Geodesic
Time-dependent electromagnetic waves in a cavity
Applications of Mathematics, Tome 54 (2009) no. 1, pp. 17-45
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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.
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.
DOI : 10.1007/s10492-009-0002-z
Classification : 35Q60, 65M70, 78A25, 78A40, 78M22
Keywords: time-dependent electromagnetic field; cavity; vector and scalar potentials; Lorenz gauge; Chebyshev collocation 
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Kjellmert, Bo; Strömberg, Thomas. Time-dependent electromagnetic waves in a cavity. Applications of Mathematics, Tome 54 (2009) no. 1, pp. 17-45. doi: 10.1007/s10492-009-0002-z

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