A Block Fourier Decomposition Method
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
Separation-of-variables as a preconditioner for an iterative Helmholtz solver
Applied Numerical Mathematics
Efficient metacomputing of elliptic linear and non-linear problems
Journal of Parallel and Distributed Computing - Special issue on computational grids
Numerical solution of the nonlinear Helmholtz equation using nonorthogonal expansions
Journal of Computational Physics
Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations
Journal of Computational Physics
A fast iterative solver for scattering by elastic objects in layered media
Applied Numerical Mathematics
Superlinearly convergent PCG algorithms for some nonsymmetric elliptic systems
Journal of Computational and Applied Mathematics
Simulation of laser propagation in a plasma with a frequency wave equation
Journal of Computational Physics
A mesh independent superlinear algorithm for some nonlinear nonsymmetric elliptic systems
Computers & Mathematics with Applications
A domain decomposition solver for acoustic scattering by elastic objects in layered media
Journal of Computational Physics
Preconditioning operators and Sobolevgradients for nonlinear elliptic problems
Computers & Mathematics with Applications
Sobolev gradient preconditioning for the electrostatic potential equation
Computers & Mathematics with Applications
Simulation of laser propagation in a plasma with a frequency wave equation
VECPAR'06 Proceedings of the 7th international conference on High performance computing for computational science
Matrix decomposition algorithms for elliptic boundary value problems: a survey
Numerical Algorithms
Fast poisson solvers for graphics processing units
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
Hi-index | 0.02 |
A parallel fast direct solution method for linear systems with separable block tridiagonal matrices is considered. Such systems appear, for example, when discretizing the Poisson equation in a rectangular domain using the five-point finite difference scheme or the piecewise linear finite elements on a triangulated, possibly nonuniform rectangular mesh. The method under consideration has the arithmetical complexity ${\mathcal O}(N\log N)$, and it is closely related to the cyclic reduction method, but instead of using the matrix polynomial factorization, the so-called partial solution technique is employed. Hence, in this paper, the method is called the partial solution variant of the cyclic reduction method (PSCR method). The method is presented and analyzed in a general radix-q framework and, based on this analysis, the radix-4 variant is chosen for parallel implementation using the MPI standard. The generalization of the method to the case of arbitrary block dimension is described. The numerical experiments show the sequential efficiency and numerical stability of the PSCR method compared to the well-known BLKTRI implementation of the generalized cyclic reduction method. The good scalability properties of the parallel PSCR method are demonstrated in a distributed-memory Cray T3E-750 computer.