To solve various problems in complicated and concave domains by the method of fundamental solutions (MFS), it is required to consider a large number of source and collocation points that increases the computational time of the analysis. This paper suggests a modification to the MFS, which can make it more efficient and reliable for solving applied problems in complicated domains. In the proposed method, each pseudo source is converted to two or more number of sub-sources with equal intensities. Therefore, the total number of sources is increased while the number of unknowns is not increased. By this approach we will be able to reduce the distance between the main and the pseudo boundaries and therefore modeling the problems with complicated boundaries can be performed effectively. The proposed method is investigated for a scalar field problem, i.e. the Laplace equation, and a vector field problem, i.e. elastostatic problem. It is shown that by using the proposed method, in addition to reducing the calculation time, the condition number of the coefficient matrix also significantly decreases. By solving several numerical example problems, it is observed that the presented method can obtain accurate solutions by using a small number of collocation points.

为了通过基本解决方案（MFS）解决复杂和凹域中的各种问题，需要考虑大量的源和搭配点，这增加了分析的计算时间。本文提出了对MFS的修改，可以使其更有效，更可靠地解决复杂领域中的应用问题。在提出的方法中，每个伪源都被转换为强度相等的两个或更多个子源。因此，增加了源总数，而增加了未知数。通过这种方法，我们将能够减小主边界和伪边界之间的距离，因此可以有效地对具有复杂边界的问题进行建模。针对标量场问题研究了所提出的方法，即 拉普拉斯方程，以及矢量场问题，即弹性静力学问题。结果表明，通过所提出的方法，除了减少了计算时间，系数矩阵的条件数也大大减少。通过解决几个数值示例问题，可以观察到，所提出的方法可以通过使用少量的搭配点来获得准确的解决方案。