Adaptive Wavelet BEM for Boundary Integral Equations: Theory and Numerical Experiments. (25th January 2018)

• Record Type: Journal Article
• Authors: Dahlke, S.; Harbrecht, H.; Utzinger, M.; Weimar, M.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 2(2018)
• Page Start: 208
• Page End: 232
• Publication Date: 2018-01-25
• Subjects: Adaptive wavelet BEM -- Besov spaces -- double layer potential operator -- integral equations -- manifolds -- non-linear approximation -- regularity -- weighted Sobolev spaces; 30H25 -- 35B65 -- 42C40 -- 45E99 -- 46E35 -- 47B38 -- 65T60; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1359623
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We are concerned with the numerical treatment of boundary integral equations by the adaptive wavelet boundary element method. In particular, we consider the second kind Fredholm integral equation for the double layer potential operator on patchwise smooth manifolds contained in ℝ 3 . The corresponding operator equations are treated by adaptive implementations that are in complete accordance with the underlying theory. The numerical experiments demonstrate that adaptive methods really pay off in this setting. The observed convergence rates fit together very well with the theoretical predictions based on the Besov regularity of the exact solution.