Browsing by Author "Alves, Carlos J. S."
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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.
- Iterative and range test methods for an inverse source problem for acoustic wavesPublication . Alves, Carlos J. S.; Kress, Rainer; Serranho, PedroWe propose two methods for solving an inverse source problem for time-harmonic acoustic waves. Based on the reciprocity gap principle a nonlinear equation is presented for the locations and intensities of the point sources that can be solved via Newton iterations. To provide an initial guess for this iteration we suggest a range test algorithm for approximating the source locations. We give a mathematical foundation for the range test and exhibit its feasibility in connection with the iteration method by some numerical examples.
- On the identification of the flatness of a sound-hard acoustic crackPublication . Alves, Carlos J. S.; Serranho, PedroIn this paper, we present results concerning the far field pattern generated by flat and almost flat cracks in 3D and the possibility of identifying these geometrical features from direct inspection of the far field pattern. We address the direct problem using a variational formulation of the boundary integral equation to avoid the hipersingularity in the double layer potential representation. Concerning the inverse problem, some estimates presenting a direct dependence on the far field behavior and the flatness of the crack are derived. From the knowledge of the plane that defines the main directions of the crack it is possible to get a first approximation that may be used as an initial guess for the Newton method. Numerical simulations validate the direct relation between a far field plane having almost null amplitude and the main directions of a plane that defines an almost flat crack.
- 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.
- 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.