| Title:
|
Time-dependent electromagnetic waves in a cavity (English) |
| Author:
|
Kjellmert, Bo |
| Author:
|
Strömberg, Thomas |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
17-45 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The electromagnetic initial-boundary value problem for a cavity enclosed by perfectly conducting walls is considered. The cavity medium is defined by its permittivity and permeability which vary continuously in space. The electromagnetic field comes from a source in the cavity. The field is described by a magnetic vector potential ${\bf A}$ satisfying a wave equation with initial-boundary conditions. This description through ${\bf A}$ is rigorously shown to give a unique solution of the problem and is the starting point for numerical computations. A Chebyshev collocation solver has been implemented for a cubic cavity, and it has been compared to a standard finite element solver. The results obtained are consistent while the collocation solver performs substantially faster. Some time histories and spectra are computed. (English) |
| Keyword:
|
time-dependent electromagnetic field |
| Keyword:
|
cavity |
| Keyword:
|
vector and scalar potentials |
| Keyword:
|
Lorenz gauge |
| Keyword:
|
Chebyshev collocation |
| MSC:
|
35Q60 |
| MSC:
|
65M70 |
| MSC:
|
78A25 |
| MSC:
|
78A40 |
| MSC:
|
78M22 |
| idZBL:
|
Zbl 1212.78005 |
| idMR:
|
MR2476019 |
| DOI:
|
10.1007/s10492-009-0002-z |
| . |
| Date available:
|
2010-07-20T12:43:53Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140347 |
| . |
| Reference:
|
[1] Assous, F., P. Ciarlet, Jr., Labrunie, S., Segre, J.: Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: The singular complement method.J. Comput. Phys. 191 (2003), 147-176. Zbl 1033.65086, MR 2008488, 10.1016/S0021-9991(03)00309-7 |
| Reference:
|
[2] Assous, F., Degond, P., Heintze, E., Raviart, P.-A., Segre, J.: On a finite-element method for solving the three-dimensional Maxwell equations.J. Comput. Phys. 109 (1993), 222-237. Zbl 0795.65087, MR 1253460, 10.1006/jcph.1993.1214 |
| Reference:
|
[3] Dautray, R., Lions, J.-L.: Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 3: Spectral Theory and Applications.Springer Berlin (1990). MR 1064315 |
| Reference:
|
[4] Dautray, R., Lions, J.-L.: Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 5: Evolution Problems I.Springer Berlin (1992). Zbl 0755.35001, MR 1156075 |
| Reference:
|
[5] Duvaut, G., Lions, J.-L.: Inequalities in Mechanics and Physics. Grundlehren der mathematischen Wissenschaften, 219.Springer Berlin-New York (1976). MR 0521262 |
| Reference:
|
[6] Evans, L. C.: Partial Differential Equations. Graduate Studies in Mathematics, 19.American Mathematical Society (AMS) Providence (1998). MR 1625845 |
| Reference:
|
[7] Hughes, T. J. R.: The Finite Element Method. Linear static and Dynamic Finite Element Analysis.Prentice-Hall Englewood Cliffs (1987). Zbl 0634.73056, MR 1008473 |
| Reference:
|
[8] Jiang, B., Wu, J., Povinelli, L. A.: The origin of spurious solutions in computational electromagnetics.J. Comput. Phys. 125 (1996), 104-123. Zbl 0848.65086, MR 1381806, 10.1006/jcph.1996.0082 |
| Reference:
|
[9] Ku, H. L., Hatziavramidis, D.: Chebyshev expansion methods for the solution of the extended Graetz problem.J. Comput. Phys. 56 (1984), 495-512. Zbl 0572.76084, MR 0768673, 10.1016/0021-9991(84)90109-8 |
| Reference:
|
[10] Munz, C.-D., Omnes, P., Schneider, R., Sonnendrücker, E., Voss, U.: Divergence correction techniques for Maxwell solvers based on a hyperbolic model.J. Comput. Phys. 161 (2000), 484-511. MR 1764247, 10.1006/jcph.2000.6507 |
| Reference:
|
[11] Panofsky, W. K. H., Phillips, M.: Classical Electricity and Magnetism, 2nd ed.Addison-Wesley Reading (1962). Zbl 0122.21401, MR 0135824 |
| Reference:
|
[12] Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, 44.Springer New York (1983). MR 0710486 |
| Reference:
|
[13] Wloka, J.: Partial Differential Equations.Cambridge University Press Cambridge (1987). Zbl 0623.35006, MR 0895589 |
| Reference:
|
[14] : COMSOL$^{®}$, The COMSOL AB's homepage, www.comsol.com.. Zbl 1220.65080 |
| Reference:
|
[15] : MATLAB$^{®}$, The MathWorks, Inc. MATLAB's homepage, www.mathworks.com.. Zbl 1234.92044 |
| . |
