Mapping large-scale FEM-graphs to highly parallel computers with grid-like topology by self-organization

We consider the problem of mapping large scale FEM graphs for
the solution of partial differential equations to highly parallel
distributed memory computers. Typically, these programs show a
low-dimensional grid-like communication structure.
We argue that conventional domain decomposition methods that are
usually employed today are not well suited for future highly
parallel computers as they do not take into account the
interconnection structure of the parallel computer resulting in a
large communication overhead.
Therefore we propose a new mapping heuristic which performs both,
partitioning of the solution domain and processor allocation in
one integrated step. Our procedure is based on the ability of
Kohonen neural networks to exploit topological similarities of an
input space and a grid-like structured network to compute a
neighborhood preserving mapping between the set of discretization
points and the parallel computer.

We report about results of mapping up to 44,000-node FEM graphs to
a 4096-processor parallel computer and demonstrate the capability
of the proposed scheme for dynamic remapping considering adaptive
refinement of the discretization graph.
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