Adaptive Hmatrix Coarsening and HLU for BEM
Lars Grasedyck (MPI Leipzig)
In this talk we give a brief introduction to the
hierarchical matrix format which is used for the
efficient storage of BEM stiffness matrices. The
basic building block of the format is the cluster
tree T_{I} of the index set I which is constructed,
e.g., by binary space partitioning. Via the
admissiblity condition the blockcluster tree T_{I x I}
is built, which describes the subdivision of the
matrix into admissible blocks. Each of the admissible
blocks is represented by a matrix of low rank.
In the second part of the talk we introduce a coarsening
strategy that aims at finding an \emph{optimal}
blockcluster tree and thus an optimal admissiblity
condition. Optimality can be gained with respect to
storage or arithmetic complexity.
In the third part of the talk we use the coarsening
procedure and the Hmatrix arithmetic in
order to define an HLU preconditioner for
BEM stiffness matrices. Complexity estimates for the
setup, storage and evaluation of the preconditioner
close the talk.
