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The method of fundamental solutions is a meshless method that belongs to the Trefftz class of numerical methods. The method needs only the boundary to be defined using the set of boundary collocation nodes; it is mathematically effortless to program. One of the imperfections in the context of MFS is the fictitious boundary without any rigorous definition. The other fact that MFS suffers from is the nature of the characteristic matrix that is non-symmetric and fully populated. This issue is overcome by adopting the...

The groundwater flow problems are often solved using numerical models. The numerical models based of known fundamental solution, known as Trefftz methods, represents one of the efficient approaches used to solve potential flow phenomena described by the Laplace differential equation. The Trefftz-like methods, such as the boundary element method (BEM), represent a very efficient approach to solving groundwater flow problems. However, the implementation of BEM is cumbersome because of the fundamental solution singul...