Sparse approximations on polygonal meshes based on boundary element domain decomposition techniques

Dipl.-Ing. David Pusch

Oct. 24, 2006, 3:30 p.m. T 1010

We present new boundary element discretizations for diffusion-type equations
on polygonal meshes. The motivation of this problem type is given by porous
media applications.

Based on boundary element domain decomposition techniques we obtain
an approximation which leads to large-scale sparse linear systems. We consider single elements as subdomains and construct corresponding local SteklovPoincar'e operators S i. Note, that the computational domain can consist of
arbitrary polygonal elements. Finally, our system matrix is represented by the
assembled Steklov-Poincar'e operator.

In our numerical experiments we are solving the matrix equation system
by the conjugate gradient method. It turned out that using algebraic multigrid
preconditioners (PEBBLES) yields an almost optimal solver.