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An isogeometric boundary element method for three dimensional potential problems. (English) Zbl 1353.65129
Summary: Isogeometric analysis (IGA) coupled with boundary element method, i.e. IGABEM, received a lot of attention in recent years. In this paper, we extend the IGABEM to solve 3D potential problems. This method offers a number of key improvements compared with conventional piecewise polynomial formulations. Firstly, the models for analysis in the IGABEM are exact geometrical representation no matter how coarse the discretization of the studied bodies is, thus the IGABEM ensures that no geometrical errors are produced in the analysis process. Secondly, a meshing process is no longer required, which means redundant computations are eliminated to allow analysis to be carried out with greatly reduced pre-processing. To accurately evaluate the singular integrals appearing in our method, the power series expansion method is employed. The integration surface is on the real surface of the model, rather than the interpolation surface, i.e. no geometrical errors. Thus, the value of integral is more accurate than the traditional boundary element method, which can improve the computation accuracy of the IGABEM. Some numerical examples for 3D potential problems are used to validate the solutions of the present method with analytical and numerical solutions available.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
Software:
BEMECH
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