[Électromagnétique harmonique temporelle avec contrôlabilité exacte et calcul extérieur discret]
Dans cet article, nous appliquons le concept de contrôlabilité exacte à la dispersion électromagnétique temporelle. Le problème est présenté en termes de formes différentielles et le calcul extérieur discret est utilisé pour la discrétisation spatiale. En conséquence, les propriétés physiques du problème sont maintenues. Bien que nous considérions des problèmes harmoniques temporels, nous nous concentrons sur les équations d’ondes transitoires traitées par l’approche de contrôlabilité exacte. Essentiellement, nous utilisons une variation contrôlée de l’approche asymptotique avec des contraintes périodiques, dans laquelle l’équation dépendant du temps est simulée dans le temps, jusqu’à ce que la solution harmonique temporelle soit atteinte.
In this paper, we apply the exact controllability concept for time-harmonic electromagnetic scattering. The problem is presented in terms of the differential forms, and the discrete exterior calculus is utilized for spatial discretization. Accordingly, the physical properties of the problem are maintained. Despite we consider time-harmonic problems, we concentrate on transient wave equations treated by the exact controllability approach. Essentially, we use a controlled variation of the asymptotic approach with periodic constraints, in which the time-dependent equation is simulated in time, until the time-harmonic solution is reached.
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Mot clés : Équations de Maxwell, Diffusion électromagnétique, Formes différentielles, Calcul extérieur discret, Contrôlabilité exacte
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@article{CRMECA_2023__351_S1_647_0,
author = {Sanna M\"onk\"ol\"a and Jukka R\"abin\"a and Tuomo Rossi},
title = {Time-harmonic electromagnetics with exact controllability and discrete exterior calculus},
journal = {Comptes Rendus. M\'ecanique},
pages = {647--665},
publisher = {Acad\'emie des sciences, Paris},
volume = {351},
number = {S1},
year = {2023},
doi = {10.5802/crmeca.234},
language = {en},
}
TY - JOUR AU - Sanna Mönkölä AU - Jukka Räbinä AU - Tuomo Rossi TI - Time-harmonic electromagnetics with exact controllability and discrete exterior calculus JO - Comptes Rendus. Mécanique PY - 2023 SP - 647 EP - 665 VL - 351 IS - S1 PB - Académie des sciences, Paris DO - 10.5802/crmeca.234 LA - en ID - CRMECA_2023__351_S1_647_0 ER -
%0 Journal Article %A Sanna Mönkölä %A Jukka Räbinä %A Tuomo Rossi %T Time-harmonic electromagnetics with exact controllability and discrete exterior calculus %J Comptes Rendus. Mécanique %D 2023 %P 647-665 %V 351 %N S1 %I Académie des sciences, Paris %R 10.5802/crmeca.234 %G en %F CRMECA_2023__351_S1_647_0
Sanna Mönkölä; Jukka Räbinä; Tuomo Rossi. Time-harmonic electromagnetics with exact controllability and discrete exterior calculus. Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 647-665. doi : 10.5802/crmeca.234. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.234/
[1] Electromagnetic theory with discrete exterior calculus, Progr. Electromagn. Res., Volume 159 (2017), pp. 59-78 | DOI
[2] A discrete exterior calculus approach to quantum transport and quantum chaos on surface, J. Comput. Theor. Nanosci., Volume 16 (2019) no. 9, pp. 3670-3682 | DOI
[3] A geometric formulation of linear elasticity based on discrete exterior calculus, Int. J. Solids Struct., Volume 236 (2022), 111345
[4] Differential forms for scientists and engineers, J. Comput. Phys., Volume 257, Part B (2014), pp. 1373-1393 | DOI | MR | Zbl
[5] Compatible Spatial Discretizations (D. N. Arnold; P. B. Bochev; R. B. Lehoucq; R. A. Nicolaides; M. Shashkov, eds.), The IMA Volumes in Mathematics and its Applications, 142, Springer, New York, USA, 2006 | DOI
