Load balancing for the parallel adaptive solution of partial differential equations

Applied Numerical Mathematics - Tập 16 - Trang 157-182 - 1994
H.L. deCougny1, K.D. Devine1, J.E. Flaherty1, R.M. Loy1, C. Özturan1, M.S. Shephard1
1Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA

Tài liệu tham khảo

S. Adjerid, M. Aiffa and J.E. Flaherty, High-order finite element methods for singularly perturbed elliptic and parabolic systems, SIAM J. Appl. Math. (to appear). Adjerid, 1992, High-order adaptive methods for parabolic systems, Phys. D, 60, 94, 10.1016/0167-2789(92)90229-G Arney, 1990, An adaptive mesh moving and local refinement method for time-dependent partial differential equations, ACM Trans. Math. Software, 16, 48, 10.1145/77626.77631 Babuška, 1988, The p- and hp-versions of the finite element method. The state of the art Biswas, 1994, Parallel, adaptive finite element methods for conservation laws, Appl. Numer. Math., 14, 255, 10.1016/0168-9274(94)90029-9 Berger, 1987, A partitioning strategy for nonuniform problems on multiprocessors, IEEE Trans. Comput., 36, 570, 10.1109/TC.1987.1676942 Berger, 1984, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53, 484, 10.1016/0021-9991(84)90073-1 Cockburn, 1989, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems, J. Comput. Phys., 84, 90, 10.1016/0021-9991(89)90183-6 Cockburn, 1990, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case, Math. Comp., 54, 545 Cockburn, 1989, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework, Math. Comp., 52, 411 Devine, 1994, Parallel partitioning strategies for the adaptive solution of conservation laws Devloo, 1988, An h-p adaptive finite element method for the numerical simulation of compressible flow, Comput. Methods Appl. Mech. Engrg., 70, 203, 10.1016/0045-7825(88)90158-2 S. Dey, Personal communication (1993). M. Dindar, Personal communication (1993). Farhat, 1988, A simple and efficient automatic FEM domain decomposer, Comput. & Structures, 28, 579, 10.1016/0045-7949(88)90004-1 Fiedler, 1973, Algebraic connectivity of graphs, Czechoslovak Math. J., 23, 298, 10.21136/CMJ.1973.101168 Gropp, 1993, Users manual for the Chameleon parallel programming tools W. Gui and I. Babuška, The h-, p- and hp-versions of the finite element method in one dimension, Part I: the error analysis of the p version; Part II: the error analysis of the h and hp versions; Part III: the adaptive hp version, Numer. Math. (to appear). Hammond, 1991, Mapping unstructured grid computations to massively parallel computers Hendrickson, 1992, An improved spectral graph partitioning algorithm for mapping parallel computations Hendrickson, 1993, Multidimensional spectral load balancing Jaja, 1992 Z. Johan, Personal communication (1993). Johan, 1993, An efficient communication strategy for finite element methods on the Connection Machine CM-5 system Leiss, 1989, Distributed load balancing: design and performance analysis, W.M. Keck Research Computation Laboratory, 5, 205 Pothen, 1990, Partitioning sparse matrices with eigenvectors of graphs, SIAM J. Matrix Anal. Appl., 11, 430, 10.1137/0611030 Rank, 1987, An expert system for the optimal mesh design in the hp-version of the finite element method, Internat. J. Numer. Methods Engrg., 24, 2087, 10.1002/nme.1620241106 Reddy, 1989, On Load Balancing Shephard, 1991, Automatic three-dimensional mesh generation by the finite octree technique, Internat. J. Numer. Methods Engrg., 32, 709, 10.1002/nme.1620320406 Simon, 1991, Partitioning of unstructured problems for parallel processing, Comput. Systems Engrg., 2, 135, 10.1016/0956-0521(91)90014-V Szymanski, 1978, A representation of a distribution power network graph, Archiwum Elektrotechniki, 27, 367 Van Leer, 1982, Flux vector splitting for the Euler equations Walshaw, 1992, Dynamic load-balancing for PDE solvers on adaptive unstructured meshes Wheat, 1992, A fine grained data migration approach to application load balancing on MP MIMD machines Wheat, 1994, Experience with automatic, dynamic load balancing and adaptive finite element computation, Proceedings 27th Hawaii International Conference on System Sciences, 2, 463 Vizing, 1964, On an estimate of a chromatic class of a multigraph, Proceedings Third Siberian Conference on Mathematics and Mechanics