Large-scale parallel numerical integration. (English) Zbl 0943.65030

Mere description of a hierarchical algorithm how to compute efficiently many integrals (e.g. in the finite element method) on a parallel computer. The objective is load balancing by distribution of integrals and subregions by a controller process. Some demonstration examples.


65D32 Numerical quadrature and cubature formulas
65Y05 Parallel numerical computation


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[1] R.L. Burden, J.D. Faires, Numerical Analysis, 3rd Edition, Prindle, Weber & Schmidt, Boston, MA, 1985. · Zbl 0788.65001
[2] E. De Doncker, A. Gupta, Distributed adaptive integration, algorithms and analysis, in: Proceedings of Transputers 94, 1994, pp. 266-277.
[3] E. De Doncker, A. Gupta, P. Ealy, A. Genz, Parint: a software package for parallel integration, in: Proceedings of the 10th ACM International Conference on Supercomputing, ACM, New York, 1996, pp. 149-156.
[4] E. De Doncker, J. Kapenga, Parallelization of adaptive integration methods, in: P. Keast, G. Fairweather (Eds.), Numerical Integration; Recent Developments, Software and Applications, NATO ASI Series, Reidel, 1987, pp. 207-218. · Zbl 0615.65017
[5] E. De Doncker, J.A. Kapenga, A portable parallel algorithm for multivariate numerical integration and its performance analysis, in: Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing, Los Angeles, 1987, pp. 109-113.
[6] De Doncker, E.; Robinson, I., An algorithm for automatic integration over a triangle using nonlinear extrapolation, ACM trans. math. software, 10, 1-16, (1984) · Zbl 0554.65011
[7] A. Genz, The numerical evaluation of multiple integrals on parallel computers, in: P. Keast, G. Fairweather (Eds.), Numerical Integration; Recent Developments, Software and Applications, NATO ASI Series, Reidel, 1987, pp. 219-229. · Zbl 0615.65028
[8] Genz, A.; Malik, A., An adaptive algorithm for numerical integration over an n-dimensional rectangular region, J. comput. appl. math., 6, 295-302, (1980) · Zbl 0443.65009
[9] Genz, A.; Malik, A., An imbedded family of multidimensional integration rules, SIAM J. numer. anal., 20, 580-588, (1983) · Zbl 0541.65012
[10] W. Gropp, E. Lusk, A. Skjellum, Using MPI: Portable Parallel Programming with the Message Passing Interface, The MIT Press, Cambridge, MA, 1994. · Zbl 0875.68206
[11] A. Gupta, A. Photiou, Load Balanced Priority Queues on Distributed Memory Machines, in: Lecture Notes in Computer Science, Vol. 817, Springer, Berlin, 1994, pp. 689-700.
[12] A.R. Krommer, C.W. Ueberhuber, Numerical Integration on Advanced Computer Systems, Lecture Notes in Computer Science, Vol. 848, Springer, Berlin, 1994. · Zbl 0825.65012
[13] J. Lyness, On handling singularities in finite elements, in Numerical Integration, Recent Developments, Software and Applications, NATO ASI Series, Kluwer Academic Publishers, Dordrecht, 1992, pp. 219-233. · Zbl 0762.65010
[14] Lyness, J.; Jespersen, P., Moderate degree symmetric quadrature rules for triangles, J. inst. math. appl., 15, 19-32, (1975) · Zbl 0297.65018
[15] S.H. Paskov, Computing high dimensional integrals with applications to finance, Tech. Rep., Columbia University Department of Computer Science, 1994, CUCS-023-94.
[16] S. Smith, R. Schnabel, Centralized and distributive dynamic scheduling for adaptive parallel algorithms, Tech. Rep., Department of Computer Science, University of Colorado at Boulder, Boulder, CO, 1991. CU-CS-516-91.
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