302 research outputs found
Solving the Poisson equation on small aspect ratio domains using unstructured meshes
We discuss the ill conditioning of the matrix for the discretised Poisson
equation in the small aspect ratio limit, and motivate this problem in the
context of nonhydrostatic ocean modelling. Efficient iterative solvers for the
Poisson equation in small aspect ratio domains are crucial for the successful
development of nonhydrostatic ocean models on unstructured meshes. We introduce
a new multigrid preconditioner for the Poisson problem which can be used with
finite element discretisations on general unstructured meshes; this
preconditioner is motivated by the fact that the Poisson problem has a
condition number which is independent of aspect ratio when Dirichlet boundary
conditions are imposed on the top surface of the domain. This leads to the
first level in an algebraic multigrid solver (which can be extended by further
conventional algebraic multigrid stages), and an additive smoother. We
illustrate the method with numerical tests on unstructured meshes, which show
that the preconditioner makes a dramatic improvement on a more standard
multigrid preconditioner approach, and also show that the additive smoother
produces better results than standard SOR smoothing. This new solver method
makes it feasible to run nonhydrostatic unstructured mesh ocean models in small
aspect ratio domains.Comment: submitted to Ocean Modellin
Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs
We design and implement a parallel algebraic multigrid method for isotropic
graph Laplacian problems on multicore Graphical Processing Units (GPUs). The
proposed AMG method is based on the aggregation framework. The setup phase of
the algorithm uses a parallel maximal independent set algorithm in forming
aggregates and the resulting coarse level hierarchy is then used in a K-cycle
iteration solve phase with a -Jacobi smoother. Numerical tests of a
parallel implementation of the method for graphics processors are presented to
demonstrate its effectiveness.Comment: 18 pages, 3 figure
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