Parallel processing in computational stochastic dynamics

Probabilistic Engineering Mechanics

Volumn 18, Issue 1, 2003, Pages 37-60

  Johnson, E A ^a   Proppe, C ^b   Spencer Jr , B F ^c   Bergman, L A ^c   Szekely G S ^b,d   Schueller G I ^b  

^a University of Southern California   (United States)

^b UNIVERSITY OF INNSBRUCK   (Austria)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^d Oerlikon Space AG   (Switzerland)

Author keywords

Computational stochastic dynamics; Fokker Planck equation; Monte Carlo simulation; Parallel computing; Random eigenvalue

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; DATA STORAGE EQUIPMENT; EIGENVALUES AND EIGENFUNCTIONS; MONTE CARLO METHODS; PROBLEM SOLVING; PROGRAM COMPILERS;

COMPUTATIONAL STOCHASTIC DYNAMICS;

PARALLEL PROCESSING SYSTEMS;

EID: 0037265449     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0266-8920(02)00041-3     Document Type: Review

References (79)

1. Aburto A. FLOPS v. 2.0 benchmark code flops20.c, aburto@marlin.nosc.mil; 1992.
2. Adeli H. Parallel processing in computational mechanics. 1992;Marcel Dekker, New York.
3. Adeli H., Kulkarni M., Vanluchene D. High performance computing in structural mechanics and engineering. J Aerospace Engng. 6:1993;249-267.
4. Amdahl G.M. Validity of the single-processor approach to achieving large-scale computing capabilities. Hoagland A.S. American federation of information processing society (AFIPS) conference proceedings (Atlantic City, NJ, April 18-20, 1967). vol. 30:1967;483-485.
5. Bathe K.J., Wilson E.L. Large eigenvalue problems in dynamic analysis. J Engng Mech ASCE. 6:1972;1471-1485.
6. Bergman L.A., Heinrich J.C. On the moments of time to first passage of the linear oscillator. Earthquake Engng Struct Dyn. 9:1981;197-204.
7. Bergman LA, Spencer BF Jr. Solution of the first passage problem for simple linear and nonlinear oscillators by the finite element method. Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, T&AM Report No. 461; 1983.
8. Bergman L.A., Spencer B.F. Jr. First passage of a sliding rigid structure on a frictional foundation. Earthquake Engng Struct Dyn. 13:(3):1985;281-291.
9. Bergman L.A., Spencer B.F. Jr. First passage time for linear systems with stochastic coefficients. Probab Engng Mech. 2:(1):1987;46-53.
10. Bergman L.A., Wojtkiewicz S.F., Johnson E.A., Spencer B.F. Jr. Robust numerical solution of the Fokker-Planck equation for second order dynamical systems under parametric and external white noise excitations. Kliemann W.H., Langford W.F., Sri Namachchivaya N. Fields institute communications: nonlinear dynamics and stochastic mechanics. 1996;23-37 American Mathematical Society, Providence.
11. Burnett D.S. Finite element analysis: from concepts to applications. 1987;Addison-Wesley, Reading, MA.
12. Caesar B., Eckert L., Hoppe A. Design parameter update of dynamic mathematical models in presence of test noise and mode pairing problems. Proc Conf Spacecraft Struct Mech Test, ESTEC Noordwijk, The Netherlands. 1991;491-499.
13. Carter W.T., Sham T.L., Law K.H. A parallel finite element method and its prototype implementation on a hypercube. Comput Struct. 31:1989;921-934.
14. Celia M.A., Gray W.G. Numerical methods for differential equations. 1992;Prentice Hall, Englewood Cliffs, NJ.
15. Cohen J. NCSA and structural mechanics. Access. 7:1993;12-14.
16. Farhat C., Wilson E. A new finite element concurrent computer program architecture. Int J Numer Meth Engng. 24:1987;1771-1792.
17. Flynn M.J. Very high-speed computing systems. Proc IEEE. 54:(12):1966;1901-1909.
18. Flynn M.J. Some computer organizations and their effectiveness. IEEE Trans Comput. C-21:(9):1972;948-960.
