| A Combination Of The Finite Element Method With GMRES To Obtain An Efficient Algorithm To Solve An Eigenvalue Problem Aurora Ferrja1; Besiana Cobani1; 1UNIVERSITY OF TIRANA, Tirana, Albania; PAPER: 452/Mathematics/Regular (Oral) SCHEDULED: 14:00/Sat. 26 Oct. 2019/Hermes (64/Mezz. F) ABSTRACT: To find an analytically solution of a problem involving a system of partial differential equation is a challenging tusk. So, we use iterative methods to obtain an approximate solution. In inverse scattering the transmission eigenvalue problem is important do determine data for the scatterer. From the complexity of the domain (scatterer) we use the finite element method because we can obtain the best approximation of the required zone. The problem we solve is nonlinear and non-selfadjoint. Using variational method and Fredholm alternative we transform it in order to be discretize. Colton and Cakoni give inferior and superior of the refractive index. This information is used in an inequality given by Colton and Haddar to determine a boundary for the eigenvalues involving the first Dirichlet eigenvalue as well. We use an algorithm to find the first eigenvalue. We have the refractive index n also The algorithm used is a combination of finite element method with GMRES algorithm. |
