Faster convergence and higher accuracy for the Dirichlet-Neumann map

Authors:
Johan Helsing
Affiliations:
Numerical Analysis, Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

New techniques allow for more efficient boundary integral algorithms to compute the Dirichlet-Neumann map for Laplace's equation in two-dimensional exterior domains. Novelties include a new post-processor which reduces the need for discretization points with 50%, a new integral equation which reduces the error for resolved geometries with a factor equal to the system size, systematic use of regularization which reduces the error even further, and adaptive mesh generation based on kernel resolution.