19. Geist A., Beguelin A., Dongarra J., Jiang W., Manchek R., Sunderam V. PVM: parallel virtual machine, a users' guide and tutorial for networked parallel computing. 1994;MIT Press, Cambridge, MA.
20. Gentleman W.M. Some complexity results for matrix computation on parallel processors. J Assoc Comput Mach. 25:1978;112-115.
21. Gropp W., Lusk E., Skjellum A. Using MPI: portable parallel programming with the message passing interface. 2nd ed: 1999;MIT Press, Cambridge, MA.
22. Harnpornchai N., Pradlwarter H.J., Schuëller G.I. Stochastic analysis of dynamical systems by phase-space-controlled Monte Carlo simulation. Comput Meth Appl Mech Engng. 168:1999;273-283.
23. Johnson EA. On-line monitoring, control, and reliability of structural dynamical systems. PhD Dissertation, Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL; 1997.
24. Johnson E.A., Bergman L.A., Goldberg D.E., Dyke S.J. Monte Carlo simulation of dynamical systems of engineering interest in a massively parallel computing environment: an application of genetic algorithms. Naess A., Krenk S. IUTAM symposium on advances in nonlinear stochastic mechanics. 1996;225-234 Kluwer, Dordrecht.
25. Johnson E.A., Bergman L.A., Spencer B.F. Jr. Parallel implementations of MCS - comparative studies from stochastic structural dynamics. Probab Engng Mech. 12:(4):1997;208-212.
26. Johnson E.A., Spencer B.F. Jr., Bergman L.A. Intelligent Monte Carlo simulation and discrepancy sensitivity. Spanos P.D. Computational stochastic mechanics. 1999;31-39 Balkema, Rotterdam.
27. Johnson E.A., Wojtkiewicz S.F., Bergman L.A. Some experiments with massively parallel computation for Monte Carlo simulation of stochastic dynamical systems. Spanos P.D. Computational stochastic mechanics. 1995;325-336 Balkema, Rotterdam.
28. Johnson E.A., Wojtkiewicz S.F., Bergman L.A., Spencer B.F. Jr. Observations with regard to massively parallel computation for Monte Carlo simulation of stochastic dynamical systems. Int J Non-Linear Mech. 32:(4):1997;721-734.
29. Kahn H. Use of different Monte Carlo sampling techniques. Mayer M.A. Symposium on Monte Carlo methods. 1956;146-190 Wiley, New York.
30. Lambert J.D. Computational methods in ordinary differential equations. 1973;Wiley, London.
31. Langley R.S. A finite element method for the statistics of nonlinear random vibration. J Sound Vib. 101:1985;41-54.
32. Langtangen H.P. A general numerical solution method for Fokker-Planck equations with applications to structural reliability. Probab Engng Mech. 6:1991;33-48.
33. Malone J.G. Automated mesh decomposition and concurrent finite element analysis for hypercube multiprocessor computers. Comput Meth Appl Mech Engng. 70:1988;27-58.
34. MPI: a message-passing interface standard. Int J Supercomput Appl High Perform Comput. 8:1994.
35. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. Equation of state calculations by fast computing machines. J Chem Phys. 21:1953;1087-1092.
36. Naess A., Moe V. Efficient path integration methods for nonlinear dynamic systems. Probab Engng Mech. 15:(2):2000;221-231.
37. Naess A., Johnsen J.M. Response statistics of nonlinear, compliant offshores structures by the path integral solution method. Probab Engng Mech. 8:(2):1993;91-106.
38. Nigam N.C. Introduction to random vibrations. 1983;MIT Press, Cambridge, MA.
39. Noor A.K., Peters J.M. A partitioning strategy for efficient nonlinear finite element dynamics analysis on multiprocessor computers. Comput Struct. 31:1989;795-810.
40. Nour-Omid B. A preconditioned conjugate gradient method for solution of finite elemet equations. Innovative methods for nonlinear problems. 1984;Pineridge Press, Swansea, UK.
41. Nour-Omid B., Partlett B.N., Raefsky A. Comparison of lanczos with conjugate gradient using element preconditioning. Proc Domain Decompos Symp, SIAM. June 1987.
