A nested-grid direct Poisson solver for concentrated source terms

AbstractFor some applications, numerical solutions of Poisson's equation are needed with a source term that is concentrated on a small part of the computational domain. Uniform-grid Poisson solvers are inefficient for these problems.A grid adaptation procedure with nested grids is described here, that uses an existing uniform-grid solver for the computation on each grid. The new aspect of this method is the error-based refinement criterion that allows the calculation of an upper bound for the total error. With this error bound, the solution can be computed up to any desired accuracy. This computation is direct: the solution on each grid is computed only once, no iteration is needed.Numerical results for two test problems show that the extra error caused by the nested-grid approach can indeed be made arbitrarily small, if desired. Significant reductions in CPU time, compared to solutions on uniform grids, are found