Abstract
An optimized version of a frontal solver for the finite element simulation of non-linear coupled multiphysic problems arising in the simulation of concrete under fire is presented. A new algorithm for UL factorization using BLAS level 3 routines is developed, and then used to implement a pivoting strategy that has shown to be well suited for the linear systems involved. Our implementation also features efficient algorithms to swap rows and columns of the matrix of the system. The resulting code shows to be effective for this kind of complex problems, being able to exhibit 850MFlops performance on a 375MHz IBM Power3 machine, with computational errors comparable with the round-off unit of double precision floating point numbers.
This work was supported, in part, by MURST of Italy within the framework of the Center for Science and Application of Advanced Computation Paradigms of the University of Padova and CISM of Udine, Italy.
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References
M. Bianco, G. Bilardi, F. Pesavento, G. Pucci, and B.A. Schrefler. An accurate and efficient solver for fully-coupled hygro-thermo-mechanical problems. Proc. of the 2002 International Conference on Computational Science ICCS-2002. To appear.
M. Bianco, G. Bilardi, F. Pesavento, G. Pucci, and B.A. Schrefler. A frontal solver tuned for fully-coupled non-linear hygro-thermo-mechanical problems. Int. J. Num. Meth. Engng. Submitted for publication.
I. S. Duff, A. M. Erisman and J. K. Reid. Direct methods for sparse matrices, Clarendon Press, 1986.
James W. Demmel and Stanley C. Eisenstat and John R. Gilbert and Xiaoye S. Li and Joseph W. H. Liu A supernodal approach to sparse partial pivoting. Technical Report CSD-95-883, Computer Science Division University of California, Berkeley, 1995.
I. S. Duff and L. K. Reid. The Multifrontal Solution of Indefinite Sparse Symmetric Linear Equations. ACM Transaction on Mathematical Software, (9)3, 302–325, September 1983.
I. S. Duff and J. A. Scott. The design of a new frontal code for solving sparse, unsymmetric systems ACM Transactions on Mathematical Software (TOMS) (22)1, 30–45, March 1996).
D. Gawin, C. E. Majorana, F. Pesavento and B. A. Schrefler. A fully coupled multiphase FE model of hygro-thermo-mechanical behaviour of concrete at high temperature. In Computational Mechanics., Onate, E. & Idelsohn, S.R. (eds.), New Trends and Applications:, Proc. of the 4th World Congress on Computational Mechanics, Buenos Aires 1998; 1–19. Barcelona: CIMNE, 1998.
D. Gawin, F. Pesavento and B. A. Schrefler. Modelling of hygro-thermal behaviour and damage of concrete at temperature above the critical point of water. Submitted for publication.
D. Gawin, C. E. Majorana and B. A. Schrefler. Numerical analysis of hygrothermic behaviour and damage of concrete at high temperature. In Mech. Cohes.-Frict. Mater. 1999; 4:37–74.
B. M. Irons. A frontal solution program for finite element analysis Int. J. Numer. Meth. Engng, 1970; 2:5–32.
Oettli W, Prager W. “Compatibility of Approximate Solution of Linear Equations with Given Error Bounds for Coefficients and Right-Hand Sides”, Numerische Mathematik, 1964; 6:405–409.
Tinney WF, Walker JW. Direct solutions of sparse network equations by optimally ordered triangular factorization, Proc. IEEE 55, 1967; 1801–1809
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Bianco, M. (2003). A High-Performance UL Factorization for the Frontal Method. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44839-X_94
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DOI: https://doi.org/10.1007/3-540-44839-X_94
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