An interpolation‐based fast multipole method for higher‐order boundary elements on parametric surfaces. (17th May 2016)

• Record Type: Journal Article
• Authors: Dölz, Jürgen; Harbrecht, Helmut; Peters, Michael
• Is Part Of: International journal for numerical methods in engineering. Volume 108:Number 13(2016)
• Page Start: 1705
• Page End: 1728
• Publication Date: 2016-05-17
• Subjects: non‐local operators -- parametric surfaces -- higher‐order ansatz functions -- ℋ2‐matrices -- fast multipole method -- isogeometric analysis; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5274
• Languages: English
• ISSNs: 0029-5981

Abstract

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 ‐ or ℋ 2 ‐matrices. In fact, several simplifications in the construction of ℋ 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.