On the design of interfaces to sparse direct solvers

Sala, Marzio; Stanley, K.; Heroux, Michael A.

doi:10.1145/1326548.1326551

Cited by 14 publications

(11 citation statements)

References 34 publications

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“…The multigrid smoothers S i for the single field problems are defined as an additive Schwartz domain decomposition using a damped Gauss-Seidel iteration (damping ω = 0.79) as sub-domain solver. The coarse level solver is the so-called KLU direct solver given in the Amesos package [61]. Figure 10 shows the average number of linear solver iterations per Newton step and the associated total CPU time (including the setup of the preconditioners) for the three preconditioners considered here and for the finest mesh in Table 4.…”

Section: Mesh Id Processors Structural Field Thermal Fieldmentioning

confidence: 99%

“…This smoother is referred to as DD(GS(ω)), where ω is the damping factor of the Gauss-Seidel iteration. The coarse level solver is the KLU direct solver given in the Amesos package [61]. Figure 18 shows the performance of the general purpose preconditioners BGS(AMG) and AMG(BGS) and their corresponding FSI-specific implementations proposed by Gee et al [8].…”

Section: Mesh Id Processorsmentioning

confidence: 99%

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Unified computational framework for the efficient solution of n-field coupled problems with monolithic schemes

Verdugo

Wall

2016

Computer Methods in Applied Mechanics and Engineering

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In this paper, we propose and evaluate the performance of a unified computational framework for preconditioning systems of linear equations resulting from the solution of coupled problems with monolithic schemes. The framework is composed by promising application-specific preconditioners presented previously in the literature with the common feature that they are able to be implemented for a generic coupled problem, involving an arbitrary number of fields, and to be used to solve a variety of applications. The first selected preconditioner is based on a generic block Gauss-Seidel iteration for uncoupling the fields, and standard algebraic multigrid (AMG) methods for solving the resulting uncoupled problems. The second preconditioner is based on the semi-implicit method for pressure-linked equations (SIMPLE) which is extended here to deal with an arbitrary number of fields, and also results in uncoupled problems that can be solved with standard AMG. Finally, a more sophisticated preconditioner is considered which enforces the coupling at all AMG levels, in contrast to the other two techniques which resolve the coupling only at the finest level. Our purpose is to show that these methods perform satisfactory in quite different scenarios apart from their original applications. To this end, we consider three very different coupled problems: thermo-structure interaction, fluid-structure interaction and a complex model of the human lung. Numerical results show that these general purpose methods are efficient and scalable in this range of applications.

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Section: Mesh Id Processors Structural Field Thermal Fieldmentioning

confidence: 99%

Section: Mesh Id Processorsmentioning

confidence: 99%

Unified computational framework for the efficient solution of n-field coupled problems with monolithic schemes

Verdugo

Wall

2016

Computer Methods in Applied Mechanics and Engineering

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“…Zoltan and Isorropia do not provide a sparse direct solver; rather, they should be used to compute a permutation vector before calling a direct solver. Isorropia provides the most convenient interfaces for Trilinos solvers such as Amesos (Ame-sos2) [54], while Zoltan may be simpler to use for other solvers.…”

Section: Fill-reducing Ordering Of Sparse Matricesmentioning

confidence: 99%

The Zoltan and Isorropia Parallel Toolkits for Combinatorial Scientific Computing: Partitioning, Ordering and Coloring

Boman

Çatalyürek

Chevalier

et al. 2012

Scientific Programming

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Partitioning and load balancing are important problems in scientific computing that can be modeled as combinatorial problems using graphs or hypergraphs. The Zoltan toolkit was developed primarily for partitioning and load balancing to support dynamic parallel applications, but has expanded to support other problems in combinatorial scientific computing, including matrix ordering and graph coloring. Zoltan is based on abstract user interfaces and uses callback functions. To simplify the use and integration of Zoltan with other matrix-based frameworks, such as the ones in Trilinos, we developed Isorropia as a Trilinos package, which supports most of Zoltan's features via a matrix-based interface. In addition to providing an easy-to-use matrix-based interface to Zoltan, Isorropia also serves as a platform for additional matrix algorithms. In this paper, we give an overview of the Zoltan and Isorropia toolkits, their design, capabilities and use. We also show how Zoltan and Isorropia enable large-scale, parallel scientific simulations, and describe current and future development in the next-generation package Zoltan2.

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“…Since the direct solver typically will run within a single UMA region, it does not need to be NUMA-aware. ShyLU uses the Amesos package [22] in Trilinos which is a common interface to multiple direct solvers. This enables ShyLU to switch between any direct solver supported by the Amesos package.…”

Section: B Diagonal Block Solvermentioning

confidence: 99%

ShyLU: A Hybrid-Hybrid Solver for Multicore Platforms

Rajamanickam

Boman

Heroux

2012

2012 IEEE 26th International Parallel and Distributed Processing Symposium

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Abstract-With the ubiquity of multicore processors, it is crucial that solvers adapt to the hierarchical structure of modern architectures. We present ShyLU, a "hybrid-hybrid" solver for general sparse linear systems that is hybrid in two ways: First, it combines direct and iterative methods. The iterative part is based on approximate Schur complements where we compute the approximate Schur complement using a value-based dropping strategy or structure-based probing strategy.Second, the solver uses two levels of parallelism via hybrid programming (MPI+threads). ShyLU is useful both in sharedmemory environments and on large parallel computers with distributed memory. In the latter case, it should be used as a subdomain solver. We argue that with the increasing complexity of compute nodes, it is important to exploit multiple levels of parallelism even within a single compute node.We show the robustness of ShyLU against other algebraic preconditioners. ShyLU scales well up to 384 cores for a given problem size. We also study the MPI-only performance of ShyLU against a hybrid implementation and conclude that on present multicore nodes MPI-only implementation is better. However, for future multicore machines (96 or more cores) hybrid/ hierarchical algorithms and implementations are important for sustained performance.

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On the design of interfaces to sparse direct solvers

Cited by 14 publications

References 34 publications

Unified computational framework for the efficient solution of n-field coupled problems with monolithic schemes

Unified computational framework for the efficient solution of n-field coupled problems with monolithic schemes

The Zoltan and Isorropia Parallel Toolkits for Combinatorial Scientific Computing: Partitioning, Ordering and Coloring

ShyLU: A Hybrid-Hybrid Solver for Multicore Platforms

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