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Comparison of three meshless methods for 2D harmonic and biharmonic problems

机译：三种谐波和双谐波问题的三种无网格方法的比较

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摘要

In this paper, three meshless methods are proposed to solve boundary value problems. The special purpose Trefftz function method, the method of fundamental solutions and the symmetry method of fundamental solutions are compared. We considered six numerical examples for harmonic and biharmonic problems as a flow through the cylindrical fibers arranged in a regular square array, deflection of a uniformly loaded square plate and torsion of a bar. The boundary value problems defined for a repeating element of the domain are solved by use of the collocation technique. The accuracy and stability of compared methods are investigated. Root mean square error on the boundary and condition number of the matrix are presented as functions of a number of collocation points.
机译：在本文中，提出了三种无网格方法来解决边值问题。比较特殊用途Trefftz功能方法，比较了基本解决方案的基础解决方法和对称方法。我们认为六个数值例子用于谐波和双音态问题，作为穿过布置成规则方阵列的圆柱形纤维的流动，均匀装载的方形板的偏转和杆的扭转。通过使用搭配技术来解决为域的重复元素定义的边界值问题。研究了比较方法的准确性和稳定性。矩阵的边界和条件号上的根均方误差作为多个配合点的函数呈现。

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