A new family of mixed finite elements in IR3
Numerische Mathematik
Numerical solution of the Helmholtz equation in 2D and 3D using a high-order Nystro¨m discretization
Journal of Computational Physics
Mimetic discretizations for Maxwell's equations
Journal of Computational Physics
Canonical construction of finite elements
Mathematics of Computation
On the Eigenvalues of the Volume Integral Operator of Electromagnetic Scattering
SIAM Journal on Scientific Computing
Fast and Efficient Algorithms in Computational Electromagnetics
Fast and Efficient Algorithms in Computational Electromagnetics
Decoupling Three-Dimensional Mixed Problems Using Divergence-Free Finite Elements
SIAM Journal on Scientific Computing
Volume and surface integral equations for electromagnetic scattering by a dielectric body
Journal of Computational and Applied Mathematics
On the complexity of aperiodic Fourier modal methods for finite periodic structures
Journal of Computational Physics
Hi-index | 31.46 |
Time-harmonic electromagnetic scattering by inhomogeneous, three-dimensional structures within a free space environment can be described by electric- and magnetic field, volume integral equations involving the free space Green function. A comprehensive set of Galerkin projection formulations (also known as moment methods) for the numerical solution of these equations is presented, together with comparative numerical results. Such formulations are widely used for particle scattering analysis, optical near field calculation, etc. Results are obtained with higher-order, divergence-and curl-conforming basis functions on iso-parametric, tetrahedral meshes. The results demonstrate that all formulations converge with similar accuracy in the case of an analytically-solvable test problem. When modeling flux densities as solution variables, it is argued that solenoidal function spaces should be used, rather than the standard divergence-conforming function spaces; this assertion is supported by the results. Some of the formulations involve solving for curl-conforming fields; such fields can be discretized with fewer unknowns than divergence-conforming ones, implying lower computational costs. Additionally, some formulations yield system matrices which are approximately halfway sparse, meaning that computational costs will be down by a factor of 2 when iterative solvers are employed, which is the case for the widely-used fast methods.