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Faster convergence and higher accuracy for the Dirichlet–Neumann map

✍ Scribed by Johan Helsing

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
359 KB
Volume
228
Category
Article
ISSN
0021-9991

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✦ Synopsis

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.

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A new approach for analyzing boundary value problems for linear and for integrable nonlinear PDEs was introduced in Fokas [A unified transform method for solving linear and certain nonlinear PDEs, Proc. Roy. Soc. London Ser. A 53 (1997) 1411-1443]. For linear elliptic PDEs, an important aspect of th