Parallel numerical algorithms for optimization of electrical cables

Abstract In this paper we propose new heuristic numerical algorithm for determination of the optimal wires diameters in electrical cables. Two multilevel parallel versions of the optimization algorithm are constructed. The first algorithm is based on master‐slave technique and the second algorithm uses the data‐parallel strategy. Multilevel structure of the algorithms gives a possibility to adapt them to parallel architecture, for example, cluster of multicore computers. Some results of numerical experiments are presented which agree well with theoretical analysis.

[1]  M. Dryja.  On Discontinuous Galerkin Methods for Elliptic Problems with Discontinuous Coefficients , 2003 .

[2]  J. K. Lenstra,et al.  Local Search in Combinatorial Optimisation. , 1997 .

[3]  Raimondas Čiegis,et al.  On Parallel Numerical Algorithms for Simulating Industrial Filtration Problems , 2007 .

[4]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5]  Y. Jaluria,et al.  An Introduction to Heat Transfer , 1950 .

[6]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[7]  Raimondas Čiegis,et al.  A Parallel Solver for the 3D Simulation of Flows Through Oil Filters , 2009 .

[8]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[9]  Raimondas Čiegis,et al.  Numerical simulation of the heat conduction in electrical cables , 2007 .

[10]  Vipin Kumar,et al.  Parallel Multilevel series k-Way Partitioning Scheme for Irregular Graphs , 1999, SIAM Rev..

[11]  Tatyana Aleinikova,et al.  On the iterative methods for linear problems with discontinuous coefficients , 1993 .

[12]  Wing Lok Wan.  Interface preserving coarsening multigrid for elliptic problems with highly discontinuous coefficients , 2000 .

[13]  A. Samarskii.  The Theory of Difference Schemes , 2001 .

[14]  Gerda Jankevičiūtė,et al.  Parallel Numerical Solver for the Simulation of the Heat Conduction in Electrical Cables , 2009 .

[15]  George Karypis,et al.  Introduction to Parallel Computing , 1994 .

[16]  Paulo Fernandes,et al.  Performance Models For Master/Slave Parallel Programs , 2005, Electron. Notes Theor. Comput. Sci..

[17]  Raimondas Ciegis,et al.  One Application of the Parallelization Tool of Master-Slave Algorithms , 2002, Informatica.