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An Implicit Interface Boundary Integral Method for Poisson’s Equation on Arbitrary Domains
Journal of Computational Physics
  • Catherine Kublik, University of Dayton
  • Nicolay M. Tanushev, Terra Inc.
  • Richard Tsai, University of Texas at Austin
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We propose a simple formulation for constructing boundary integral methods to solve Poisson’s equation on domains with smooth boundaries defined through their signed distance function. Our formulation is based on averaging a family of parameterizations of an integral equation defined on the boundary of the domain, where the integrations are carried out in the level set framework using an appropriate Jacobian. By the coarea formula, the algorithm operates in the Euclidean space and does not require any explicit parameterization of the boundaries. We present numerical results in two and three dimensions.
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The version available for download is the authors' accepted manuscript, posted in compliance with publisher policies on self-archiving. Some differences may exist between this version and the final published version. As such, it is suggested that researchers quoting directly from this source consult the version of record, available online.

This research was supported by NSF Grants DMS-0914465 and DMS-0914840. Catherine Kublik was supported in part by a Bing Fellowship.

Permission documentation is on file.

Peer Reviewed
  • Integral equations,
  • Level set methods,
  • Elliptic problems
Citation Information
Catherine Kublik, Nicolay M. Tanushev and Richard Tsai. "An Implicit Interface Boundary Integral Method for Poisson’s Equation on Arbitrary Domains" Journal of Computational Physics Vol. 247 (2013)
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