A generalized method is presented that accommodates the linear form of the diffusion equation in regions with irregular boundaries. The region of interest many consist of subregions with spatially variable thermal properties. The solution function for the diffusion equation is decomposed into two solutions: one with homogeneous and the other with nonhomogeneous boundary conditions. The Galerkin functions are used to provide a solution for a diffusion problem with homogeneous boundary condition and linear initial condition. Problems with nonhomogeneous boundary conditions can be dealt with by many other schemes, including the standard Galerkin method. The final solution is a combination of these two solutions.

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