver Campus)