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- Olsson, Pelle, et al.
(författare)
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Boundary Modifications of the Dissipation Operators for the Three–Dimensional Euler Equations
- 1989
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Ingår i: Journal of Scientific Computing. - 0885-7474 .- 1573-7691. ; 4:2, s. 159-195
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Tidskriftsartikel (refereegranskat)abstract
- Explicit methods for the solution of fluid flow problems are of considerable interest in supercomputing. These methods parallelize well. The treatment of the boundaries is of particular interest with respect to both the numeric behavior of the solution and the computational efficiency. We have solved the three-dimensional Euler equations for a twisted channel using second-order, centered difference operators, and a three-stage Runge-Kutta method for the integration. Three different fourth-order dissipation operators were studied for numeric stabilization: one positive definite, one positive semidefinite, and one indefinite. The operators only differ in the treatment of the boundary. For computational efficiency all dissipation operators were designed with a constant bandwidth in matrix representation, with the bandwidth determined by the operator in the interior. The positive definite dissipation operator results in a significant growth in entropy close to the channel walls. The other operators maintain constant entropy. Several different implementations of the semidefinite operator obtained through factoring of the operator were also studied. We show the difference both in convergence rate and robustness for the different dissipation operators, and the factorizations of the operator due to Eriksson. For the simulations in this study one of the factorizations of the semidefinite operator required 70%–90% of the number of iterations required by the positive definite operator. The indefinite operator was sensitive to perturbations in the inflow boundary conditions. The simulations were performed on a 8,192 processor Connection Machine system CM-2. Full processor utilization was achieved, and a performance of 135 Mflops/sec in single precision was obtained. A performance of 1.1 Gflops/sec for a fully configured system with 65,536 processors was demonstrated.
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- Eriksson, T., et al.
(författare)
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Successive Encoding of Correlated Sources
- 1982
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The encoding of a discrete memoryless multiple source for reconstruction of a sequence with is considered. We require that the encoding should be such that is encoded first without any consideration of , while in a seeond part of the encoding this latter sequence is encoded based on knowledge of the outcome of the first encoding. The resulting scheme is called successive encoding. We find general outer and inner bounds for the corresponding set of achievable rates along with a complete single letter characterization for the special case . Comparisons with the Slepian-Wolf problem [3] and the Ahlswede-Körner-Wyner side information problem [2 ], [9) are carried out.
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3. |
- Engquist, Björn, et al.
(författare)
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Automatic analysis in PDE software
- 1984
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Ingår i: PDE Software. - Amsterdam, The Netherlands : Elsevier Science. - 0444876200 ; , s. 399-409
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Konferensbidrag (refereegranskat)
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- Engquist, Björn, et al.
(författare)
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Automatic computer code generation for hyperbolic and parabolic differential equations
- 1980
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Ingår i: SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING. - : Society for Industrial & Applied Mathematics (SIAM). - 0196-5204 .- 2168-3417. ; 1:2, s. 249-259
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Tidskriftsartikel (refereegranskat)abstract
- A program system which generates computer code for the numerical solution of systems of hyperbolic and parabolic differential equations is described. The input to the program is a mathematical formulation of a hyperbolic or parabolic initial boundary value problem in one space dimension. The differential equations and boundary conditions are analyzed by the program system, and a finite difference algorithm is designed for the given problem. The output is an executable FORTRAN program.
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10. |
- Engquist, Björn
(författare)
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Inverse imaging methods in exploration seismology
- 1980
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Ingår i: Computing Methods in Applied Sciences and Engineering. - Amsterdam, The Netherlands : Elsevier Science. ; , s. 547-552
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Konferensbidrag (refereegranskat)
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