Related papers: Efficient Large Scale Electromagnetics Simulations…
This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretization, we introduce an auxiliary variable analogous to the…
Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps…
Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is…
We extend the applicability of the popular interior-penalty discontinuous Galerkin (dG) method discretizing advection-diffusion-reaction problems to meshes comprising extremely general, essentially arbitrarily-shaped element shapes. In…
The study of the continuum radiative transfer problem inside circumstellar envelopes is both a theoretical and numerical challenge, especially in the frequency-dependent and multi-dimensional case. While approximate methods are easier to…
In this paper, we apply a specifically designed dissipative spatial filter as sub-grid scale model within the increasingly popular discontinuous Galerkin methods and the closely related flux reconstruction high order methods for large eddy…
The discontinuous Galerkin (DG) method is an established method for computing approximate solutions of partial differential equations in many applications. Unlike continuous finite elements, in DG methods, numerical fluxes are used to…
We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…
This paper presents a high-order discontinuous Galerkin (DG) scheme for the simulation of wave propagation through coupled elastic-acoustic media. We use a first-order stress-velocity formulation, and derive a simple upwind-like numerical…
In this paper we present a new multiscale discontinuous Petrov--Galerkin method (MsDPGM) for multiscale elliptic problems. This method utilizes the classical oversampling multiscale basis in the framework of Petrov--Galerkin version of…
This paper generalizes the earlier work on the energy-based discontinuous Galerkin method for second-order wave equations to fourth-order semilinear wave equations. We first rewrite the problem into a system with a second-order spatial…
This study introduces the divergence-conforming discontinuous Galerkin finite element method (DGFEM) for numerically approximating optimal control problems with distributed constraints, specifically those governed by stationary generalized…
Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by…
We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled…
Plasmonic nanostructures significantly improve the performance of photoconductive devices (PCDs) in generating terahertz radiation. However, they are geometrically intricate and result in complicated electromagnetic (EM) field and carrier…
In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on…
A Discontinuous Galerkin (DG) Finite Element Method (FEM) approach for the 3D time dependent Maxwell equations in unbounded domains is presented. The method (implemented in the FEM library NGsolve) is based on the covariant transformation…
A conforming discontinuous Galerkin finite element method is introduced for solving the biharmonic equation. This method, by its name, uses discontinuous approximations and keeps simple formulation of the conforming finite element method at…
In this paper, a new strategy for a sub-element based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collection of data and construct a hierarchy of low to high order…