Abstract: 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 conditioned
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 Dirichlet
to Neumann map associated with the Laplace-s equation
on regular polygons with the same boundary conditions on
all edges.
Abstract: The problem addressed herein is the efficient management of the Grid/Cluster intense computation involved, when the preconditioned Bi-CGSTAB Krylov method is employed for the iterative solution of the large and sparse linear system arising from the discretization of the Modified Helmholtz-Dirichlet problem by the Hermite Collocation method. Taking advantage of the Collocation ma-trix's red-black ordered structure we organize efficiently the whole computation and map it on a pipeline architecture with master-slave communication. Implementation, through MPI programming tools, is realized on a SUN V240 cluster, inter-connected through a 100Mbps and 1Gbps ethernet network,and its performance is presented by speedup measurements included.