Abstract
In this paper, we present the concept of Partial Factorization [1] And discuss its possible applications to the Finite Element method. We consider: (1) reduction of the element tangent matrix, which is particularly important for mixed/enhanced elements and (2) reduction of the sub-domain matrices of the Domain Decomposition (DD) equation solvers run either sequentially on a single machine or in parallel on a cluster of computers. We demonstrate that Partial Factorization can be beneficial for these applications.Keywords:
multi-scale models of multi-layer shells, mixed/enhanced finite elements, parallel computing, Domain Decomposition, solversReferences
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2. Jarzębski P., Wiśniewski K., Taylor R.L., On paralelization of the loop over elements in FEAP, Computational Mechanics, 56(1): 77–86, 2015.
3. Jarzębski P., Wiśniewski K., Performance of the parallel FEAP in calculations of effective material properties using RVE, [in:] Advances in Mechanics, Kleiber M. et al. [Eds.], Taylor & Francis, London, pp. 241–244, 2016.
4. Jarzębski P., Wiśniewski K., Application of partial factorization for domain decomposition solver, In preparation, 2016.
5. MacNeal R.H., Harder R.L., A proposed standard set of problems to test finite element accuracy, Finite Element in Analysis and Design, 1: 3–20, 1985.
6. Press W.H. et al., Numerical Recipes in Fortran 77, Cambridge Univeristy Press, 1999.
7. Anderson E. et al., LAPACK Users’ Guide, SIAM, Philadelphia, 1999.
8. HSL 2013, A collection of Fortran codes for large scale scientific computation, http://www.hsl.rl.ac.uk/.
9. Wiśniewski K., Finite Rotation Shells. Basic Equations and Finite Elements for Reissner Kinematics, Springer, 2010.
10. Wiśniewski K., Turska E., Four-node mixed Hu-Washizu shell element with drilling rotation, Int. J. Num. Meth. Engng., 90(4): 506–536, 2012.
11. Gupta A., WSMP: Watson Sparse Matrix Package, IBM Research Report,Watson, 2015.