42. Ortiz M., Nour-Omid B. Unconditionally stable concurrent procedures for transient finite element analysis. Comput Meth Appl Mech Engng. 58:1986;151-174.
43. Pradlwarter HJ. A selective MC simulation technique for non-linear structural reliability. Sixth ASCE specialty conference on probabilistic mechanics and structural and geotechnical reliability, Denver, CO; July 8-10, 1992. Proceedings. p. 69-72.
44. Pradlwarter H.J., Schuëller G.I. On advanced Monte Carlo simulation procedures in stochastic structural dynamics. Int J Non-Linear Mech. 32:1997;735-744.
45. Pradlwarter H.J., Schuëller G.I. Assessment of low probability events of dynamical systems by controlled Monte Carlo simulation. Probab Engng Mech. 14:1999;213-227.
46. Pradlwarter H.J., Schuëller G.I., Melnik-Melnikov P.G. Reliability of MDOF-systems. Probab Engng Mech. 9:1994;235-243.
47. Press W.H., Teukolsky S.A., Vetterling W.T., Flanery B.P. Numerical recipes in FORTRAN 77. 2nd ed: 1992;Cambridge University Press, Cambridge, UK.
48. Proppe C. Distributed computing with weight controlled Monte Carlo simulation algorithms. Schuëller G.I., Spanos P.D. Proceedings of the International Conference on Monte Carlo Simulation (MCS2000), Monte Carlo, Monaco, June 18-21, 2000. 2001;49-54 Balkema, Rotterdam.
49. Roache P.J. Elliptic marching methods and domain decomposition. 1995;CRC Press, Boca Raton, FL.
50. Schuëller G.I., Bucher C.G., Bourgund U., Ouypornpraesert W. On efficient computational schemes to calculate structural failure probabilities. Probab Engng Mech. 4:(1):1989;10-18.
51. Schuëller G.I., Pradlwarter H.J. On the stochastic response of nonlinear FE models. Arch Appl Mech. 69:1999;765-784.
52. Schuëller G.I., Pradlwarter H.J., Vasta M., Harnpornchai N. Benchmark study on non-linear stochastic structural dynamics. Shiraishi N., Shinozuka M., Wen Y.K. Seventh international conference on structural safety and reliability (ICOSSAR'97), November 24-28, 1997, Kyoto, Japan. 1998;355-361.
53. Smith B.F., Bjørstad P.E., Gropp W. Domain decomposition. 1996;Cambridge University Press, New York.
54. Snir M., Otto S.W., Huss-Lederman S., Walker D.W., Dongana J. MPI - the complete reference. 1996;MIT Press, Cambridge, MA.
55. Soong T.T., Grigoriu M. Random vibration of mechanical and structural systems. 1993;Prentice Hall, Englewood Cliffs, NJ.
56. Spencer B.F. Jr. Reliability of randomly excited hysteretic structures. Lecture notes in engineering. vol. 21:1986;Springer, Berlin.
57. Spencer B.F. Jr., Bergman L.A. On the reliability of a simple hysteretic system. J Engng Mech ASCE. 111:(12):1985;1502-1514.
58. Spencer B.F. Jr., Bergman L.A. On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems. Nonlinear Dyn. 4:1993;357-372.
59. Stochastic structural analysis - ASKA_RV. Version 2.0, a user's manual, CERRAM, München, LASSO, Stuttgart; 1995.
60. Sues RH, Chen H-C, Twisdale LA. Probabilistic structural mechanics research for parallel processing computers. NASA CR-187162; 1991.
61. Sues RH, Lua YJ, Smith MD. Parallel computing for probabilistic response analysis of high temperature composites. NASA CR-194467; 1994.
62. Sun J.Q., Hsu C.S. Effects of small random uncertainties on non-linear systems studied by the generalized cell mapping method. J Sound Vib. 147:(2):1991;185-201.
63. Sun J.Q., Hsu C.S. Global analysis of nonlinear dynamical systems with fuzzy uncertainties by the cell mapping method. Comput Meth Appl Mech Engng. 83:(2):1990;109-120.
64. Sun J.Q., Hsu C.S. First-passage time probability of non-linear stochastic systems by generalized cell mapping method. J Sound Vib. 124:(2):1988;233-248.
