Abstract: We study the behaviour of the optimal shape parameter for the meshless Gaussian RBF-FD method with multipoint stencils on irregular centres for Poisson equations with smooth solution. Numerical experiments show that its value does not depend significantly on the density of the centres. Therefore an algorithm based on comparison of RBF solutions on two nested sets of centres effectively computes a near-optimal shape parameter and helps to obtain more accurate solutions of the PDE than those computed by linear finite elements on the same discretisation centres and with comparable density/bandwidth of the system matrix.

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