Archives of Acoustics, 44, 3, pp. 475–492, 2019
10.24425/aoa.2019.129263

Isogeometric Fast Multipole Boundary Element Method Based on Burton-Miller Formulation for 3D Acoustic Problems

Leilei CHEN
Xinyang Normal University
China

Wenchang ZHAO
University of Science and Technology of China
China

Cheng LIU
University of Science and Technology of China
China

Haibo CHEN
University of Science and Technology of China
China

Steffen MARBURG
Technical University of Munich
Germany

An isogeometric boundary element method is applied to simulate wave scattering problems governed by the Helmholtz equation. The NURBS (non-uniform rational B-splines) widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The singular integrals existing in Burton-Miller formulation are evaluated directly and accurately using Hadamard’s finite part integration. Fast multipole method is applied to accelerate the solution of the system of equations. It is demonstrated that the isogeometric boundary element method based on NURBS performs better than the conventional approach based on Lagrange basis functions in terms of accuracy, and the use of the fast multipole method both retains the accuracy for isogeometric boundary element method and reduces the computational cost.
Keywords: isogeometric analysis; boundary element method; Burton-Miller method; acoustic scattering; fast multipole method
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DOI: 10.24425/aoa.2019.129263