High order accurate methods for the evaluation of layer heat potentials

Jing Rebecca Li, Leslie Greengard

Research output: Contribution to journalArticlepeer-review

Abstract

We discuss the numerical evaluation of single and double layer heat potentials in two dimensions on stationary and moving boundaries. One of the principal difficulties in designing high order methods concerns the local behavior of the heat kernel, which is both weakly singular in time and rapidly decaying in space. We show that standard quadrature schemes suffer from a poorly recognized form of inaccuracy, which we refer to as "geometrically induced stiffness," but that rules based on product integration of the full heat kernel in time are robust. When combined with previously developed fast algorithms for the evolution of the "history part" of layer potentials, diffusion processes in complex, moving geometries can be computed accurately and in nearly optimal time.

Original languageEnglish (US)
Pages (from-to)3847-3860
Number of pages14
JournalSIAM Journal on Scientific Computing
Volume31
Issue number5
DOIs
StatePublished - 2009

Keywords

  • Diffusion
  • Heat potentials
  • High order accuracy
  • Moving boundaries
  • Quadrature

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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