Radiation Boundary Conditions for Maxwell's Equations: A Review of Accurate Time-Domain Formulations

Hagstrom, Thomas; Lau, Stephen R.

doi:10.21236/ada470448

Cited by 29 publications

(48 citation statements)

References 70 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To derive these, first let M = {(t, x) : x ≤ T − t} represent the solid past null cone of the spacetime point (T, 0, 0, 0). For a generic time t < T , let M t represent the closed portion of M lying to the future of time level t. Partial spherical means formulas arise from the following (also given in [14]). …”

Section: Partial Spherical Means Formulas and Boundary Conditions 183mentioning

confidence: 99%

“…Combining (2.13) with 14) that is, the ordinary spherical means formula (2.11), we obtain the mirror formula of (2.13),…”

Section: Partial Spherical Means Formulas and Boundary Conditions 183mentioning

confidence: 99%

“…After all differentiations, t 0 can be set to zero. Precisely, an order-multipole solution is given by 14) or in the Burke formalism [24],…”

Section: General Multipole Sourcesmentioning

confidence: 99%

“…This appendix shows that (2.24) is equivalent to the boundary condition of [4]. We have given the same argument before in [14]. For simplicity, we now take t 0 = 0, stop using capital letters T, X, Y, Z for the evaluation point, and suspend the CID notation (cf.…”

Section: Dωu (T (T − T)ν)mentioning

confidence: 99%

See 3 more Smart Citations

On partial spherical means formulas and radiation boundary conditions for the 3+1 wave equation

Lau

2010

Quart. Appl. Math.

View full text Add to dashboard Cite

Abstract. We derive various partial spherical means formulas for the 3+1 wave equation. Such formulas, considered earlier by both Weston and Teng, involve only partial integration over a solid angle in addition to history-dependent boundary terms, and are appropriate for faces, edges, and corners of "computational domains". For example, a hemispherical means formula corresponds to a face (plane boundary). Exploiting the theory of wave front sets for linear operators developed by Hörmander, Warchall has proved theorems which suggest the existence of "one-sided update formulas" for wave equations. We attempt to realize such an update formula via an explicit construction based on our hemispherical means formula. We focus on face points and plane boundaries, but also introduce one-fourth and one-eighth spherical means formulas with most of our arguments going through for a point located on either a domain edge or a corner. Throughout our analysis we encounter a number of, we believe, heretofore unknown identities for classical solutions to the wave equation.

show abstract

Section: Partial Spherical Means Formulas and Boundary Conditions 183mentioning

confidence: 99%

“…Combining (2.13) with 14) that is, the ordinary spherical means formula (2.11), we obtain the mirror formula of (2.13),…”

Section: Partial Spherical Means Formulas and Boundary Conditions 183mentioning

confidence: 99%

“…After all differentiations, t 0 can be set to zero. Precisely, an order-multipole solution is given by 14) or in the Burke formalism [24],…”

Section: General Multipole Sourcesmentioning

confidence: 99%

Section: Dωu (T (T − T)ν)mentioning

confidence: 99%

See 2 more Smart Citations

On partial spherical means formulas and radiation boundary conditions for the 3+1 wave equation

Lau

2010

Quart. Appl. Math.

View full text Add to dashboard Cite

show abstract

“…Strategies which follow this route are called analytical ABCs (AABCs). Even though higher-order schemes are available [10], in practice one usually employs lower order approximations of AABCs. While being relatively straightforward to implement, they suffer from mediocre performance for oblique incidence and small distances between the radiation source and the boundary [1].…”

Section: Introductionmentioning

confidence: 99%

Stretched-coordinate PMLs for Maxwell’s equations in the discontinuous Galerkin time-domain method

et al. 2011

View full text Add to dashboard Cite

Abstract:The discontinuous Galerkin time-domain method (DGTD) is an emerging technique for the numerical simulation of time-dependent electromagnetic phenomena. For many applications it is necessary to model the infinite space which surrounds scatterers and sources. As a result, absorbing boundaries which mimic its properties play a key role in making DGTD a versatile tool for various kinds of systems. Popular techniques include the Silver-Müller boundary condition and uniaxial perfectly matched layers (UPMLs). We provide novel instructions for the implementation of stretched-coordinate perfectly matched layers in a discontinuous Galerkin framework and compare the performance of the three absorbers for a three-dimensional test system.

show abstract

Numerical approximation based on a decoupled dimensionality reduction scheme for Maxwell eigenvalue problem

Jiang

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

We present a high‐accuracy numerical method based on a decoupled dimensionality reduction scheme for Maxwell eigenvalue problem in spherical domains. Using the orthogonality of vector spherical harmonics and the variable separation approach, we decompose the original problem into two classes of decoupled one‐dimensional TE mode and TM mode. For the TE mode, we establish a variational formulation and its discrete scheme and give the error estimations of the approximate eigenvalues and eigenfunctions. For the TM mode, it is different from TE mode which naturally meets the divergence‐free condition and will not generate some spurious eigenvalues. We design a numerical algorithm based on a parameterized method to filter out the spurious eigenvalues. Finally, some numerical results are presented to confirm the theoretical results and validate the algorithms.

show abstract

Radiation Boundary Conditions for Maxwell's Equations: A Review of Accurate Time-Domain Formulations

Cited by 29 publications

References 70 publications

On partial spherical means formulas and radiation boundary conditions for the 3+1 wave equation

On partial spherical means formulas and radiation boundary conditions for the 3+1 wave equation

Stretched-coordinate PMLs for Maxwell’s equations in the discontinuous Galerkin time-domain method

Numerical approximation based on a decoupled dimensionality reduction scheme for Maxwell eigenvalue problem

Contact Info

Product

Resources

About