Related papers: A multi-moment scheme for the two dimensional Maxw…
The ion distribution around charged colloids in solution has been investigated intensely during the last decade. However, few theoretical approaches have included the influence of variation in the dielectric permittivity within the system,…
A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…
We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order~$\alpha \in (0,1)$. The basic idea of our scheme is based on local integration followed by linear…
When solving the Helmholtz equation numerically, the accuracy of numerical solution deteriorates as the wave number $k$ increases, known as `pollution effect' which is directly related to the phase difference between the exact and numerical…
Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…
In this article, we study a two-dimensional singularly perturbed parabolic equation of the convection-diffusion type, characterized by discontinuities in the source term and convection coefficient at a specific point in the domain. These…
We combine two important recent advancements of MCMC algorithms: first, methods utilizing the intrinsic manifold structure of the parameter space; then, algorithms effective for targets in infinite-dimensions with the critical property that…
Error estimates of cubic interpolated pseudo-particle scheme (CIP scheme) for the one-dimensional advection equation with periodic boundary conditions are presented. The CIP scheme is a semi-Lagrangian method involving the piecewise cubic…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing…
We present a six-moment multi-fluid model, which solves the governing equations for both ions and electrons, with pressure anisotropy along and perpendicular to the magnetic field direction, as well as the complete set of Maxwell equations.…
This is the first part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In this first part, the Fourier Singular Complement Method is introduced and analysed,…
We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…
The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and…
A novel approach to computing time-harmonic solutions of Maxwell's equations by time-domain simulations is presented. The method, EM-WaveHoltz, results in a positive definite system of equations which makes it amenable to iterative solution…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…
We present a new numerical scheme for solving the advection equation and its application to the Vlasov simulation. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent…
A reaction-diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the exact solution is proposed. The truncation error estimate of the discretization…
A new splitting is proposed for solving the Vlasov-Maxwell system. This splitting is based on a decomposition of the Hamiltonian of the Vlasov-Maxwell system and allows for the construction of arbitrary high order methods by composition…
Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Maxwell equations, conventional methods…