Evaluation of partial factorization for reduction of finite element matrices

• Autorzy: Jarzębski P. , Wiśniewski K.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

multi-scale models of multi-layer shells; parallel computing; domain decomposition; solvers; mixed finite elements; enhanced finite elements

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2017
• Tom: Vol. 65, iss. 1
• Strony: 163--170
• Opis fizyczny: Bibliogr. 11 poz., tab., wykr.

Twórcy

autor

Jarzębski P.

• Institute of Fundamental Technological Research Polish Academy of Sciences Pawińskiego 5B, 02-106 Warsaw, Poland

autor

Wiśniewski K.

• Institute of Fundamental Technological Research Polish Academy of Sciences Pawińskiego 5B, 02-106 Warsaw, Poland

Bibliografia

• 1. Petra C.G. et al., An augmented incomplete factorization approach for computing the Schur complement in stochastic optimization, SIAM J. Sci. Comput., 36(2): C139–C162, 2014.
• 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.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).