Numerical solution of shape optimization problems using the Method of Fundamental Solutions

Pedro Antunes
Instituto tecnico superior, Lisbonne

Date(s) : 22/11/2022   iCal
11 h 00 min - 12 h 00 min

In this talk we give an overview of the application of the Method of Fundamental Solutions (MFS) for solving boundary value problems with elliptic PDE’s. The MFS is a meshfree numerical method for which the solution is approximated by a linear combination of shifts of the fundamental solution of the elliptic differential operator. We present a theoretical framework providing density results and bounds for the error that justify the convergence of the method. Finally, we describe the application of the MFS for solving some shape optimization problems for eigenvalues, such as the classical Laplacian eigenvalue problem, Steklov eigenvalue problems or problems arising from musical acoustics.


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