Optimal additive Schwarz methods for the hp-BEM: The hypersingular integral operator in 3D on locally refined meshes. (October 2015)

• Record Type: Journal Article
• Authors: Führer, T.; Melenk, J.M.; Praetorius, D.; Rieder, A.
• Is Part Of: Computers & mathematics with applications. Volume 70:issue 7(2015)
• Page Start: 1583
• Page End: 1605
• Publication Date: 2015-10
• Subjects: Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2015.06.025
• Languages: English
• ISSNs: 0898-1221

Abstract

<abstract xml:lang="en" abstract-type="author" id="a000005"> <title id="st000005">Abstract</title> <sec> <p id="sp000090">We propose and analyze an overlapping Schwarz preconditioner for the <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2nc5m425" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si23.gif" display="inline" overflow="scroll" id="d13e930" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math></alternatives></inline-formula> and <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2nc5n123" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si29.gif" display="inline" overflow="scroll" id="d13e934" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>h</mml:mi><mml:mi>p</mml:mi></mml:math></alternatives></inline-formula> boundary element method for the hypersingular integral equation in 3D. We consider surface triangulations consisting of triangles. The condition number is bounded uniformly in the mesh size <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2nc5t445" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si11.gif" display="inline" overflow="scroll" id="d13e940" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>h</mml:mi></mml:math></alternatives></inline-formula> and the polynomial order <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2nc5m425" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si23.gif" display="inline" overflow="scroll" id="d13e944" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math></alternatives></inline-formula>. The preconditioner handles adaptively refined meshes and is based on a local multilevel preconditioner for the lowest order space. Numerical experiments on different geometries illustrate its robustness.</p> </sec> </abstract>