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Per-Gunnar Martinsson, Department of Applied Mathematics, ����������

Fast numerical techniques for solving partial differential equations

There exists a multitude of techniques for computing approximate solutions to partial differential equations. In this talk, we will describe a set of such techniques that are based on a combination of integral equation formulations and “fast” numerical algorithms. The principle advantage of such techniques is that they are very stable, and capable of producing highly accurate results. In most environments, they are at least as fast as competing methods, and in many environments (most conspicuously, in linear problems involving constant coefficient operators, and no body loads) they are orders of magnitude faster than competing methods. Limitations of techniques based on integral equations, real and perceived, will also be discussed.