Alternating Direction Methods on Multiprocessors
Copyright policy )Alternating Direction Methods on Multiprocessors
We propose several implementations of the alternating direction method (ADM) for solving parabolic partial differential equations on multiprocessors. A complexity analysis of these implementations shows that the method can be made highly efficient on parallel architectures by using pipelining and variations of the classical Gaussian elimination algorithm for solving tridiagonal systems. Previously, we showed that we could obtain linear speedups for moderate numbers of processors in a ring architecture. In this paper we discuss extensions to a large number of processors in a 2-D grid architecture and a hypercube.
- Yale University United States
- University of Illinois at Urbana Champaign United States
- University of Illinois at Urbana–Champaign United States
ensemble architectures, Analysis of algorithms and problem complexity, multiprocessors, Parallel numerical computation, concurrent computation, Numerical solution of discretized equations for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, alternating direction method, hypercube, Initial-boundary value problems for second-order parabolic equations, Gaussian elimination, complexity
ensemble architectures, Analysis of algorithms and problem complexity, multiprocessors, Parallel numerical computation, concurrent computation, Numerical solution of discretized equations for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, alternating direction method, hypercube, Initial-boundary value problems for second-order parabolic equations, Gaussian elimination, complexity
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