A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems
A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems
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DOI：
10.1016/j.cma.2017.10.020
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发表时间：
2017-08
影响因子：
7.2
通讯作者：
J. Dolz;H. Harbrecht;S. Kurz;S. Schops;Felix Wolf
中科院分区：
文献类型：
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作者：
J. Dolz;H. Harbrecht;S. Kurz;S. Schops;Felix Wolf
我们提出了一种利用 NURBS 映射进行精确几何表示的间接高阶边界元方法，以及一种用于压缩和降低计算复杂性的基于插值的快速多极方法，以抵消由于边界元方法产生的密集矩阵而产生的问题。通过单层方法解决拉普拉斯和亥姆霍兹问题，我们通过一系列易于与其他数值方案进行比较的数值示例表明，通过利用基于高阶 B 样条的 ansatz 函数，确实可以实现点位势的极高收敛率。
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract the problems arising due to the dense matrices produced by boundary element methods. By solving Laplace and Helmholtz problems via a single layer approach we show, through a series of numerical examples suitable for easy comparison with other numerical schemes, that one can indeed achieve extremely high rates of convergence of the pointwise potential through the utilisation of higher order B-spline-based ansatz functions.