Model Order Reduction of Large-Scale Finite Element Systems in an MPI Parallelized Environment for Usage in Multibody Simulation

Open access


The use of elastic bodies within a multibody simulation became more and more important within the last years. To include the elastic bodies, described as a finite element model in multibody simulations, the dimension of the system of ordinary differential equations must be reduced by projection. For this purpose, in this work, the modal reduction method, a component mode synthesis based method and a moment-matching method are used. Due to the always increasing size of the non-reduced systems, the calculation of the projection matrix leads to a large demand of computational resources and cannot be done on usual serial computers with available memory. In this paper, the model reduction software Morembs++ is presented using a parallelization concept based on the message passing interface to satisfy the need of memory and reduce the runtime of the model reduction process. Additionally, the behaviour of the Block-Krylov-Schur eigensolver, implemented in the Anasazi package of the Trilinos project, is analysed with regard to the choice of the size of the Krylov base, the block size and the number of blocks. Besides, an iterative solver is considered within the CMS-based method.

[1] A. Antoulas. Approximation of Large-Scale Dynamical Systems. SIAM, Philadelphia, 2005.

[2] W. Schiehlen and P. Eberhard. Applied Dynamics. Springer, Heidelberg, 1 edition, 2014.

[3] A.A. Shabana. Dynamics of Multibody Systems. Cambridge University Press, New York, 4 edition, 2013.

[4] P. Holzwarth, M. Baumann, T. Volzer, I. Iroz, P. Bestle, J. Fehr, and P. Eberhard. Software Morembs. University of Stuttgart, Institute of Engineering and Computational Mechanics, Stuttgart, Germany, 2016. Last accessed April, 24, 2016.

[5] M. Fischer and P. Eberhard. Simulation of moving loads in elastic multibody systems with parametric model reduction techniques. Archive of Mechanical Engineering, 61(2):209-226, 2014.

[6] M.A. Heroux, R.A. Bartless, V.E. Howle, R.J. Hoekstra, J.J. Hu, T.G. Kolda, R.B. Lehoucq, K.R. Long, R.P. Pawlowski, E.T. Phipps, A.G. Salinger, H.K. Thornquist, R.S. Tuminaro, J.M. Willenbring, A. Williams, and K.S. Stanley. An overview of the Trilinos Project. ACM Transactions on Mathematical Software, 31(3):397-423, 2005.

[7] Y. Zhou and Y. Saad. Block Krylov-Schur method for large symmetric eigenvalue problems. Numerical Algorithms, 47(4):341-359, 2008.

[8] P. Gosselet and C. Rey. Non-overlapping domain decomposition methods in structural mechanics. Archives of Computational Methods in Engineering, 13(4):515-572, 2006.

[9] A. Toselli and O.B. Widlund. Domain Decomposition Methods: Algorithms and Theory. Springer, Heidelberg, 2005.

[10] J. Mandel. Balancing domain decomposition. Communications in Numerical Methods in Engineering, 9(3):233-241, 1993.

[11] C. Farhat and F.-X. Roux. A method of finite element tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering, 32(6):1205-1227, 1991.

[12] A. Prokopenko, C.M. Siefert, J.J. Hu, M. Hoemmen, and A. Klinvex. Ifpack2 Users Guide 1.0. Technical Report SAND2016-5338, Sandia National Labs, 2016.

[13] PERMAS, User’s Reference Manual, PERMAS Version 11.00.445. INTES Publication No. 450. INTES GmbH, Stuttgart, 2006.

[14] M. Lehner and P. Eberhard. On the use of moment-matching to build reduced order models in flexible multibody dynamics. Multibody System Dynamics, 16(2):191-211, 2006.

[15] P. Holzwarth and P. Eberhard. SVD-based improvements for component mode synthesis in elastic multibody systems. European Journal of Mechanics - A/Solids, 49:408-418, 2015.

[16] Y. Saad. Numerical Methods for Large Eigenvalue Problems. SIAM, Philadelphia, 2 edition, 2011.

[17] R. Craig. Coupling of substructures for dynamic analyses: An overview. In Proceedings of the AIAA Dynamics Specialists Conference, Atlanta, April 5, 2000. Paper-ID 2000-1573.

[18] HDF Group: Hierarchical Data Format 5. Last accessed April, 24, 2016.

[19] MUMPS: A MUltifrontal Massively Parallel Sparse Direct Solver., 2016. Last accessed April 24, 2016.

[20] X.S. Li and J.W. Demmel. SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems. ACM Transactions on Mathematical Software, 29(2):110-140, 2003.

[21] O. Schenk and K. Gärtner. Solving unsymmetric sparse systems of linear equations with PARDISO. Future Generation Computer Systems, 20(3):475-487, 2004.

[22] G. Karypis and V. Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing, 20(1):359-392, 1998.

[23] Y. Saad. Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, 2 edition, 2003.

[24] J.J. Hu, A. Prokopenko, C.M. Siefert, R.S. Tuminaro, and T.A. Wiesner. MueLu Multigrid Framework., 2014. Last accessed June, 8, 2016.

[25] A. Prokopenko, J.J. Hu, T.A. Wiesner, C.M. Siefert, and R.S. Tuminaro. MueLu Users Guide 1.0. Technical Report SAND2014-18874, Sandia National Labs, 2014.

Archive of Mechanical Engineering

The Journal of Committee on Machine Building of Polish Academy of Sciences

Journal Information

CiteScore 2016: 0.44

SCImago Journal Rank (SJR) 2016: 0.162
Source Normalized Impact per Paper (SNIP) 2016: 0.459


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 120 120 11
PDF Downloads 40 40 5