Sparse approximations on polygonal meshes based on boundary element domain decomposition techniques
Dipl.-Ing. David PuschOct. 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
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.