Abstract
In this work we present a parallel version of two preconditioners. The first one, is based on a partially decoupled block form of the ILU. We call it Block-ILU(fill,τ,overlap), because it permits the control of both, the block fill and the block overlap. The second one, is based on the SPAI (SParse Approximate Inverse) method. Both methods are analysed and compared to the ILU preconditioner using the Bi-CGSTAB to solve general sparse, nonsymmetric systems. Results have been obtained for different matrices. The preconditioners have been compared in terms of robustness, speedup and time of execution, to determine which is the best one in each situation. These solvers have been implemented for distributed memory multicomputers, making use of the MPI message passing standard library.
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References
Barrett, R., Berry, M., et al.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM, Philadelphia (1994)
Radicati di Brozolo, G., Robert, Y.: Parallel Conjugate Gradient-like algorithms for solving sparse nonsymmetric linear systems on a vector multiprocessor. Parallel Computing 11, 223–239 (1989)
Chapman, A., Saad, Y., Wigton, L.: High order ILU preconditioners for CFD problems. Technical report, Minnesota Supercomputer Institute. Univ. of Minnesota (1996)
d’Almeidaand, F.D., Vasconcelos, P.B.: Preconditioners for nonsymmetric linear systems in domain decomposition applied to a coupled discretisation of Navier-Stokes equations. In: Vector and Parallel Processing - VECPAR 1996, pp. 295–312. Springer, Heidelberg (1996)
Deshpande, V., Grote, M., Messmer, P., Sawyer, W.: Parallel implementation of a sparse approximate inverse preconditioner. In: Proceedings of Irregular 1996, pp. 63–74. Springer, Heidelberg (1996)
García-Loureiro, A.J., López-González, J.M., Pena, T.F., Prat, L.: Numericalanalysis of abrupt heterojunction bipolar transistors. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 8(11), 221–229 (1998)
García-Loureiro, A.J., Pena, T.F., López-González, J.M., Prat, L.: Preconditioners and nonstationary iterative methods for semiconductor device simulation. In: Conferencia de Dispositivos Electrónicos (CDE 1997), Universitat Politecnica de Catalunya, Barcelona, February 1997, pp. 403–409 (1997)
Grote, M.J., Huckle, T.: Parallel preconditioning with sparse approximate inverses. Siam J. Sci. Comput. 18(3), 838–853 (1997)
Horio, K., Yanai, H.: Numerical modeling of heterojunctions including the heterojunction interface. IEEE Trans. on ED 37(4), 1093–1098 (1990)
Lopez-Gonzalez, J.M., Prat, L.: Numerical modelling of abrupt InP/InGaAs HBTs. Solid-St. Electron 39(4), 523–527 (1996)
Pena, T.F., Bruguera, J.D., Zapata, E.L.: Finite element resolution of the 3D stationary semiconductor device equations on multiprocessors. J. Integrated Computer-Aided Engineering 4(1), 66–77 (1997)
Rafferty, C.S., Pinto, M.R., Dutton, R.W.: Iterative methods in semiconductors device simulation. IEEE trans on Computer-Aided Design 4(4), 462–471 (1985)
Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing Co. (1996)
Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7, 856–869 (1986)
Scharfetter, D.L., Gummel, H.K.: Large-signal analysis of a silicon read diode oscillator. IEEE Trans. on ED, 64–77 (1969)
Schwarz, H.R.: Numerical Analysis. John Wiley & Sons, Chichester (1989)
Scott, S.L.: Synchronization and communication in the T3E multiprocessor. Technical report, Inc. Cray Research (1996)
Van der Vorst, A.: Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 13, 631–644 (1992)
Wolfe, C.M., Holonyak, N., Stillman, G.E.: Physical Properties of Semiconductors, vol. 8. Prentice Hall, Englewood Cliffs (1989)
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García-Loureiro, A.J., Pena, T.F., López-González, J.M., Viñas, L.P. (1999). Parallel Preconditioners for Solving Nonsymmetric Linear Systems. In: Hernández, V., Palma, J.M.L.M., Dongarra, J.J. (eds) Vector and Parallel Processing – VECPAR’98. VECPAR 1998. Lecture Notes in Computer Science, vol 1573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703040_11
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DOI: https://doi.org/10.1007/10703040_11
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