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3 edition of On the optimal number of subdomains for hyperbolic problems on parallel computers found in the catalog.

On the optimal number of subdomains for hyperbolic problems on parallel computers

Paul Fischer

On the optimal number of subdomains for hyperbolic problems on parallel computers

by Paul Fischer

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  • 31 Currently reading

Published by Institute for Computer Applications in Science and Engineering, NASA Langley Research Center in Hampton, Va .
Written in English

    Subjects:
  • Spectral geometry,
  • Computational complexity,
  • Differential equation, Hyperbolic,
  • Parallel processing (Electronic computers)

  • Edition Notes

    StatementPaul Fischer, David Gottlieb.
    SeriesICASE report -- no. 96-68., NASA contractor report -- NASA CR-201625.
    ContributionsGottlieb, David., Institute for Computer Applications in Science and Engineering.
    The Physical Object
    Paginationi, 12 p. :
    Number of Pages12
    ID Numbers
    Open LibraryOL17593539M
    OCLC/WorldCa40998754

    A key use of massively parallel computers is to perform large-scale sim-ulations in similar amount of time as typical industrial simulations on com-modity hardware, through the use of parallelization. Thus, “optimal” al-gorithms are desired, for which the work scales linearly with the number . of the interface of the subdomain s, and S is the total number of subdomains. The parameter r• is a real number between 0 and 1. The value r• - 1 corresponds to a pure upwind scheme. In this case, the density equation is solved in the subdomain number 1, without boundary conditions. In the second domain the equation is solved by using the.

    Parallel Implementation. Domain decomposition is implemented on a parallel computer by letting each processor handle a sub-domain (or at most a few sub-domains). Therefore the choice of these sub-domains becomes crucial in obtaining good performance. The strategy in choosing the sub-domains must be guided by the following requirements.   As a purely parallel algorithm, the parareal algorithm has been applied to many practical problems, such as hyperbolic problems [5], fluid mechanics [6], quantum control [7, 8], and optimized control problem [9,10].

    This tells us that in hyperbolic geometry the defect of any triangle is a positive real number. We shall see that it is a very important quantity in hyperbolic geometry. Corollary 1 In H2 all convex quadrilaterals have angle sum less than Saccheri Quadrilaterals Girolamo Saccheri was a Jesuit priest who lived from to Parallel solution of a traffic flow simulation problem. Parallel Computing, Vol. 22, Issue. 14, p. and conquer techniques for solving partial differential equations by iteratively solving subproblems defined on smaller subdomains. The principal advantages include enhancement of parallelism and localized treatment of complex and.


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On the optimal number of subdomains for hyperbolic problems on parallel computers by Paul Fischer Download PDF EPUB FB2

On the optimal number of subdomains for hyperbolic problems on parallel computers i, 12 p. (OCoLC) Document Type: Book: All Authors / Contributors: P F Fischer; David Gottlieb; Institute for Computer Applications in Science and Engineering.

@ARTICLE{Fischer96onthe, author = {Paul Fischer and David Gottlieb}, title = {On The Optimal Number Of Subdomains For Hyperbolic Problems On Parallel Computers}, journal = {ON PARALLEL COMPUTERS, INT.

SUPERCOMPUTER APPL. HIGH PERFORM. On The Optimal Number Of Subdomains For Hyperbolic Problems On Parallel Computers. The computational complexity for parallel implementation of multidomain spectral methods is studied to derive the optimal number of subdomains, q, and spectral order, n, for numerical solution of hyperbolic problems.

from the optimal uni-processor values Author: Paul Fischer and David Gottlieb. On the Optimal Number of Subdomains for Hyperbolic Problems on Parallel Computers March International Journal of High Performance Computing Applications Paul Fischer. In [4] a spectral method to solve hyperbolic initial boundary value problems on parallel computers in one space dimension has been proposed.

In [11] these results are generalized to a domain in. Gottlieb, Fischer, P., On the optimal number of subdomains for hyperbolic problems on parallel computers, 11(), 65– Gottlieb, Gustafsson, B., Generalized Du-Fort Frankel methods for parabolic initial boundary value problems, SIAM J.

Appl. Math., 29(), – Gottlieb, D., Gustafsson, Forsse’n, P. Fischer P and Gottlieb D () On the Optimal Number of Subdomains for Hyperbolic Problems on Parallel Computers, International Journal of High Performance Computing Applications,(), Online publication date: 1-Mar   Besides supplying the required geometric flexibility, the multi-domain formulation also provides a very natural load-balanced data-decomposition, suitable for parallel environments.

