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- 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.
- Solving boundary value problems on manifolds with a plane waves methodPublication . Alves, Carlos J. S.; Antunes, Pedro R. S.; Martins, Nuno F. M.; Valtchev, Svilen S.In this paper we consider a plane waves method as a numerical technique for solving boundary value problems for linear partial di erential equations on man- ifolds. In particular, the method is applied to the Helmholtz–Beltrami equations. We prove density results that justify the completeness of the plane waves space and justify the approximation of domain and boundary data. A-posteriori error estimates and numerical experiments show that this simple technique may be used to accurately solve boundary value problems on manifolds.