PARALLEL APPLICATION PACKAGE HELMHOLTZ3D
DOI:
https://doi.org/10.14529/cmse130202Abstract
The paper present parallel application package Helmholtz3D, which allows to compute
three-dimensional time-harmonic electromangetic fields propagating in domains with complicated geometry. In order to solve systems of linear algebraic equations (SLAEs) with complex ill conditioned non-hermitian matrices arising in the finite element discretizations, the package uses state-of-the-art iterative methods in Krylov subspace combined with original parallel preconditioners. Package approbation was performed on the series of model and real-life problems of electromangetic field computation in the microwave devices and well logging problems.
References
Соловейчик, Ю.Г. Метод конечных элементов для решения скалярных и векторных задач / Ю.Г. Соловейчик, М.Э. Рояк, М.Г. Персова. — Новосибирск: Изд-во НГТУ, 2007.
Monk, P. Finite Element Methods for Maxwell’s Equations / P. Monk. — Oxford University Press, 2003.
Ingelstr¨om, P. A new set of H(curl)-conforming hierarchical basis functions for tetrahedral meshes / P. Ingelstr¨om // IEEE Transactions on Microwave Theory and Techniques. — 2006. — Vol. 54, № 1. — P. 160–114.
Ильин, В.П. Методы и технологии конечных элементов / В.П. Ильин. — Новосибирск: Изд-во ИВМиМГ СО РАН, 2007.
Eigen. URL: http://eigen.tuxfamily.org (дата обращения 12.12.2012).
Intel (R) Math Kernel Library from Intel. URL: http://software.intel.com/en-us/intel-mkl (дата обращения 12.02.2013).
Sch¨oberl, J. NETGEN — An advancing front 2D/3D-mesh generator based on abstract rules / J. Sch¨oberl // Computing and Visualization in Science. — 1997. — Vol. 1, № 1. — P. 41–52.
Бутюгин, Д.С. Алгоритмы решения СЛАУ на системах с распределенной памятью в применении к задачам электромагнетизма / Д.С. Бутюгин // Вестник ЮУрГУ. Серия «Вычислительная математика и информатика». — 2012. — № 46(305). — С. 5–18.
Fuchs, H. On visible surface generation by a priori tree structures / H. Fuchs, Z.M. Kedem, B.F. Naylor // ACM Computer Graphics. — 1980. — Vol. 14, № 3. — P. 124–133.
Saad, Y. Iterative Methods for Sparse Linear Systems, Second Edition / Y. Saad. — SIAM, 2003.
Bramble, J. The construction of preconditioners for elliptic problems by substructuring. I. / J. Bramble, J. Pasciak, A. Schatz // Mathematics of Computation. — 1986. — Vol. 47, № 175. — P. 103–134.
Nabben, R. A comparison of deflation and coarse grid correction applied to porous media flow / R. Nabben, C. Vuik // SIAM Journal on Numerical Analysis. — 2004. — Vol. 42, № 4. — P. 1631–1647.
Butyugin, D.S. Efficient iterative solvers for time-harmonic Maxwell equations using domain decomposition and algebraic multigrid / D.S. Butyugin // Journal of Computational Science. — 2012. — Vol. 3, № 6. — P. 480–485.
Бутюгин, Д.С. Параллельный предобуславливатель SSOR для решения задач электро-магнетизма в частотной области / Д.С. Бутюгин // Вычислительные методы и программирование. — 2011. — Т. 12, № 1. — С. 110–117.
Toward an h-independent algebraic multigrid method for Maxwell’s equations / J. Hu, R. Tuminaro, P. Bochev et al. // SIAM Journal on Scientific Computing. — 2005. — Vol. 27, № 5. — P. 1669–1688.
