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Abstract
In this article we propose a novel unstructured multigrid method for the solution of matrix equations. This method is based on the additive correction strategy to construct the coarse grids and their associated operators. An equation agglomeration process is devised to aggregate related equations to form the reduced approximate intermediate equations in the multigrid methodology. Only the information in the initial matrix equation is needed to initiate the solution procedure. Several heat transfer model problems with different characteristics are solved to show the performance of the suggested method. Both initially structured and unstructured grid arrangements are employed to derive the corresponding difference equations. Two linear equation solvers, the point Gauss-Seidel and the preconditioned conjugate gradient squared, are used to relax the discretized equations in all grid levels. From the numerical experiments, it is shown that the present method is quite effective for increasing the convergence rate over a wide range of applications.