An improved pseudospectral method for fluid dynamics boundary value problems
Journal of Computational Physics
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
High-Accuracy Finite-Difference Schemes for Linear Wave Propagation
SIAM Journal on Scientific Computing
Spectral simulations of electromagnetic wave scattering
Journal of Computational Physics
A block pseudospectral method for Maxwell's equations
Journal of Computational Physics
On the construction and analysis of absorbing layers in CEM
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
High-order compact-difference schemes for time-dependent Maxwell equations
Journal of Computational Physics
SIAM Journal on Scientific Computing
On the construction of a high order difference scheme for complex domains in a Cartesian grid
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Fourth order compact implicit method for the Maxwell equations with discontinuous coefficients
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Multidomain pseudospectral computation of Maxwell's equations in 3-D general curvilinear coordinates
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Journal of Computational Physics
An explicit fourth-order orthogonal curvilinear staggered-grid FDTD method for Maxwell's equations
Journal of Computational Physics
Comparison of High-Accuracy Finite-Difference Methods for Linear Wave Propagation
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Nodal high-order methods on unstructured grids
Journal of Computational Physics
An explicit fourth-order staggered finite-difference time-domain method for Maxwell's equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
A note on the numerical solution of high-order differential equations
Journal of Computational and Applied Mathematics
DSC time-domain solution of Maxwell's equations
Journal of Computational Physics
Journal of Computational Physics
Comparison of Taylor finite difference and window finite difference and their application in FDTD
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation
Journal of Computational Physics
Journal of Computational Physics
Optimized three-dimensional FDTD discretizations of Maxwell's equations on Cartesian grids
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
An interpolation matched interface and boundary method for elliptic interface problems
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Differential geometry based solvation model I: Eulerian formulation
Journal of Computational Physics
Multiscale molecular dynamics using the matched interface and boundary method
Journal of Computational Physics
Journal of Computational Physics
MIB method for elliptic equations with multi-material interfaces
Journal of Computational Physics
Second-order Poisson-Nernst-Planck solver for ion transport
Journal of Computational Physics
Journal of Computational Physics
The Journal of Supercomputing
Weak Galerkin methods for second order elliptic interface problems
Journal of Computational Physics
A molecular level prototype for mechanoelectrical transducer in mammalian hair cells
Journal of Computational Neuroscience
Hi-index | 31.53 |
This paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high-order finite-difference time-domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in one (1D) and two spatial dimensions (2D). By making use of fictitious points, systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage, to arbitrarily high orders of accuracy in principle. While often limited by numerical instability, orders up to 16 and 12 are achieved, respectively, in 1D and 2D. Detailed stability analyses are presented for the present approach to examine the upper limit in constructing embedded FDTD methods. As natural generalizations of the high-order FDTD schemes, the proposed derivative matching methods automatically reduce to the standard FDTD schemes when the material interfaces are absent. An interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code. Another feature of the present approach is that it can be robustly implemented with other high accuracy time-domain approaches, such as the multiresolution time-domain method and the local spectral time-domain method, to cope with material interfaces. Numerical experiments on both 1D and 2D problems are carried out to test the convergence, examine the stability, access the efficiency, and explore the limitation of the proposed methods. It is found that operating at their best capacity, the proposed high-order schemes could be over 2000 times more efficient than their fourth-order versions in 2D. In conclusion, the present work indicates that the proposed hierarchical derivative matching methods might lead to practical high-order schemes for numerical solution of time-domain Maxwell's equations with material interfaces.