Related papers: Controlled-source electromagnetic modelling using …
In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is…
The timestep of the Finite-Difference Time-Domain method (FDTD) is constrained by the stability limit known as the Courant-Friedrichs-Lewy (CFL) condition. This limit can make FDTD simulations quite time consuming for structures containing…
We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as…
This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…
The calculation of the local density of states (LDOS) in lossy materials has long been disputed due to the divergence of the homogeneous Green function with equal space arguments. For arbitrary shaped lossy structures, such as those of…
Solving the three-dimensional (3D) Bratu equation is highly challenging due to the presence of multiple and sharp solutions. Research on this equation began in the late 1990s, but there are no satisfactory results to date. To address this…
This letter is devoted to point out a specific character of the Finite-Difference-Time-Domain method through the study of nano-structures supporting geometrical symmetry-protected modes that can not be excited at certain conditions of…
This paper proposes a novel Generalized Non-Standard Finite Difference (GNSFD) scheme for the numerical solution of a class of fractional partial differential equations (FrPDEs). The formulation of the method is grounded in optimization and…
A class of nonstandard pseudospectral time domain (PSTD) schemes for solving time-dependent hyperbolic and parabolic partial differential equations (PDEs) is introduced. These schemes use the Fourier collocation spectral method to compute…
In this paper, we propose a novel numerical method for modeling nanostructures containing dispersive and nonlinear two-dimensional (2D) materials, by incorporating a nonlinear generalized source (GS) into the finite-difference time-domain…
Among several techniques available for solving Computational Electromagnetics (CEM) problems, the Finite Difference Time Domain (FDTD) method is one of the best suited approaches when a parallelized hardware platform is used. In this paper…
We show how two-dimensional mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo-uniform…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
Large power systems are complex and real-time modeling of the grid for electromagnetic simulation (EMT) studies is impractical. In general, there are methods that reduce large power system into an equivalent network that requires less…
We describe a simple and intuitive implementation of the method of finite difference time domain simulations for propagating electromagnetic waves using the simplest possible tools available in Microsoft Excel. The method overcomes the…
We propose a high-order FDTD scheme based on the correction function method (CFM) to treat interfaces with complex geometry without increasing the complexity of the numerical approach for constant coefficients. Correction functions are…
Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset/wide-azimuth node data can be designed with a few discrete frequencies. However, 3D frequency-domain seismic modeling remains challenging since it requires solving a…
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…
In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…