4,245 research outputs found
A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements
A parallel fast direct solver for rank-compressible block tridiagonal linear
systems is presented. Algorithmic synergies between Cyclic Reduction and
Hierarchical matrix arithmetic operations result in a solver with arithmetic complexity and memory footprint. We provide a
baseline for performance and applicability by comparing with well known
implementations of the -LU factorization and algebraic multigrid
with a parallel implementation that leverages the concurrency features of the
method. Numerical experiments reveal that this method is comparable with other
fast direct solvers based on Hierarchical Matrices such as -LU and
that it can tackle problems where algebraic multigrid fails to converge
h-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems
In this work we exploit agglomeration based -multigrid preconditioners to
speed-up the iterative solution of discontinuous Galerkin discretizations of
the Stokes and Navier-Stokes equations. As a distinctive feature -coarsened
mesh sequences are generated by recursive agglomeration of a fine grid,
admitting arbitrarily unstructured grids of complex domains, and agglomeration
based discontinuous Galerkin discretizations are employed to deal with
agglomerated elements of coarse levels. Both the expense of building coarse
grid operators and the performance of the resulting multigrid iteration are
investigated. For the sake of efficiency coarse grid operators are inherited
through element-by-element projections, avoiding the cost of numerical
integration over agglomerated elements. Specific care is devoted to the
projection of viscous terms discretized by means of the BR2 dG method. We
demonstrate that enforcing the correct amount of stabilization on coarse grids
levels is mandatory for achieving uniform convergence with respect to the
number of levels. The numerical solution of steady and unsteady, linear and
non-linear problems is considered tackling challenging 2D test cases and 3D
real life computations on parallel architectures. Significant execution time
gains are documented.Comment: 78 pages, 7 figure
A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes
We describe a finite-volume method for solving the Poisson equation on
oct-tree adaptive meshes using direct solvers for individual mesh blocks. The
method is a modified version of the method presented by Huang and Greengard
(2000), which works with finite-difference meshes and does not allow for shared
boundaries between refined patches. Our algorithm is implemented within the
FLASH code framework and makes use of the PARAMESH library, permitting
efficient use of parallel computers. We describe the algorithm and present test
results that demonstrate its accuracy.Comment: 10 pages, 6 figures, accepted by the Astrophysical Journal; minor
revisions in response to referee's comments; added char
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