MESH FREE PARALLEL PROGRAMMING FOR ELECTROMAGNETIC PROBLEMS
Keywords:Parallel Programming, Mesh Free Methods, MLPG, SPH
Mesh free parallel implementations using multi-core processors are discussed. Particularly, parallelization of the MLPG and SPEM are shown. The appropriate strategies to correctly parallelize the mesh free methods are discussed. Parallel versions run up to 1.96 times faster on dual-core processor and 3.78 on quad-core processor when compared to the sequential one.
G. F. Parreira, E. J. Silva, A. R. Fonseca, and R. C. Mesquita, "The element-free galerkin method in threedimensional electromagnetic problems.`` Magnetics, IEEE Transactions on, vol. 42, no. 4, pp. 711â€“714, 2006.
G. R. Liu, Mesh Free Methods: Moving Beyond the Finite Element Method. CRC Press, 2002.
T. Belytschko, Y. Y. Lu, and L. Gu, "Element-free Galerkin methods,`` International Journal for Numerical Methods in Engineering, vol. 37, no. 2, pp. 229 â€“ 256, 1994.
S. N. Atluri and T. Zhu, "A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics,`` Computational Mechanics, vol. 22, no. 2, pp. 117 â€“ 127, 1998.
S. A. Viana, D. Rodger, and H. C. Lai, "Meshless Local Petrov-Galerkin Method with Radial Basis Functions Applied to Electromagnetics,`` Science, Measurement and Technology, IEE Proceedings, vol. 6, no. 151, pp. 449â€“451, 2004.
A. R. Fonseca, S. A. Viana, E. J. Silva, and R. C. Mesquita, "Imposing boundary conditions in the meshless local petrovâ€“galerkin method,`` IET Science, Measurement & Technology, vol. 2, no. 6, pp. 387â€“394, 2008.
G. R. Liu and M. B. Liu, Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific Publishing Co. Pte. Ltd, 2003.
L. B. Lucy,"A numerical approach totesting the fission hypothesis,``The Astronomical Journal, vol. 82, pp. 1013â€“1024, 1977.
G. Ala, E. Francomano, A. Tortorici, E. Toscano, and F. Viola, "Smoothed particle electromagnetics: a mesh-free solver for transients,`` Journal of Computational and Applied Mathematics, vol. 191, no. 2, pp. 194â€“205, 2006.
C. Bischof, D. a. Mey, C. Terboven, and S. Sarholz, "Parallel Computers Everywhere,`` in 16th International Conference on the Computation of Electromagnetic Fields, June 2007, pp. 693â€“700.
G, Karypis, V. Kumar, "METIS: Unstructured Graph Partitioning and Sparse Matrix Ordering System``, University of Minnesota, Department of Computer Science, (1995)
G. Karypis, V. Kumar, "Multilevel k-way Partiotioning Scheme for Irregular Graphs,`` Journal of Parallel and Distributed Computing, vol. 48, pp 96-129, (1998).
I.V. Singha, P.K. Jain, "Parallel EFG algorithm for heat transfer problems", Advances in Engineering Software, vol 36, pp. 554â€“560, (2005).
L. Wang H., L. Guangyao, Han X., Z. Z. Hua, "Development of parallel 3D RKPM meshless bulk forming simulation system", Advances in Engineering Software vol 38, pp 87â€“101 (2007).
S. Ikuno, T. Hanawa, T. Takayama, and A. Kamitani,"Evaluation of parallelized meshless approach: Application to shielding current analysis in hts,``Magnetics, IEEE Transactions on, vol. 44, no. 6, pp. 1230â€“1233, 2008.
BOOST, "Boost.Thread library,`` http://www.boost.org/doc/html/thread.html, 2007.
S. Ikuno, K. Takakura, and A. Kamitani, "Influence of method for imposing essential boundary condition on meshless Galerkin/Petrov-Galerkin approaches,``Magnetics, IEEE Transactions on, vol. 43, no. 4, pp. 1501â€“1504, 2007.
W.R. Stevens. "UNIX Network Programming, Volume 2, Second Edition: Interprocess Communications,`` Prentice Hall, 1999.
T. A. Davis, "A column pre-ordering strategy for the unsymmetric-pattern multifrontal method," ACM Transactions on Mathematical Software, vol 30, no. 2, pp. 165-195, (2004).
T. A. Davis, "Algorithm 832: UMFPACK, an unsymmetric-pattern multifrontal method," ACM Transactions on Mathematical Software, vol 30, no. 2, pp. 196-199, (2004).
G. Ala, E. Francomano, A. Tortorici, E. Toscano, and F. Viola, "A smoothed particle interpolation scheme for transient electromagnetic simulation,``Magnetics, IEEE Transactions on, vol. 42, no. 4, pp. 647â€“650, 2006.
G. Ala, E. Francomano, A. Tortorici, E. Toscano, and F. Viola,"Corrective meshless particle formulations for time domain maxwell's equations,``Journal of Computational and Applied Mathematics, vol. 210, pp. 34â€“46, 2007.
J. P. Berenger, "A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,`` Journal of Computational Physics, vol. 114, pp. 185-200, (1994).
M. L. Mendes, L. C. A. Pimenta, R. C. Mesquita, E. J. d. Silva, and T. C. Santana,"Smoothed particle electromagnetics with boundary absorbing condition using perfectly matched layers,`` in The IET 7th International Conference on Computation in Electromagnetics - CEM2008, 2008, pp. 164â€“165.
M. N. O. Sadiku., "Elements of Electromagnetics,`` Oxford University Press, 2001, 4th edn. 2006.