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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 12
PROGRESS IN ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, C.A. Mota Soares
Chapter 14
A Parallel Environment and Associated Strategies in Structural NonLinear Analysis J.Y. Cognard*, A. Poulhalec*, F. Thomas+ and P. Verpeaux#
*Laboratoire de Mécanique des Structures Navales, ENSIETA, Brest, France J.Y. Cognard, A. Poulhalec, F. Thomas, P. Verpeaux, "A Parallel Environment and Associated Strategies in Structural NonLinear Analysis", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Progress in Engineering Computational Technology", SaxeCoburg Publications, Stirlingshire, UK, Chapter 14, pp 323352, 2004. doi:10.4203/csets.12.14
Keywords: nonlinear computations, parallel strategies, algorithms, large scale problems, load balancing.
Summary
The joint use of parallel computers and powerful algorithms is necessary to
strongly reduce the numerical costs of complex non linear Finite Element
simulations [1]. To reach this goal, we have created a parallel environment language
that eases the development of parallel algorithms either at the programming level or
at the user level. It is based on the development environment of the Finite Element
code CAST3M. On the other hand, we use a parallel approach that is well suited to
the simulation of a large class of nonlinear problems and which allows a good
balancing of the workload between the tasks without using dynamic loadbalancing.
This property is obtained by using two domain decompositions, each using the
mechanical properties of the different subproblems to be solved.
The developed parallel language, which is based on an objectbased virtual shared memory system, offers the user the vision of a unique and global address space over the individual memories [2]. It ensures the data coherence and hides data exchanges between processors and a great part of the sequential code can be reused. This system frees the programmer from parallel programming intricacies (management of data, coherence of data,...) and lets him focus on the program design, the most critical aspect for the application efficiency. The propounded system can be implemented on most parallel computers as it is developed with machineindependent programming techniques and it is important to notice that the different concepts can be used in other objectbased parallel languages. Moreover the objectbased shared virtual system allows two levels of parallelization: at the programming level and at the user level. Nonlinear problems are usually solved by means of NEWTON methods and lead mainly to compute two types of subproblems. The proposed parallel strategy uses the mechanical properties of these subproblems. On one hand, a domain decomposition technique with a direct resolution of the condensed problem is proposed to solve the linear global problems, in order to be compatible with the BFGS type convergence speedup. One can also use a parallel direct solver associated to a "nested dissection" ordering approach which limits the fillin effect in the factorization of the matrix [3]. In fact, this strategy is similar to a decomposition domain technique and gives good numerical results on shared memory computers. On the other hand, it is nearly impossible to predict the space evolution of the CPU time spent to integrate the constitutive laws. Therefore, in order to have a wellbalanced load, without communication, we propose the use of a second domain decomposition. An optimisation of the communications between the two domain decompositions is necessary to obtain good performances. The implementation of this strategy is carried out starting from the parallel user language of CAST3M. An extension of the previous strategy to solving problems associating frictional contact and material nonlinearities is also proposed in case the contact zones are small compared to the dimensions of the structure. To solve the global problem associated in the search of solutions verifying the kinematic conditions and equilibrium equation, which contains nonlinearities relations through contact conditions involving friction, we propose to use an iterative algorithm based on the LATIN method [4]. For this strategy the equations governing contact and friction are expressed as an explicit way, as the solution is sought at a given time. Furthermore, it is important to notice that the NEWTON type algorithm uses a constant stiffness. Therefore the problem can be condensed on the interface where contact is defined and the various nonlinearities are solved on their definition domains which have not the same dimensions. Numerical examples, in the case of large scale problems (nonlinear material behaviour, geometrical nonlinearities, frictional contact) are presented to validate the propounded parallel approach. References
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