Implementation of an element-by-element solution algorithm for the finite element method on a coarse-grained parallel computer

King, R. S.; Sonnad, V.

doi:10.1016/0045-7825(87)90182-4

Cited by 36 publications

(8 citation statements)

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“…Hence, the computational costs and memory space associated with zero fill-ins can be greatly reduced by using a suitable storage scheme. Some researcher have successfully brought some new algorithms into the practical use, such as King et al [16], Hughes et al [17], Law [18], Farhat et al [19]. Thus, this paper will also focus on the establishment of algorithm which can be used to implement parallel computing on the solution of the linear system of equations.…”

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confidence: 99%

Efficient parallel algorithms for elastic–plastic finite element analysis

et al. 2007

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This paper presents our new development of parallel finite element algorithms for elastic-plastic problems. The proposed method is based on dividing the original structure under consideration into a number of substructures which are treated as isolated finite element models via the interface conditions. Throughout the analysis, each processor stores only the information relevant to its substructure and generates the local stiffness matrix. A parallel substructure oriented preconditioned conjugate gradient method, which is combined with MR smoothing and diagonal storage scheme are employed to solve linear systems of equations. After having obtained the displacements of the problem under consideration, a substepping scheme is used to integrate elastic-plastic stress-strain relations. The procedure outlined controls the error of the computed stress by choosing each substep size automatically according to a prescribed tolerance. The combination of these algorithms shows a good speedup when increasing the number of processors and the effective solution of 3D elastic-plastic problems whose size is much too large for a single workstation becomes possible.

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confidence: 99%

Efficient parallel algorithms for elastic–plastic finite element analysis

et al. 2007

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“…This procedure is repeated until the end, concentrating the maximum possible amount of operations in each processor and using the shared memory to synchronize informations between neighbor regions or, in some cases, globally. (KING & SONNAD, 1987) found an ingenius solution with the limited computational tools available that time to generate an element-based domain decomposition in order to apply the EBE procedure. This allowed them to obtain very high speedup values in numerical experiments, as shown in Fig.…”

Section: Parallelization Of the Ebe Methodsmentioning

confidence: 99%

“…The following works have employed the PCG algorithm on the development of the EBE method:(WINGET & HUGHES, 1985),(CAREY & JIANG, 1986),(HUGHES & FERENCZ, 1987),(LEVIT, 1987),(KING & SONNAD, 1987), (HUGHES & FERENCZ, 1988), (ADELI & KUMAR, 1995), (GULLERUD & DODDS JR, 2001), (THIAGARAJAN & ARAVAMUTHAN, 2002), (LIU, ZHOU, & YANG, 2007), (MARTÍNEZ-FRUTOS & HERRERO-PÉREZ, 2015) and (MARTÍNEZ-FRUTOS, MARTÍNEZ-CASTEJÓN, & HERRERO-PÉREZ, 2015).…”

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confidence: 99%

“…Their implementation was tested on several computers of that time and compared it with a direct solution method, obtaining great results regarding the processing time and memory consumption. However, despite discussing the necessity of synchronization, they have not presented or discussed the aspects involving the parallelism of the solution (KING & SONNAD, 1987). introduced a parallel implementation of the Crout EBE preconditioned conjugate gradient method.…”

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confidence: 99%

“…The architecture of the computer used to run the code consisted of an array of loose processors, each one with a large memory (to the stardards of that time) and all of them connected to a shared memory via communication bus. Despite the outdate hardware, the synchronization logics and challenges resulting from this architecture are similar to those found with MPI programming (KING & SONNAD, 1987). subdivided the element mesh into regions (where is the number of available processors), each of which was handled by a separate processor, as shown inFig.…”

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Parallelized element-by-element architecture for structural analysis of flexible pipes using finite macroelements.

Toni¹

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Flexible pipes are used in the offshore oil production to transport fluid and gas from the sea bead to the floating stations, and vice versa. These pipes have several concentric layers, of different materials, geometries and structural functions, since they are exposed to adverse operating environments, subjected to high internal and external pressures, high axial stresses and a series of dynamic loads. The local analysis is an important stage of a flexible pipe design and it consists on determining the stresses and strains distributions along the layers of the pipe. Multipurpose finite element packages are commonly used in the local analysis of flexible pipes, but they possess many limitations due to its generic nature, varying from the absence of specific tools for model creation to heavy restrictions of the number of degrees-of-freedom to make computational processing feasible. At the Polytechnic School of the University of São Paulo, within a research line in progress, several finite macroelements were formulated specifically for structural analysis of flexible pipes, taking into account their particularities, such as geometric patterns and layers assemblage. However, the numerical tools that implement these elements present very high memory and processing consumptions, limiting its usage for large-scale models. Therefore, this work has been motivated by memory and processing limitations of finite element structural analysis of flexible pipes for offshore applications. In this context, the Element-by-Element method, which does not require the global stiffness matrix, was chosen for its potential in memory reduction and processing capabilities, given its scalability and ease of parallelization. After an extensive literature review on numerical methods regarding the EBE method, it was chosen the Element-by-Element Diagonal Preconditioned Conjugate Gradient Method (EBE-PCG) algorithm. Aiming higher computational performance, the finite macroelements formulated by (PROVASI, 2013) were converted to the C++ language, implemented and parallelized in a new analysis tool, named as PipeFEM. The diagonal preconditioned EBE-PCG algorithm was implemented and parallelized with OpenMP. The scalability of the PCG algorithm is directly influenced by the efficiency of the matrix-vector product, an operation that, in the element-by-element method, is computed in a local basis with the blocks that comprise the model, and that requires synchronization techniques when performed in parallel. Four different synchronization strategies were developed, being the one based on geometric-and meshbased mappings the most efficient of them. Numerical experiments showed a reduction of almost 92% in the EBE-PCG solution time of the parallelized version in comparison to the sequential one. In order to compare the efficiency of PipeFEM with the well-established finite element package ANSYS, a simplified flexible pipe was modeled in both software. PipeFEM was approximately 82 times faster than ANSYS to solve the problem, spending 24.27 seconds ag...

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Application of the EBE (Element-By-Element) Preconditioned Conjugate Gradient Algorithm to the Fluid (Acoustic)/Structure Problem

Chapman¹,

Cox²

2011

Solution of Superlarge Problems in Computational Mechanics

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Implementation of an element-by-element solution algorithm for the finite element method on a coarse-grained parallel computer

Cited by 36 publications

References 5 publications

Efficient parallel algorithms for elastic–plastic finite element analysis

Efficient parallel algorithms for elastic–plastic finite element analysis

Parallelized element-by-element architecture for structural analysis of flexible pipes using finite macroelements.

Application of the EBE (Element-By-Element) Preconditioned Conjugate Gradient Algorithm to the Fluid (Acoustic)/Structure Problem

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