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- The method of fundamental solutions applied to boundary value problems on the surface of a spherePublication . Alves, Carlos J. S.; Antunes, Pedro R. S.In this work we propose using the method of fundamental solutions (MFS) to solve boundary value problems for the Helmholtz–Beltrami equation on a sphere. We prove density and convergence results that justify the proposed MFS approximation. Several numerical examples are considered to illustrate the good performance of the method.
- Determination of elastic resonance frequencies and eigenmodes using the method of fundamental solutionsPublication . Alves, Carlos J. S.; Antunes, Pedro R. S.In this paper, we present the method of fundamental solutions applied to the determination of elastic resonance frequencies and associated eigenmodes. The method uses the fundamental solution tensor of the Navier equations of elastodynamics in an isotropic material. The applicability of the the method is justified in terms of density results. The accuracy of the method is illustrated through 2D numerical examples for the disk and non trivial shapes.