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首页> 外文期刊>Applied Mathematical Modelling >A meshless method based on boundary integral equations and radial basis functions for biharmonic-type problems
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A meshless method based on boundary integral equations and radial basis functions for biharmonic-type problems

机译：基于边界积分方程和径向基函数的双调和型问题的无网格方法

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This paper presents a meshless method, which replaces the inhomogeneous biharmonic equation by two Poisson equations in terms of an intermediate function. The solution of the Poisson equation with the intermediate function as the right-hand term may be written as a sum of a particular solution and a homogeneous solution of a Laplace equation. The intermediate function is approximated by a series of radial basis functions. Then the particular solution is obtained via employing Kansa's method, while the homogeneous solution is approximated by using the boundary radial point interpolation method by means of boundary integral equations. Besides, the proposed meshless method, in conjunction with the analog equation method, is further developed for solving generalized biharmonic-type problems. Some numerical tests illustrate the efficiency of the method proposed.
机译：本文提出了一种无网格方法，该方法以中间函数的形式用两个泊松方程代替了非均匀双调和方程。具有中间函数作为右手项的泊松方程的解可以写为拉普拉斯方程的特定解和齐次解的总和。中间函数由一系列径向基函数近似。然后，采用Kansa方法获得特定解，同时利用边界积分方程通过边界径向点插值法近似求同构解。此外，进一步提出的无网格方法与模拟方程方法相结合，进一步解决了广义双调和型问题。一些数值测试说明了所提出方法的有效性。

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