Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A domain decomposition method for the Helmholtz equation and related optimal control problems
Journal of Computational Physics
Multigrid Method for Maxwell's Equations
SIAM Journal on Numerical Analysis
Optimized Schwarz Methods without Overlap for the Helmholtz Equation
SIAM Journal on Scientific Computing
An Optimal Parallel Nonoverlapping Domain Decomposition Iterative Procedure
SIAM Journal on Numerical Analysis
Conservative load transfer along curved fluid-solid interface with non-matching meshes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Journal of Computational Physics
Hi-index | 31.50 |
A non-overlapping domain decomposition method (DDM) is proposed herein to solve Maxwell equations in R^3. In this work, the Maxwell equations are discretized using a vector finite element method with hierarchical H(curl) vector basis functions. There are two major ingredients in the proposed non-overlapping DDM: (a) A proper 1st order transmission condition to enforce field continuity across domain boundaries and (b) A cement technique to allow non-matching grids for neighboring domains. Moreover, a detail Fourier analysis of the transmission condition for a canonical half-space example is presented. The analysis provides significant insights into the convergence behavior of the proposed non-overlapping DDM for solving electromagnetic radiation problems, such as the large finite antenna arrays. Particularly for the antenna arrays, the proposed non-overlapping DDM is extremely efficient since the formulation can easily incorporate geometrical repetitions. Exponentially tapered notch (Vivaldi) antenna arrays with size up to 100x100 elements are solved on a common PC to validate the proposed non-overlapping DDM.