Seminars & Events

Mathematics and Computer Science Division
"A Fast Direct Solver for Non-Oscillatory Integral Equations"

DATE: January 10, 2012
TIME: 10:30 AM - 11:30 AM
SPEAKER: Kenneth Ho, Wilkinson Fellowship Interview
LOCATION: Building 240, Seminar Room 4301, Argonne National Laboratory
HOST: Mihai Anitescu

Description:
Over the past two decades, integral equation methods have become very successful at the numerical solution of many important differential equations. This has been due in large part to the development of algorithms to rapidly apply certain Greens function matrices, which, when coupled with Krylov subspace methods, have enabled fast iterative solvers with optimal or near-optimal complexities. Although such techniques have transformed many aspects of computational science and engineering, they remain somewhat ineffective in the face of ill-conditioning or the need to solve many related systems. Here, we discuss a fast direct solver for non-oscillatory integral equations that overcomes these deficiencies. The algorithm is based on a new form of multilevel matrix compression extending that underlying classical fast matrix-vector multiplication schemes, and has some connection with sparse direct solvers. Time permitting, we will also touch on similar investigations for oscillatory integral equations, for which much remains to be discovered. This is joint work with Leslie Greengard.

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