THE LOCALIZED METHOD OF FUNDAMENTAL SOLUTIONS FOR PLANAR GROUNDWATER FLOW PROBLEMS.

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 localization strategy, which adds internal nodes into the model but results in a sparse linear system that can be solved efficiently. Moreover, the advantages possed by MFS are preserved. This article presents the application of the localized method of fundamental solutions for the simulation of planar 2D steady-state groundwater flow problems. Numerical results are compared with those obtained by the boundary element method and analytical solutions. The localized method of fundamental solutions showed its high potential in dealing with ongoing planar groundwater flow problems. [ABSTRACT FROM AUTHOR]