[6] Topics in structure-preserving discretization, Acta Numer., Volume 20 (2011), pp. 1-119 | MR | Zbl
[7] Differential Forms, Kershaw Publishing Company, London, 1971
[8] Discrete exterior calculus, 2005 (preprint) | arXiv
[9] Yee-like schemes on a tetrahedral mesh, with diagonal lumping, Int. J. Numer. Model., Volume 12 (1999) no. 1–2, pp. 129-142 | Zbl
[10] Discrete differential forms for computational modeling, Discrete Differ. Geom. Oberwolfach Semin., Volume 38 (2008), pp. 287-324 | MR | Zbl
[11] On high order finite element spaces of differential forms, Math. Comput., Volume 85 (2016) no. 298, pp. 517-548 | MR | Zbl
[12] Well-posedness via monotonicity—an overview, Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics, Springer, Cham, Switzerland, 2015, pp. 397-452 | Zbl
[13] On a connection between the Maxwell system, the extended Maxwell system, the Dirac operator and gravito-electromagnetism, Math. Methods Appl. Sci., Volume 40 (2017) no. 2, pp. 415-434 | MR | Zbl
[14] Efficient time integration of Maxwell’s equations by generalized finite-differences, SIAM J. Sci. Comput., Volume 37 (2015) no. 6, p. B834-B854 | Zbl
[15] Generalized wave propagation problems and discrete exterior calculus, ESAIM: Math. Model. Numer. Anal., Volume 52 (2018) no. 3, pp. 1195-1218 | MR | Zbl
[16] Controllability methods for the computation of time-periodic solutions; application to scattering, J. Comput. Phys., Volume 147 (1998) no. 2, pp. 265-292 | MR | Zbl
[17] Ensuring well-posedness by analogy; Stokes problem and boundary control for the wave equation, J. Comput. Phys., Volume 103 (1992) no. 2, pp. 189-221 | MR | Zbl
[18] Numerical simulation of high frequency scattering waves using exact controllability methods, Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects: Proceedings of the Fourth International Conference on Hyperbolic Problems, Taormina, Italy, April 3–8, 1992, Vieweg+Teubner Verlag, Wiesbaden, Germany, 1993, pp. 86-108 | Zbl
[19] Scattering waves using exact controllability methods, 31st Aerospace Sciences Meeting, American Institute of Aeronautics and Astronautics, Washington, USA, 1993
[20] 3D harmonic Maxwell solutions on vector and parallel computers using controllability and finite element methods (1999) no. RR-3607 (Technical report)
[21] A mixed formulation and exact controllability approach for the computation of the periodic solutions of the scalar wave equation. (I) Controllability problem formulation and related iterative solution, C. R. Acad. Sci. Paris, Volume 343 (2006) no. 7, pp. 493-498 | Numdam | MR
[22] Solution of time-periodic wave equation using mixed finite-elements and controllability techniques, J. Comput. Acoust., Volume 19 (2011) no. 4, pp. 335-352 | MR | Zbl
[23] A controllability method for Maxwell’s equations, SIAM J. Sci. Comput., Volume 44 (2022) no. 6, p. A3700-A3727 | MR | Zbl
[24] On a numerical solution of the Maxwell equations by discrete exterior calculus, Phd thesis, University of Jyväskylä (2014) http://urn.fi/URN:ISBN:978-951-39-5951-7
[25] Theoretical considerations on the computation of generalized time-periodic waves, Adv. Math. Sci. Appl., Volume 21 (2011) no. 1, pp. 105-131 | MR | Zbl
[26] Three-dimensional splitting dynamics of giant vortices in Bose–Einstein condensates, Phys. Rev. A, Volume 98 (2018), 023624 | DOI
[27] GPU-accelerated time integration of Gross–Pitaevskii equation with discrete exterior calculus, Comput. Phys. Commun., Volume 278 (2022), 108427 | MR | Zbl
[28] Evolution and decay of an Alice ring in a spinor Bose–Einstein condensate, Phys. Rev. Res., Volume 5 (2023) no. 2, 023104
[29] Systematisation of systems solving physics boundary value problems, Numerical Mathematics and Advanced Applications ENUMATH 2019: European Conference, Egmond aan Zee, The Netherlands, September 30–October 4, Springer, Cham, Switzerland, 2020, pp. 35-51 | Zbl
