publication . Article . Preprint . 2017

High-Performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method

Kruglyakov, Mikhail; Bloshanskaya, Lidia;
Open Access
  • Published: 03 Mar 2017 Journal: Mathematical Geosciences, volume 49, pages 751-776 (issn: 1874-8961, eissn: 1874-8953, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
  • Country: Switzerland
Abstract
Comment: The main results of this paper were presented at IAMG 2015 conference Frieberg, Germany. 28 pages, 11 figures
Subjects
free text keywords: Integral equations; Forward modeling; Electromagnetic sounding; Galerkin method; Green’s tensor; High-performance computing, General Earth and Planetary Sciences, Mathematics (miscellaneous), Degree of parallelism, Computational science, Statistics, Integral equation, Matrix (mathematics), Galerkin method, Electromagnetics, Solver, Supercomputer, Mathematics, Scalability, Mathematics - Numerical Analysis, Physics - Geophysics
33 references, page 1 of 3

Anderson W (1979) Numerical integration of related hankel transforms of order 0 and 1 by adaptive digital filtering. Geophysics 44:1287-1305

Avdeev D, Knizhnik S (2009) 3D integral equation modeling with a linear dependence on dimensions. Geophysics 74:89-94 [OpenAIRE]

Avdeev D, Kuvshinov A, Pankratov O, Newman G (2002) Three-dimensional induction logging problems, Part I: An integral equation solution and model comparisons. Geophysics 67(2):413-426 [OpenAIRE]

Avdeev DB, Kuvshinov AV, Pankratov OV, Newman GA (1997) High-performance three-dimensional electromagnetic modelling using modified neumann series. wide-band numerical solution and examples. J Geomagn Geoelectr 49:1519-1539

Bo¨rner RU (2010) Numerical modelling in geo-electromagnetics: advances and challenges. Surv Geophys 31:225-245

Chave A, Jones A (2012) The Magnetotelluric Method: Theory and Practice. Cambridge Univ. Press [OpenAIRE]

Delves LM, Mohamed JL (1985) Computational Methods for Integral Equations. Cambridge University Press [OpenAIRE]

Dmitriev V, Silkin A, Farzan R (2002) Tensor Green function for the system of Maxwell's equations in a layered medium. Comput Math and Modeling 13(2):107- 118 [OpenAIRE]

Ernst O, Gander M (2012) Why it is difficult to solve helmholtz problems with classical iterative methods. In: Graham IG, Hou TY, Lakkis O, Scheichl R (eds) Numerical Analysis of Multiscale Problems, Lecture Notes in Computational Science and Engineering, vol 83, Springer Berlin Heidelberg, pp 325-363

Fraysse V, Giraud L, Gratton S, Langou J (2003) A set of GMRES routines for real and complex arithmetics on high performance computers. URL http://www. cerfacs.fr/algor/reports/2003/TR_PA_03_03.pdf

Grayver A, Kolev T (2015) Large-scale 3d geo-electromagnetic modeling using parallel adaptive high-order finite element method. Geophysics 80(6):277-291

Hursan G, Zhdanov MS (2002) Contraction integral equation method in threedimensional electromagnetic modeling. Radio Sci 37(6):1-13 [OpenAIRE]

Kamm J, Pedersen LB (2014) Inversion of airborne tensor VLF data using integral equations. Geophys J Int 198(2):775-794 [OpenAIRE]

Koyama T, Utada H, Avdeev D (2008) Fast and memory-saved 3-D forward modeling code for MT by using integral equation method. In: Abstract book, 19th workshop on electromagnetic induction in the Earth, China

Kruglyakov M (2011) Modified integral current methods in electrodynamics of nonhomogeneous media. Comput Math and Modeling 22(3):246-254 [OpenAIRE]

33 references, page 1 of 3
Related research
Abstract
Comment: The main results of this paper were presented at IAMG 2015 conference Frieberg, Germany. 28 pages, 11 figures
Subjects
free text keywords: Integral equations; Forward modeling; Electromagnetic sounding; Galerkin method; Green’s tensor; High-performance computing, General Earth and Planetary Sciences, Mathematics (miscellaneous), Degree of parallelism, Computational science, Statistics, Integral equation, Matrix (mathematics), Galerkin method, Electromagnetics, Solver, Supercomputer, Mathematics, Scalability, Mathematics - Numerical Analysis, Physics - Geophysics
33 references, page 1 of 3

Anderson W (1979) Numerical integration of related hankel transforms of order 0 and 1 by adaptive digital filtering. Geophysics 44:1287-1305

Avdeev D, Knizhnik S (2009) 3D integral equation modeling with a linear dependence on dimensions. Geophysics 74:89-94 [OpenAIRE]

Avdeev D, Kuvshinov A, Pankratov O, Newman G (2002) Three-dimensional induction logging problems, Part I: An integral equation solution and model comparisons. Geophysics 67(2):413-426 [OpenAIRE]

Avdeev DB, Kuvshinov AV, Pankratov OV, Newman GA (1997) High-performance three-dimensional electromagnetic modelling using modified neumann series. wide-band numerical solution and examples. J Geomagn Geoelectr 49:1519-1539

Bo¨rner RU (2010) Numerical modelling in geo-electromagnetics: advances and challenges. Surv Geophys 31:225-245

Chave A, Jones A (2012) The Magnetotelluric Method: Theory and Practice. Cambridge Univ. Press [OpenAIRE]

Delves LM, Mohamed JL (1985) Computational Methods for Integral Equations. Cambridge University Press [OpenAIRE]

Dmitriev V, Silkin A, Farzan R (2002) Tensor Green function for the system of Maxwell's equations in a layered medium. Comput Math and Modeling 13(2):107- 118 [OpenAIRE]

Ernst O, Gander M (2012) Why it is difficult to solve helmholtz problems with classical iterative methods. In: Graham IG, Hou TY, Lakkis O, Scheichl R (eds) Numerical Analysis of Multiscale Problems, Lecture Notes in Computational Science and Engineering, vol 83, Springer Berlin Heidelberg, pp 325-363

Fraysse V, Giraud L, Gratton S, Langou J (2003) A set of GMRES routines for real and complex arithmetics on high performance computers. URL http://www. cerfacs.fr/algor/reports/2003/TR_PA_03_03.pdf

Grayver A, Kolev T (2015) Large-scale 3d geo-electromagnetic modeling using parallel adaptive high-order finite element method. Geophysics 80(6):277-291

Hursan G, Zhdanov MS (2002) Contraction integral equation method in threedimensional electromagnetic modeling. Radio Sci 37(6):1-13 [OpenAIRE]

Kamm J, Pedersen LB (2014) Inversion of airborne tensor VLF data using integral equations. Geophys J Int 198(2):775-794 [OpenAIRE]

Koyama T, Utada H, Avdeev D (2008) Fast and memory-saved 3-D forward modeling code for MT by using integral equation method. In: Abstract book, 19th workshop on electromagnetic induction in the Earth, China

Kruglyakov M (2011) Modified integral current methods in electrodynamics of nonhomogeneous media. Comput Math and Modeling 22(3):246-254 [OpenAIRE]

33 references, page 1 of 3
Related research
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publication . Article . Preprint . 2017

High-Performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method

Kruglyakov, Mikhail; Bloshanskaya, Lidia;