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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 90

An Explicit Parallel Procedure for Non-linear Structural Mechanics with Distributed Computing

M.L. Romero+, J.I. Aliaga*, J.L. Bonet$, M.A. Fernandez$ and P.F. Miguel$

+Department of Technology, *Computing Department, University Jaume I, Castellon, Spain
$Civil Engineering Department, Polytechnic University, Valencia, Spain

Full Bibliographic Reference for this paper
M.L. Romero, J.I. Aliaga, J.L. Bonet, M.A. Fernandez, P.F. Miguel, "An Explicit Parallel Procedure for Non-linear Structural Mechanics with Distributed Computing", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 90, 2001. doi:10.4203/ccp.73.90
Keywords: high performance computing, parallel algorithms, non-linear, reinforced concrete, cluster of personal computers, distributed memory.

Summary
In previous researches, the authors have been working in the parallelisation of a complex three dimensional software for nonlinear structural analysis [1]. The investigation was focussed in the improvement of the algorithmic parallelism and not in the domain decomposition, Topping [2]. The nonlinear finite element model adopted a fibber decomposition approach for the cross-section of beam elements to capture nonlinear behaviour of concrete. Since the complex analysis of reinforced concrete structures involves nonlinear equations, the numerical solution is extremely demanding of machine resources. An analysis of the local functions runtime was performed. It was demonstrated that the computation of stiffness, the assembly of equations and the computations of the force have bigger runtime in the process. These functions are relationed with the function that is the responsible of the fibber creation and latter characterisation of the sections integration points.

But in the case of nonlinear finite element analysis, the relative expensiveness of each operation depends on the type of nonlinearity, and the solution method chosen. The disagreement in percentage of the computation that the authors present in the literature for different nonlinear problems addresses to not have a "general rule", becoming important to check for each particular problem of nonlinearity which is the time that the internal procedures are consuming.

This paper presents a scalable and efficient parallelisation strategy for the explicit solution techniques and offers the portable functionality for cluster of personal computers. In the study of high-rise frame-works and 3D buildings, the automatic partitioning can be simplified decomposing the structure in equal subdomains, neglecting the important issue of load balancing strategies.

A cluster of personal computers provides a cost-effective environment for high performance computing and the productivity of an engineering consulting firm can be improved at no additional cost, Adeli [3]. The results of this work focus the application of the finite element method on clusters of personal computers with Windows2000, because the practical application for engineering purposes is an issue of the research.

The implementation is based on the important work made by the Cornell Theory Center, CTC [4] in the AC3 high performance cluster project and the spin-off MPI- PRO Softtech company [5]. In this paper an explicit parallel algorithm for the complete analysis of 3D high-rise frameworks on distributed-memory cluster of personal computers has been presented. The algorithm has been implemented in the programming language Visual C++ for Windows2000, using MPI-Pro, Intel Kernel, and Lapack-Blas libraries. It has been applied to a very symmetric configuration of a 3D building with different number of floors.

The algorithm is based in the parallelisation of the arc-length method using the Schur complement. The domain is divided in N-1 equal and balanced subdomains, and a master node of the cluster computes the boundary degrees of freedom. The stiffness matrix, the resolution of partial displacements, and the calculation of internal equilibrium forces is obtained in a concurrent form. The number of communications between the nodes are reduced at maximum and are pivoting through the master node.

The overall speed-up and efficiency obtained are really high for a 100 Mb Ethernet cluster of personal computers. Moreover, it should be increased reducing the time consumed in the communications with a VIA or Mirinet cluster. There is still a bottleneck in the resolution of partial displacements for the inner nodes.

The automatic configuration of the cluster and the management of the communications using the a Cluster controller program developed by the Cornell theory Center and the MPI-Sofftech company will extend in the future the use of parallel computing in all the engineering companies, because a cluster of personal computers provides a cost-effective environment for high performance computing and the productivity of an engineering consulting firm can be improved at no additional cost.

References
1
M.L. Romero, J.J. Cano, P.F. Miguel, "Development of geometrical and material nonlinear analysis software for civil engineering structures with cluster of personal computers", Advances in Finite Element Technologies, Civil Comp Press, Edinburgh, 1999.
2
Topping, B.H.V. "Parallel and Distributed Processing for Computational Mechanics: Systems and Tools". Saxe-Coburg Publications, Edinburgh, 1999. doi:10.4203/csets.2
3
Adeli, H. "High Performance Computing for Large Scale Analysis, Optimization and Control", J. Aerosp. Engrg., ASCE, vol 13, no 1, pag 1-10. 2000. doi:10.1061/(ASCE)0893-1321(2000)13:1(1)
4
High Performance Clusters, http://www.tc.cornell.edu/AC3/, 2001.
5
MPI, http://www.mpi-softtech.com/, 2001.

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