65. Székely GS. Random eigenvalue problems (literature review). Internal Working Report No. 36-96, Institute of Engineering Mechanics, Leopold-Franzens Universität, Innsbruck, Austria; 1996.
66. Székely GS. An efficient computational method for the calculation of eigenvectors and eigenvalues within the Monte Carlo simulation - a contribution to the reliability analysis of large structural systems. Dissertation, Leopold-Franzens University, Innsbruck, Austria; 1997.
67. Székely G.S., Schuëller G.I. Computational procedure for a fast calculation of eigenvectors and eigenvalues of structures with random properties. Comput Meth Appl Mech Engng. 191:2001;799-816.
68. CM-5 CM Fortran performance guide, version 2.1. January 1994;Thinking Machines Corporation, Cambridge, MA.
69. Tylikowski A., Marowski W. Vibration of a non-linear single degree of freedom system due to Poissonian impulse excitation. Int J Nonlinear Mech. 21:(3):1986;229-238.
70. Wedig W.V., von Wagner U. Extended Laguerre polynomials for nonlinear stochastic polynomials. Spanos P.D. Computational stochastic mechanics. 1999;293-298 Balkema, Rotterdam.
71. Wilson G.V. Practical parallel programming. 1995;MIT Press, Cambridge, MA.
72. Wojtkiewicz SF, Bergman LA, Spencer BF Jr. Robust numerical solution of the Fokker-Planck-Kolmogorov equation for two dimensional stochastic dynamical systems. Technical Report AAE 94-08, Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL; 1994.
73. Wojtkiewicz S.F., Bergman L.A., Spencer B.F. Jr. Numerical solution of some three-state random vibration problems. Symposium on 'Dynamics and Control of Stochastic Dynamical Systems,' 15th ASME Biennial Conference on Mechanical Vibration and Noise, Boston, MA. 1995;939-947.
74. Wojtkiewicz S.F., Bergman L.A., Spencer B.F. Jr., Johnson E.A. Numerical solution of the four-dimensional nonstationary Fokker-Planck equation. Narayanan S., Iyengar R.N. Presented at the IUTAM symposium on nonlinearity and stochastic structural dynamics, Indian Institute of Technology (Madras), Chennai, India, January 4-8, 1999. Presented at the IUTAM symposium on nonlinearity and stochastic structural dynamics, Indian Institute of Technology (Madras), Chennai, India, January 4-8, 1999. 2001;277-288 Kluwer, Dordrecht.
75. Wojtkiewicz S.F., Bergman L.A. Numerical solution of high dimensional Fokker-Planck equations. Kareem A., Haldar A., Spencer B.F. Jr., Johnson E.A. Proceedings of the Eighth ASCE Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability (PMC2000). CD-ROM paper PMC2000-167. CD-ROM paper PMC2000-167. 2000;6 pp.
76. Wojtkiewicz S.F., Bergman L.A., Spencer B.F. Jr. High fidelity numerical solutions of the Fokker-Planck equation. Shiraishi N., Shinozuka M., Wen Y.K. Seventh International Conference on structural safety and reliability (ICOSSAR'97), November 24-28, 1997, Kyoto, Japan. vol. 2:1998;933-940.
77. Wojtkiewicz S.F., Bergman L.A., Spencer B.F. Jr. Computational issues arising in the solution of the Fokker-Planck equation in higher dimensions: use of iterative solution methods. Shiraishi N., Shinozuka M., Wen Y.K. Seventh International Conference on Structural Safety and Reliability (ICOSSAR'97), November 24-28, 1997, Kyoto, Japan. vol. 2:1998;851-858.
78. Yi W. Concurrent finite element solution of the Fokker-Planck equation. Master's Thesis, Department of Civil Engineering and Geological Sciences, University of Notre Dame; 1997.
79. Yi W., Spencer B.F. Jr., Bergman L.A. Solution of the Fokker-Planck equation in higher dimensions: application of the concurrent finite element method. Shiraishi N., Shinozuka M., Wen Y.K. Seventh International Conference on Structural Safety and Reliability (ICOSSAR'97), November 24-28, 1997, Kyoto, Japan. vol. 2:1998;859-865.