Faster convergence and higher accuracy for the Dirichlet-Neumann map

Summary, in English

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.

• Author: Johan Helsing
• Department/s: Mathematics (Faculty of Engineering); Harmonic Analysis and Applications
• Publishing year: 2009
• Language: English
• Pages: 2578-2586
• Publication/Series: Journal of Computational Physics
• Volume: 228
• Issue: 7
• Full text: - 198 kB; Download statistics
• Links: http://www.maths.lth.se/na/staff/helsing/JCP09a.pdf; http://dx.doi.org/10.1016/j.jcp.2008.12.025
• Document type: Journal article
• Publisher: Elsevier
• Topic: Mathematics
• Keywords: Fast multipole method; Integral equations; Dirichlet–Neumann map; Potential theory; Nyström method
• Status: Published
• Research group: Harmonic Analysis and Applications; Harmonic Analysis and Applications
• ISBN/ISSN/Other: ISSN: 0021-9991