Abstract
A parallel LOD algorithms for solving the 3D problem with nonlocal boundary condition is considered. The algorithm is implemented using the parallel array object tool ParSol, then a parallel algorithm follows semi-automatically from the serial one. Results of computational experiments are presented.
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Balay, S., Buschelman, K., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M.G., Curfman McInnes, L., Smith, B.F., Zhang, H.: PETSc Users Manual. ANL-95/11 - Revision 2.3.0, Argonne National Laboratory (2005)
Cannon, J.R., Lin, Y., Matheson, A.L.: Locally explicit schemes for three–dimensional diffusion with non–local boundary specification. Appl. Anal. 50, 1–19 (1993)
Čiegis, R.: Economical difference schemes for the solution of a two dimensional parabolic problem with an integral condition. Differential Equations 41(7), 1025–1029 (2005)
Čiegis, R.: Numerical Schemes for 3D Parabolic Problem with Non–Local Boundary Condition. In: Proceedings of 17th IMACS World congress, Scientific Computation, Applied Mathematics and Simulation, Paris, France, T2-T-00-0365, June 11-15 (2005)
Čiegis, R.: Finite-Difference Schemes for Nonlinear Parabolic Problem with Nonlocal Boundary Conditions. In: Ahues, M., Constanda, C., Largillier, A. (eds.) Integral Methods in Science and Engineering: Analytic and Numerical Techniques, Birkhauser, Boston, pp. 47–52 (2004) ISBN 0-8176-3228-X
Čiegis, R., Jakušev, A., Krylovas, A., Suboč, O.: Parallel algorithms for solution of nonlinear diffusion problems in image smoothing. Math. Modelling and Analysis 10(2), 155–172 (2005)
Čiegis, R., Štikonas, A., Štikonienė, O., Suboč., O.: Monotone finite-difference scheme for parabolical problem with nonlocal boundary conditions. Differential Equations 38(7), 1027–1037 (2002)
Čiegis, R., Štikonas, A., Štikonienė, O., Suboč., O.: Stationary problems with nonlocal boundary conditions. Mathematical Modelling and Analysis 6, 178–191 (2001)
Dehghan, M.: Efficient techniques for the second-order parabolic equation subject to nonlocal specifications. Applied Numer. Math. 52, 39–62 (2005)
Dehghan, M.: Locally explicit schemes for three–dimensional diffusion with non–local boundary specification. Applied Mathematics and Computation 135, 399–412 (2002)
Ekolin, G.: Finite difference methods for a nonlocal boundary value problem for the heat equation. BIT 31(2), 245–255 (1991)
Fairweather, G., Lopez-Marcos, J.C.: Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions. Adv. Comput. Math. 6, 243–262 (1996)
Hockney, R.: Performance parameters and benchmarking on supercomputers. Parallel Computing 17, 1111–1130 (1991)
Kumar, V., Grama, A., Gupta, A., Karypis, G.: Introduction to parallel computing: design and analysis of algorithms. Benjamin/Cummings, Redwood City (1994)
Langtangen, H.P., Tveito, A.: Advanced Topics in Computational Partial Differential Equations. Numerical Methods and Diffpack Programming. Springer, Berlin (2003)
Noye, B.J., Dehghan, M.: New explicit finite difference schemes for two–dimensional diffusion subject specification of mass. Numer. Meth. for PDE 15, 521–534 (1999)
Samarskii, A.A.: The theory of difference schemes. Marcel Dekker, Inc., New York–Basel (2001)
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Čiegis, R. (2006). Parallel LOD Scheme for 3D Parabolic Problem with Nonlocal Boundary Condition. In: Nagel, W.E., Walter, W.V., Lehner, W. (eds) Euro-Par 2006 Parallel Processing. Euro-Par 2006. Lecture Notes in Computer Science, vol 4128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11823285_71
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DOI: https://doi.org/10.1007/11823285_71
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