Fast direct solvers for integral equations in complex three-dimensional domains

Leslie Greengard, Denis Gueyffier, Per Gunnar Martinsson, Vladimir Rokhlin

Research output: Contribution to journalArticle

Abstract

Methods for the solution of boundary integral equations have changed significantly during the last two decades. This is due, in part, to improvements in computer hardware, but more importantly, to the development of fast algorithms which scale linearly or nearly linearly with the number of degrees of freedom required. These methods are typically iterative, based on coupling fast matrix-vector multiplication routines with conjugate-gradient-type schemes. Here, we discuss methods that are currently under development for the fast, direct solution of boundary integral equations in three dimensions. After reviewing the mathematical foundations of such schemes, we illustrate their performance with some numerical examples, and discuss the potential impact of the overall approach in a variety of settings.

Original languageEnglish (US)
Pages (from-to)243-275
Number of pages33
JournalActa Numerica
Volume18
DOIs
StatePublished - May 2009

ASJC Scopus subject areas

  • Numerical Analysis
  • Mathematics(all)

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