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An interpolation‐based fast multipole method for higher‐order boundary elements on parametric surfaces
Author(s) -
Dölz Jürgen,
Harbrecht Helmut,
Peters Michael
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5274
Subject(s) - multipole expansion , mathematics , interpolation (computer graphics) , piecewise , galerkin method , representation (politics) , parametric statistics , boundary element method , boundary (topology) , surface (topology) , fast multipole method , polynomial , rate of convergence , mathematical analysis , finite element method , geometry , computer science , animation , statistics , physics , computer graphics (images) , thermodynamics , quantum mechanics , computer network , channel (broadcasting) , politics , political science , law
Summary In this article, a black‐box higher‐order fast multipole method for solving boundary integral equations on parametric surfaces in three spatial dimensions is proposed. Such piecewise smooth surfaces are the topic of recent studies in isogeometric analysis. Due to the exact surface representation, the rate of convergence of higher‐order methods is not limited by approximation errors of the surface. An element‐wise clustering strategy yields a balanced cluster tree and an efficient numerical integration scheme for the underlying Galerkin method. By performing the interpolation for the fast multipole method directly on the reference domain, the cost complexity in the polynomial degree is reduced by one order. This gain is independent of the application of either ℋ ‐ orℋ 2 ‐matrices. In fact, several simplifications in the construction ofℋ 2 ‐matrices are pointed out, which are a by‐product of the surface representation. Extensive numerical examples are provided in order to quantify and qualify the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.