MPI-based implementation of a PCG solver using an EBE architecture and preconditioner for implicit, 3-D finite element analysis

Gullerud, Arne S.; Dodds, Robert H.

doi:10.1016/s0045-7949(00)00153-x

Cited by 37 publications

(26 citation statements)

References 39 publications

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“…Once each processor has the updated version of the diagonal terms for all of its nodes, the preconditioning calculation can be performed independently on each domain. For other types of preconditioners, such as element-by-element [23] or incomplete Choleski factorizations [24], the parallel implementation would be more involved; see Reference [25] for an example.…”

Section: Preconditioner Computationmentioning

confidence: 99%

A distributed memory parallel implementation of the multigrid method for solving three‐dimensional implicit solid mechanics problems

Namazifard

Parsons

2004

Numerical Meth Engineering

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SUMMARYWe describe the parallel implementation of a multigrid method for unstructured finite element discretizations of solid mechanics problems. We focus on a distributed memory programming model and use the MPI library to perform the required interprocessor communications. We present an algebraic framework for our parallel computations, and describe an object-based programming methodology using Fortran90. The performance of the implementation is measured by solving both fixed-and scaled-size problems on three different parallel computers (an SGI Origin2000, an IBM SP2 and a Cray T3E). The code performs well in terms of speedup, parallel efficiency and scalability. However, the floating point performance is considerably below the peak values attributed to these machines. Lazy processors are documented on the Origin that produce reduced performance statistics. The solution of two problems on an SGI Origin2000, an IBM PowerPC SMP and a Linux cluster demonstrate that the algorithm performs well when applied to the unstructured meshes required for practical engineering analysis.

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Section: Preconditioner Computationmentioning

confidence: 99%

A distributed memory parallel implementation of the multigrid method for solving three‐dimensional implicit solid mechanics problems

Namazifard

Parsons

2004

Numerical Meth Engineering

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“…It is worth noting here that MPI based parallel finite element approaches [17,18] have also been developed for implicit nonlinear dynamic analysis utilising linear preconditioned conjugate gradient (PCG) solvers for the iterative analysis as opposed to the frontal solver, conventionally considered to be direct solution method [19]. The use of PCG solvers requires significant modification of existing finite element programs as most of these utilise direct solvers based on Gaussian elimination.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, unlike the previous approaches [17,81], neighbouring partitions in the present approach do not exchange boundary displacement/force entities directly; instead information flow is controlled by the parent coordinator, which is responsible for ensuring compatibility and equilibrium at the partition boundaries. A clear and natural extension of the proposed approach is hierarchic multi-level partitioning, which cannot be accommodated by previous approaches [17,18], and which maps readily to hierarchic HPC architecture with ensuing reduction in inter-processor communication overheads.…”

Section: Introductionmentioning

confidence: 99%

A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

Jokhio

Izzuddin

2015

International Journal for Computational Methods in Engineering

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This paper presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realised by replacing one or more subdomains in a 'parent system' each with a placeholder super-element, where the subdomains are processed separately as 'child partitions' each wrapped by a dual super-element along the partition boundary. The analysis of the overall system including the satisfaction of equilibrium and compatibility at all partition boundaries is realised through direct communication between all pairs of placeholder and dual superelements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelisation on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of largescale problems. Several examples are presented in this paper, which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.

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“…Also, a large number of EBE based preconditioners is available in literature. We may cite the works of Bova and Carey [12] and Gullerud and Dodds [13] as examples of MPI-based SBS implementations using EBE schemes. Okuda et al [25] presents an EBE scheme for massively parallel computers.…”

Section: Introductionmentioning

confidence: 99%

Parallel implementation of the finite element method using compressed data structures

Ribeiro

Ferreira

2007

Comput Mech

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This paper presents a parallel implementation of the finite element method designed for coarsegrain distributed memory architectures. The MPI standard is used for message passing and tests are run on a PC cluster and on an SGI Altix 350. Compressed data structures are employed to store the coefficient matrix and obtain iterative solutions, based on Krylov methods, in a subdomain-by-subdomain approach. Two mesh partitioning schemes are compared: non-overlapping and overlapping. The pros and cons of these partitioning methods are discussed. Numerical examples of symmetric and non-symmetric problems in two and three dimensions are presented.

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MPI-based implementation of a PCG solver using an EBE architecture and preconditioner for implicit, 3-D finite element analysis

Cited by 37 publications

References 39 publications

A distributed memory parallel implementation of the multigrid method for solving three‐dimensional implicit solid mechanics problems

A distributed memory parallel implementation of the multigrid method for solving three‐dimensional implicit solid mechanics problems

A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

Parallel implementation of the finite element method using compressed data structures

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