A Fast Direct Solver for Boundary Integral Equations in Two Dimensions

Abstract

We describe an algorithm for the direct solution of systems of linear algebraic equations associated with the discretization of boundary integral equations with non-oscillatory kernels in two dimensions. The algorithm is "fast" in the sense that its asymptotic complexity is O(NlogkN), where N is the number of nodes in the discretization, and K depends on the kernel and the geometry of the contour (k= 1 or 2). Unlike previous fast techniques based on iterative solvers, the present algorithm directly constructs a sparse factorization of the inverse of the matrix; thus it is suitable for problems involving relatively ill-conditioned matrices, and is particularly efficient in situations involving multiple right hand sides. The performance of the scheme is illustrated with several numerical examples.

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Document Details

Document Type
Technical Report
Publication Date
Dec 13, 2003
Accession Number
ADA635871

Entities

People

  • P. G. Martinsson
  • Vladimir Rokhlin

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Equations
  • Geometry
  • Information Operations
  • Integral Equations
  • Integrals
  • Linear Algebraic Equations
  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Potential Theory

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)