The performance of the overall scheme is illustrated by solving two dimensional hyperbolic problems. Books. M.O. Deville, P.F. Fischer, and E.H. Mund, High-Order Methods for Incompressible Fluid Flow, Cambridge University Press ().

Journal articles and book. The numerical technique employed here assumes that the uncertainty on the considered parameter λ T lays in a bounded set, the dimensions of which are defined through the robust parameter γ. Hence, an increase of γ increases also the uncertainty on the parameter adding safety margin.

A robust counterpart problem, i.e., a worst-case scenario or min-max optimal control problem is formulated. We introduce a nonoverlapping variant of the Schwarz waveform relaxation algorithm for wave propagation problems with variable coefficients in one spatial dimension.

We derive transmission conditions which lead to convergence of the algorithm in a number of iterations equal to the number of subdomains, independently of the length of the time interval. In mathematics, numerical analysis, and numerical partial differential equations, domain decomposition methods solve a boundary value problem by splitting it into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains.

A coarse problem with one or few unknowns per subdomain is used to further coordinate the solution between the. On the optimal number of subdomains for hyperbolic problems on parallel computers, Int. of Supercomp. Appl.

and High Perf. Comp. 11 (). Greiner, M., Spencer, G., and Fischer, P.F., Direct numerical simulation of three-dimensional flow and augmented heat transfer in a grooved channel ASME Natl.

Heat Transfer Conf. () Neumann-Neumann waveform relaxation algorithm in multiple subdomains for hyperbolic problems in 1D and 2D. Numerical Methods for Partial Differential Equations() A new parallel subspace correction method for advection–diffusion equation.

methods based on the Neumann-Neumann algorithm to solve hyperbolic problems in parallel computer, and present convergence results for the method. The Neumann-Neumann algorithm was introduced for solving elliptic problems by Bourgat et al.

[1], see also [26] and [28]. The iteration involves solving the subdomain problems using. problems and computed target errors often agree closely with those specified.

If there is significant deviation, the process is repeated. Parallel versions have been developed and implemented successfully on a processor Intel iPSC/ For hyperbolic problems, a 4-step variation of the scheme has also been implemented [10].

subject to the hyperbolic problem, ∆, ∈Ω, ˘0,0 0,0 0, ∈Ω, 0, ∈ˇΩ, ˘0 where ∈˙˝ 0,˛. Benamou [6] has used the domain decomposition method to solve the optimal control problem in the hyperbolic system and has taken the set of admissible control as a convex subset of 0,˛˚Ω.

arXivv1 [] 8 Oct Explicit Parallel-in-time Integration of a Linear Acoustic-Advection System D. Ruprechta,∗, R. Krausea aInstitute of Computational Science, Universita` della Svizzera italiana, Via Giuseppe Buffi 13, Lugano, Switzerland Abstract The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional.

Abstract. A general tool for solving MHD and hydrodynamical problems typical of astrophysical applications is designed and implemented. The code allows the user to solve a hyperbolic system of partial differential equations with a variety of modern high resolution numerical schemes on 1, 2 or 3D non-uniform Cartesian grids with slab or axial symmetry.

For any real number x, we have cos 2 x + sin 2 x = 1; thus the point (cos x, sin x) lies on the circle u 2 + v 2 = 1. Now consider the hyperbolic functions. For any real number x, we have cosh 2 x – sinh 2 x = 1; thus the point (cosh x, sinh x) lies on the curve u 2 – v 2 = 1, which is a hyperbola.

This explains the name hyperbolic functions. the proof of the parallel postulate and consequently tried to turn his son away from its study. Nevertheless, J anos attacked the problem with vigor and had constructed the foundations of hyperbolic geometry by the year His work appeared in or as .ON THE OPTIMAL NUMBER OF SUBDOMAINS F OR HYPERBOLIC PR OBLEMS ON P ARALLEL COMPUTERS P aul Fisc her 12 and Da vid Gottlieb 23 Division of Applied Mathematics Bro wn Univ ersit y Pro vidence, RI Abstract The computational complexit y for parallel implemen tation of m ultidomain sp ectral metho ds is studied to deriv e the optimal n um b er.In hyperbolic geometry, there are two kinds of parallel two lines do not intersect within a model of hyperbolic geometry but they do intersect on its boundary, then the lines are called asymptotically parallel or hyperparallel.

(Note that, in the upper half plane model, any two vertical rays are asymptoticallyfor consistency, ∞ is considered to be part of the boundary.).