Journal
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
Volume 31, Issue 3, Pages 346-369Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2011.01.008
Keywords
Fast solvers; Boundary value problems; Integral equations; Layer potentials; Laplace's equation
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Funding
- Office of Naval Research [N00014-09-1-0318, 00014-07-1-0711]
- Air Force Office of Scientific Research [FA9550-09-1-0241]
- Schlumberger Limited [1040834.1.R07554.622002]
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We describe an algorithm for the rapid direct solution of linear algebraic systems arising from the discretization of boundary integral equations of potential theory in two dimensions. The algorithm is combined with a scheme that adaptively rearranges the parameterization of the boundary in order to minimize the ranks of the off-diagonal blocks in the discretized operator, thus obviating the need for the user to supply a parameterization r of the boundary for which the distance parallel to r(s) - r(t)parallel to between two points on the boundary is related to their corresponding distance vertical bar s - t vertical bar in the parameter space. The algorithm has an asymptotic complexity of O(N log(2) N), where N is the number of nodes in the discretization. The performance of the algorithm is illustrated with several numerical examples. (C) 2011 Elsevier Inc. All rights reserved.
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