ﻻ يوجد ملخص باللغة العربية
A new finite difference method on irregular, locally perturbed rectangular grids has been developed for solving electromagnetic waves around curved perfect electric conductors (PEC). This method incorporates the back and forth error compensation and correction method (BFECC) and level set method to achieve convenience and higher order of accuracy at complicated PEC boundaries. A PDE-based local second order ghost cell extension technique is developed based on the level set framework in order to compute the boundary value to first order accuracy (cumulatively), and then BFECC is applied to further improve the accuracy while increasing the CFL number. Numerical experiments are conducted to validate the properties of the method.
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly, and high ord
In this paper, we combine the nonlinear HWENO reconstruction in cite{newhwenozq} and the fixed-point iteration with Gauss-Seidel fast sweeping strategy, to solve the static Hamilton-Jacobi equations in a novel HWENO framework recently developed in ci
We propose a controllability method for the numerical solution of time-harmonic Maxwells equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the controllability method
We develop a stable finite difference method for the elastic wave equations in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equations are discretized in second order form by a fourth or sixth o
The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334] is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is based on a fix