Sparse matrix factorization on massively parallel computers

Gupta, Anshul; Korić, Seid; George, Thomas

doi:10.1145/1654059.1654061

Cited by 22 publications

(16 citation statements)

References 26 publications

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“…This only needs to be done once, as long as the kinematic graph of the simulated system does not change. For parallel computation, a Nested Dissection ordering is more adequate, but gives similar results with respect to the amount of fill-in [GKG09].…”

Section: Fill-in Of the Cholesky Factorizationmentioning

confidence: 96%

Efficient enforcement of hard articulation constraints in the presence of closed loops and contacts

Tomcin

Sibbing

Kobbelt

2014

Computer Graphics Forum

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In rigid body simulation, one must distinguish between contacts (so-called unilateral constraints) and articulations (bilateral constraints). For contacts and friction, iterative solution methods have proven most useful for interactive applications, often in combination with Shock-Propagation in cases with strong interactions between contacts (such as stacks), prioritizing performance and plausibility over accuracy. For articulation constraints, direct solution methods are preferred, because one can rely on a factorization with linear time complexity for tree-like systems, even in ill-conditioned cases caused by large mass-ratios or high complexity. Despite recent advances, combining the advantages of direct and iterative solution methods wrt. performance has proven difficult and the intricacy of articulations in interactive applications is often limited by the convergence speed of the iterative solution method in the presence of closed kinematic loops (i.e. auxiliary constraints) and contacts. We identify common performance bottlenecks in the dynamic simulation of unilateral and bilateral constraints and are able to present a simulation method, that scales well in the number of constraints even in ill-conditioned cases with frictional contacts, collisions and closed loops in the kinematic graph. For cases where many joints are connected to a single body, we propose a technique to increase the sparsity of the positive definite linear system. A solution to these bottlenecks is presented in this paper to make the simulation of a wider range of mechanisms possible in real-time without extensive parameter tuning.

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Section: Fill-in Of the Cholesky Factorizationmentioning

confidence: 96%

Efficient enforcement of hard articulation constraints in the presence of closed loops and contacts

Tomcin

Sibbing

Kobbelt

2014

Computer Graphics Forum

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“…Task graphs have been used for parallelization in dense linear algebra [38,39], sparse linear algebra [17], and linear transforms [40]. The KDG is a generalization of classic task graphs because it can handle the creation of new tasks and changes in dependences during execution.…”

Section: Related Workmentioning

confidence: 99%

Kinetic Dependence Graphs

Hassaan

Nguyen

Pingali

2015

SIGARCH Comput. Archit. News

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Task graphs or dependence graphs are used in runtime systems to schedule tasks for parallel execution. In problem domains such as dense linear algebra and signal processing, dependence graphs can be generated from a program by static analysis. However, in emerging problem domains such as graph analytics, the set of tasks and dependences between tasks in a program are complex functions of runtime values and cannot be determined statically. In this paper, we introduce a novel approach for exploiting parallelism in such programs. This approach is based on a data structure called the kinetic dependence graph (KDG), which consists of a dependence graph together with update rules that incrementally update the graph to reflect changes in the dependence structure whenever a task is completed.We have implemented a simple programming model that allows programmers to write these applications at a high level of abstraction, and a runtime within the Galois system [15] that builds the KDG automatically and executes the program in parallel. On a suite of programs that are difficult to parallelize otherwise, we have obtained speedups of up to 33 on 40 cores, out-performing third-party implementations in many cases.

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“…These are either multifrontal [16] and supernodal techniques [34]. Multifrontal techniques are basically the multifrontal massively parallel solver (MUMPS) [28] and the Watson Sparse Matrix package (WSMP) [40]. SuperLUDIST [58] is a MPI parallel version of SuperLU family of solvers for unsymmetric systems based on supernodal right LU factorization.…”

Section: Algebraic Solversmentioning

confidence: 99%

“…[16], which is supported by MPI. The WSMP software package WSMP [40] is also developed using an hybrid implementation with MPI and Pthreads, among others. Abstracting the solver interface in this manner allows the application writer to choose the most effective solver for the particular problem.…”

Section: Librariesmentioning

confidence: 99%

Alya: Computational Solid Mechanics for Supercomputers

Casoni

Jérusalem

Samaniego

et al. 2014

Arch Computat Methods Eng

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While solid mechanics codes are now conventional tools both in industry and research, the increasingly more exigent requirements of both sectors are fuelling the need for more computational power and more advanced algorithms. For obvious reasons, commercial codes are lagging behind academic codes often dedicated either to the implementation of one new technique, or the upscaling of current conventional codes to tackle massively large scale computational problems. Only in a few cases, both approaches have been followed simultaneously. In this article, a solid mechanics simulation strategy for parallel supercomputers based on a hybrid approach is presented. Hybrid parallelization exploits the thread-level parallelism of multicore architectures, com- bining MPI tasks with OpenMP threads. This paper describes the proposed strategy, programmed in Alya, a parallel multiphysics code. Hybrid parallelization is specially well suited for the current trend of supercomputers, namely large clusters of multicores. The strategy is assessed through transient non-linear solid mechanics problems, both for explicit and implicit schemes, running on thousands of cores. In order to demonstrate the flexibility of the proposed strategy under advance algorithmic evolution of computational mechanics, a non-local parallel overset meshes method (Chimera-like) is implemented and the conservation of the scalability is demonstrated.

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Sparse matrix factorization on massively parallel computers

Cited by 22 publications

References 26 publications

Efficient enforcement of hard articulation constraints in the presence of closed loops and contacts

Efficient enforcement of hard articulation constraints in the presence of closed loops and contacts

Kinetic Dependence Graphs

Alya: Computational Solid Mechanics for Supercomputers

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