Related papers: High-Order Accurate FDTD Schemes for Dispersive Ma…
We consider the numerical solution of partial differential equations with coefficients that are strongly heterogeneous in space. We provide an overview of higher-order localized orthogonal decomposition (LOD) methods for the elliptic…
Propagation characteristics of a wave are defined by the dispersion relationship, from which the governing partial differential equation (PDE) can be recovered. PDEs are commonly solved numerically using the finite-difference (FD) method,…
In this paper, an efficient algorithm is presented by the extrapolation technique to improve the accuracy of finite difference schemes for solving the fractional boundary value problems with non-smooth solution. Two popular finite…
A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion…
A class of second order approximations, called the weighted and shifted Gr\"{u}nwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the…
In this work, we introduce a novel Hermite method to handle Maxwell's equations for nonlinear dispersive media. The proposed method achieves high-order accuracy and is free of any nonlinear algebraic solver, requiring solving instead small…
Time domain simulations of electromagnetic problems are highly valuable in engineering applications, as they allow for the analysis of transient behavior and broadband responses. These simulations utilize time stepping schemes, where each…
Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
In this paper, we present how high-order accurate solutions to elliptic partial differential equations can be achieved in arbitrary spatial domains using radial basis function-generated finite differences (RBF-FD) on unfitted node sets…
Anomalous diffusion is often modelled in terms of the subdiffusion equation, which can involve a weakly singular source term. For this case, many predominant time stepping methods, including the correction of high-order BDF schemes [{\sc…
In this paper, we present an accurate numerical method for the time-harmonic Maxwell's equations for bi-periodic multilayered media with quasi-periodic incident waves using the Method of Fundamental Solutions in conjunction with a…
Based on the weighted and shifted Gr\"{u}nwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then the discretization schemes are used to approximate the…
A high-order space-time flux reconstruction (FR) method has been developed to solve conservation laws on moving domains. In the space-time framework, the moving domain simulation is similar to that on a stationary domain, except that the…
Computational electrodynamics (CED), the numerical solution of Maxwell's equations, plays an incredibly important role in several problems in science and engineering. High accuracy solutions are desired, and the discontinuous Galerkin (DG)…
We describe a method for incorporating ambipolar diffusion in the strong coupling approximation into a multidimensional magnetohydrodynamics code based on the total variation diminishing scheme. Contributions from ambipolar diffusion terms…
In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…
We present a simple and efficient Finite-Difference Time-Domain (FDFD) scheme for simulating dispersive (Lorentz-Debye) bianisotropic metasurfaces. This scheme replaces the conventional FDTD update equations by augmented update equations…