The method of fundamental solutions for linear diffusion-reaction equations

The paper presents an extension of the solution procedure based on the method of fundamental solutions proposed earlier in the literature for solving linear diffusion reaction equations in nonregular geometries in two and three dimensions. The solution procedure utilizes the fundamental solution to the problem along with boundary collocation to result in a grid-free numerical scheme. A new heuristic for source location is utilized along with orthogonal collocation in nonsmooth domains to improve the accuracy of the solution. The efficacy of the solution procedure is demonstrated for a variety of problems in nonregular simply and multiply connected geometries with nonuniform boundary conditions.