A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
The fast multipole method: numerical implementation
Journal of Computational Physics
Computational aspects of the ultra-weak variational formulation
Journal of Computational Physics
Coupling of Finite Elements and Boundary Elements in Electromagnetic Scattering
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Discontinuous Galerkin methods with plane waves for time-harmonic problems
Journal of Computational Physics
An ultra-weak method for acoustic fluid-solid interaction
Journal of Computational and Applied Mathematics
Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the $p$-Version
SIAM Journal on Numerical Analysis
Combining the Ultra-Weak Variational Formulation and the multilevel fast multipole method
Applied Numerical Mathematics
The ultra weak variational formulation of thin clamped plate problems
Journal of Computational Physics
Hi-index | 31.46 |
We investigate the ultra weak variational formulation for simulating time-harmonic Maxwell problems. This study has two main goals. First, we introduce a novel derivation of the UWVF method which shows that the UWVF is an unusual version of the standard upwind discontinuous Galerkin (DG) method with a special choice of basis functions. Second, we discuss the practical implementation of an electromagnetic UWVF solver. In particular, we propose a method to avoid the conditioning problems that are known to hamper the use of the UWVF for problems in general geometries and inhomogeneous media. In addition, we show how to implement the PML in the UWVF to accurately approximate physically unbounded problems and discuss the parallelization of the UWVF. Three-dimensional numerical simulations are used to examine the feasibility of the UWVF for simulating wave propagation in inhomogeneous media and scattering from complex structures.