[30] Systematic derivation of partial differential equations for second order boundary value problems, Int. J. Numer. Model.: Electronic Networks, Devices and Fields, Volume 36 (2023) no. 3, e3078
[31] Whitney forms and their extensions, J. Comput. Appl. Math., Volume 393 (2021), 113520 | MR | Zbl
[32] Generalized finite difference schemes with higher order Whitney forms, ESAIM: Math. Model. Numer. Anal., Volume 55 (2021) no. 4, pp. 1439-1460 | MR | Zbl
[33] Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus, Numer. Algorithms, Volume 91 (2022) no. 3, pp. 1261-1285 | MR | Zbl
[34] Controllability method for the Helmholtz equation with higher-order discretizations, J. Comput. Phys., Volume 225 (2007) no. 2, pp. 1553-1576 | MR | Zbl
[35] Time-harmonic elasticity with controllability and higher order discretization methods, J. Comput. Phys., Volume 227 (2008) no. 11, pp. 5513-5534 | MR | Zbl
[36] An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes, J. Comput. Phys., Volume 242 (2013), pp. 439-459 | MR | Zbl
[37] Fully scalable solver for frequency-domain visco-elastic wave equations in 3D heterogeneous media: a controllability approach, J. Comput. Phys., Volume 468 (2022), 111514 | MR | Zbl
[38] Asynchronous variational integrators, Arch. Rational Mech. Anal., Volume 167 (2003) no. 2, pp. 85-146 | MR | Zbl
[39] Geometric computational electrodynamics with variational integrators and discrete differential forms, Geometry, Mechanics, and Dynamics: The Legacy of Jerry Marsden, Springer, New York, USA, 2015, pp. 437-475 | Zbl
[40] Stability and numerical dispersion analysis of CE-FDTD method, IEEE Trans. Antennas Propag., Volume 53 (2005) no. 1, pp. 332-338 | MR | Zbl
[41] EM-WaveHoltz: a flexible frequency-domain method built from time-domain solvers, IEEE Trans. Antennas Propag., Volume 70 (2022) no. 7, pp. 5659-5671
[42] Differential Forms in Electromagnetics, IEEE Press Series on Electromagnetic Wave Theory, Wiley, New Jersey, USA, 2004
[43] Differential forms and electromagnetic field theory, Progr. Electromagnet. Res., Volume 148 (2014), pp. 83-112 | DOI
[44] Differential Forms in Mathematical Physics, Studies in Mathematics and its Applications, North Holland, Amsterdam, Netherlands, 1978 | MR
[45] Delaunay Hodge star, Comput. Aided Des., Volume 45 (2013) no. 2, pp. 540-544 (Solid and Physical Modeling 2012) | DOI | MR
[46] Discrete exterior calculus for photonic crystal waveguides, Int. J. Numer. Methods Eng., Volume 124 (2023) no. 5, pp. 1035-1054 | DOI | MR
[47] Absorbing boundary conditions for Maxwell’s equations, Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects, Vieweg+Teubner Verlag, Wiesbaden, Germany, 1993, pp. 315-322 | Zbl
[48] A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., Volume 114 (1994) no. 2, pp. 185-200 | DOI | MR | Zbl
[49] Comparison of discrete exterior calculus and discrete-dipole approximation for electromagnetic scattering, J. Quant. Spectrosc. Rad. Transf., Volume 146 (2014), pp. 417-423 | DOI
[50] HOT: Hodge-optimized triangulations, ACM Trans. Graph., Volume 30 (2011) no. 4, 103 (p. 1–12) | DOI
[51] A novel method to analyse electromagnetic scattering of complex object, IEEE Trans. Electromagn. Compat., Volume 24 (1982) no. 4, pp. 397-405 | DOI
[52] Radar cross section of general three-dimensional scatterers, IEEE Trans. Electromagn. Compat., Volume 25 (1983) no. 4, pp. 433-440 | DOI
[53] Absorption and Scattering of Light by Small Particles, Wiley & Sons, New York, 1983, pp. 53-56
[54] MATLAB Functions for Mie scattering and absorption. Version 2 (2002) no. 2002–11 (Technical report)
[55] Zippered polygon meshes from range images, Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’94, ACM, New York, NY, USA, 1994, pp. 311-318 | DOI
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