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Numerical study of iterative methods for the solution of the dirichlet-neumann map for elliptic PDEs on regular polygon domains

Saridakis Ioannis, Papadopoulou Eleni, Sifalakis Anastasios

Πλήρης Εγγραφή

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Περίληψη

A generalized Dirichlet to Neumann map is one of the main aspects characterizing a recently introduced method for analyzing linear elliptic PDEs, through which it became possible to couple known and unknown components of the solution on the boundary of the domain without solving on its interior. For its numerical solution, a well con- ditioned quadratically convergent sine-Collocation method was developed, which yielded a linear system of equations with the diagonal blocks of its associated coefficient matrix being point diagonal. This structural property, among others, initiated interest for the employment of iterative methods for its solution. In this work we present a conclusive numerical study for the behavior of classical (Jacobi and Gauss-Seidel) and Krylov subspace (GMRES and Bi-CGSTAB) iterative methods when they are applied for the solution of the Dirich- let to Neumann map associated with the Laplace’s equation on regular polygons with the same boundary conditions on all edges.

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