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The MFS and MAFS for solving Laplace and biharmonic equations

机译:求解拉普拉斯和双调和方程的MFS和MAFS

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The method of fundamental solutions (MFS) has been known as an effective boundary meshless method for solving homogeneous differential equations with smooth boundary conditions and boundary shapes. Despite many attractive features of the MFS, the determination of the source location and the boundaries with sharp corners still pose a certain degree of challenges. In this paper, we revisit another powerful boundary method, the method of approximate fundamental solutions (MAFS), which approximates the fundamental solution using trigonometric functions. In the MAFS, the fundamental solutions for various governed equations can be easily constructed. The placement of the source points is also simple. In this paper, we will apply the MAFS for solving the Laplace equation with non-harmonic boundary conditions and the biharmonic equation with non-biharmonic boundary conditions with highly irregular or non-smooth domains. We will compare the performance of the MAFS and the MFS in these types of problems.
机译:基本解法(MFS)是一种有效的无边界无边界方法,用于求解具有光滑边界条件和边界形状的齐次微分方程。尽管MFS具有许多吸引人的功能,但是确定源位置和带有尖角的边界仍然带来一定程度的挑战。在本文中,我们将回顾另一种强大的边界方法,即近似基本解(MAFS)方法,该方法使用三角函数对基本解进行近似。在MAFS中,可以轻松构造各种控制方程的基本解。源点的放置也很简单。在本文中,我们将应用MAFS求解具有非调和边界条件的Laplace方程和具有非规则或非光滑域的具有非双调和边界条件的双调和方程。我们将在这些类型的问题中比较MAFS和MFS的性能。

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