zbMATH — the first resource for mathematics

A parallel Poisson solver using the fast multipole method on networks of workstations. (English) Zbl 0932.65119
Summary: We present a parallel Poisson solver on distributed computing environments. In the solver, the parallel implementation of the fast multipole method is designed to minimize the amount of data communication and the number of data transfers and synchronizations. The experimental results show linear speedup, good load balancing, and reasonable performance under failure and demonstrate the viability of loosely coupled heterogeneous workstations for large scale scientific computations.

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65Y05 Parallel numerical computation
65Y10 Numerical algorithms for specific classes of architectures
Full Text: DOI
[1] Chan, T.F.; Resasco, D.C., A domain-decomposed fast Poisson solver on a rectangle, SIAM J. sci. stat. comput., 8, 1, S14-26, (1987) · Zbl 0624.65100
[2] Lee, D., Fast parallel solution of the Poisson equation on irregular domains, Numer. algorithms, 8, 2-4, 347-362, (1994) · Zbl 0811.65098
[3] Schumann, U.; Strietzel, M., Parallel solution of tridiagonal systems for the Poisson equation, J. sci. comput., 10, 2, 181-190, (1995) · Zbl 0840.65015
[4] Swarztrauber, P.N.; Sweet, R.A., Vector and parallel methods for the direct solution of Poisson’s equation, J. comput. appl. math., 27, 1-2, 241-263, (1989) · Zbl 0677.65097
[5] Greengard, L.; Lee, J.-Y., A direct adaptive Poisson solver of arbitrary order accuracy, J. comput. phys., 125, 415-424, (1996) · Zbl 0851.65090
[6] Canuto, M.Y.; Hussaini, M.Y.; Quarteroni, A.; Zang, T.A., Spectral methods in fluid dynamics, (1988), Society for Industrial and Applied Mathematics Philadelphia, PA · Zbl 0658.76001
[7] Patera, A.T., A spectral element method for fluid dynamics: laminar flow in a fluid expansion, J. comput. phys., 54, 468-488, (1984) · Zbl 0535.76035
[8] Greengard, L.; Rokhlin, V., A fast algorithm for particle simulations, J. comput. phys., 73, 325-348, (1987) · Zbl 0629.65005
[9] Carrier, J.; Greegard, L.; Rokhlin, V., A fast adaptive multipole algorithm for particle simulation, SIAM J. sci. stat. comput., 9, 4, 669-686, (1987) · Zbl 0656.65004
[10] Dorr, F.W., The direct solution of the discrete Poisson equation on a rectangle, SIAM rev., 12, 248-263, (1970) · Zbl 0208.42403
[11] Anderson, C., Domain decomposition techniques and the solution of Poisson’s equation in infinite domains, (), 129-139
[12] Brandt, A., Multi-level adaptive solutions to boundary value problems, Math. comp., 31, 330-390, (1977) · Zbl 0373.65054
[13] Griebel, M., Parallel domain-oriented multilevel methods, SIAM J. sci. comput., 16, 5, 1105-1125, (September 1995)
[14] Kim, S., Parallel multidomain iterative algorithms for the Helmholtz wave equation, Appl. numer. math., 17, 411-429, (1995) · Zbl 0838.65119
[15] Carriero, N.; Gelernter, D., How to write parallel programs: A first course, (1992), MIT Press Cambridge
[16] Jeong, K., Fault-tolerant parallel processing combining linda, checkpointing, and transactions, ()
[17] Jeong, K.; Shasha, D., Plinda 2.0: A transactional/checkpointing approach to fault tolerant linda, ()
[18] Jeong, K.; Shasha, D.; Talla, S.; Wyckoff, P., An approach to fault-tolerant parallel processing on intermittently idle, heterogeneous workstations, ()
[19] Carriero, N., Implementing tuple space machines, ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.