Domain decomposition methods for systems of conservation laws: spectral collocation approximations
SIAM Journal on Scientific and Statistical Computing
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
SIAM Journal on Scientific Computing
Elementary Numerical Analysis: An Algorithmic Approach
Elementary Numerical Analysis: An Algorithmic Approach
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
A High-Order Accurate Parallel Solver for Maxwell’s Equations on Overlapping Grids
SIAM Journal on Scientific Computing
| Hi-index | 0.00 |
The domain decomposition method based on overlapping grids is developed to solve the two-dimensional Maxwell equations in the time domain. The finite difference schemes for rectangular and polar coordinate systems are presented. Since interpolation plays a crucial role in our method, the Newton and the Fourier interpolation methods are surveyed in detail. The computational studies of the electromagnetic wave propagation in free space and the back-scattering by a perfect electric conducting object of a circular shape are performed to test the accuracy, the convergence, and the efficiency of our method. Moreover, we give a methodology to model dispersive media in time domain simulations by introducing Drude conductivity in the constitutive equations. The problem of light scattering by metallic nanoparticles is solved, and its results show that our algorithm is efficient and reliable in capturing the small scale phenomena.