Parallel implementation of multifrontal schemes☆
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Cited by (84)
Cached Gaussian elimination for simulating Stokes flow on domains with repetitive geometry
2020, Journal of Computational PhysicsCitation Excerpt :These methods were replaced with multifrontal methods, which are based on the observation that elimination dependencies take the form of an elimination tree, and a new independent elimination front can be started from each leaf of the tree [24]. Since these fronts are independent, they may be eliminated in parallel [25–28]. A process of amalgamation (also called supernodes) is used to eliminate multiple rows with similar sparsity patterns at the same time to exploit more efficient level-3 BLAS operations [24,29,30].
Optimized sparse Cholesky factorization on hybrid multicore architectures
2018, Journal of Computational ScienceCitation Excerpt :The structure of the elimination tree holds information about data dependencies between supernodes. The underlying tree structure [9] can help us determine which supernodes may be factorized concurrently. In our algorithm, we use multithreading (using OpenMP on the CPU) to leverage the task parallelism in the underlying tree structure.
A Multithreaded Algorithm for Sparse Cholesky Factorization on Hybrid Multicore Architectures
2017, Procedia Computer ScienceParallel and fully recursive multifrontal sparse Cholesky
2004, Future Generation Computer SystemsThe impact of high-performance computing in the solution of linear systems: Trends and problems
2000, Journal of Computational and Applied MathematicsCitation Excerpt :An important aspect of these approaches is that the parallelism is obtained directly because of the sparsity in the system. In general, we exhibit this form of parallelism through the assembly tree of Section 4 where operations at nodes which are not on the same (unique) path to the root (that is none is a descendant of another) are independent and can be executed in parallel (see, for example, [37,70]). The set of pivots discussed above could correspond to leaf nodes of such a tree.
Multifrontal parallel distributed symmetric and unsymmetric solvers
2000, Computer Methods in Applied Mechanics and Engineering
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Work supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38 when the author was visiting MCS division. Argonne National Laboratory, IL 60439, U.S.A. United Kingdom Atomic Energy Authority.