scholarly journals On the approximation of electromagnetic fields by edge finite elements. Part 2: A heterogeneous multiscale method for Maxwell’s equations

2017 ◽  
Vol 73 (9) ◽  
pp. 1900-1919 ◽  
Author(s):  
Patrick Ciarlet Jr. ◽  
Sonia Fliss ◽  
Christian Stohrer
Keyword(s):  
Finite Elements ◽  
Electromagnetic Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Multiscale Method ◽  
Heterogeneous Multiscale

scholarly journals Heterogeneous Multiscale Method for Maxwell's Equations

2019 ◽  
Vol 17 (4) ◽  
pp. 1147-1171 ◽  
Author(s):  
Marlis Hochbruck ◽  
Bernhard Maier ◽  
Christian Stohrer
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Multiscale Method ◽  
Heterogeneous Multiscale

scholarly journals A New Heterogeneous Multiscale Method for Time-Harmonic Maxwell's Equations

2016 ◽  
Vol 54 (6) ◽  
pp. 3493-3522 ◽  
Author(s):  
Patrick Henning ◽  
Mario Ohlberger ◽  
Barbara Verfürth
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Multiscale Method ◽  
Time Harmonic ◽  
Heterogeneous Multiscale

scholarly journals Heterogeneous Multiscale Method for the Maxwell equations with high contrast

2019 ◽  
Vol 53 (1) ◽  
pp. 35-61 ◽  
Author(s):  
Barbara Verfürth
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Scattering Problem ◽  
Stability Result ◽  
Multiscale Method ◽  
High Contrast ◽  
Effective Parameters ◽  
Time Harmonic ◽  
Heterogeneous Multiscale ◽  
The Stability

In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the (time-harmonic) Maxwell scattering problem with high contrast. The method is constructed for a setting as in Bouchitté, Bourel and Felbacq [C.R. Math. Acad. Sci. Paris347(2009) 571–576], where the high contrast in the parameter leads to unusual effective parameters in the homogenized equation. We present a new homogenization result for this special setting, compare it to existing homogenization approaches and analyze the stability of the two-scale solution with respect to the wavenumber and the data. This includes a new stability result for solutions to time-harmonic Maxwell’s equations with matrix-valued, spatially dependent coefficients. The HMM is defined as direct discretization of the two-scale limit equation. With this approach we are able to show quasi-optimality anda priorierror estimates in energy and dual norms under a resolution condition that inherits its dependence on the wavenumber from the stability constant for the analytical problem. This is the first wavenumber-explicit resolution condition for time-harmonic Maxwell’s equations. Numerical experiments confirm our theoretical convergence results.

Plane wave ℋ (curl; Ω) conforming finite elements for Maxwell's equations

2003 ◽  
Vol 31 (3) ◽  
pp. 272-283 ◽  
Author(s):  
P. D. Ledger ◽  
K. Morgan ◽  
O. Hassan ◽  
N. P. Weatherill
Keyword(s):  
Finite Elements ◽  
Plane Wave ◽  
Maxwell’S Equations ◽  
Maxwell's Equations

Utilization of wavelet concepts in finite elements for an efficient solution of Maxwell's equations

Radio Science ◽  
1994 ◽  
Vol 29 (4) ◽  
pp. 965-977 ◽  
Author(s):  
Tapan K. Sarkar ◽  
Raviraj S. Adve ◽  
Luis Emilio García-Castillo ◽  
Magdalena Salazar-Palma
Keyword(s):  
Finite Elements ◽  
Maxwell’S Equations ◽  
Efficient Solution ◽  
Maxwell's Equations
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