相关论文: Multidomain Galerkin-Collocation method: character…

Distributed order fractional operators offer a rigorous tool for mathematical modelling of multi-physics phenomena, where the differential orders are distributed over a range of values rather than being just a fixed integer/fraction as it…

We introduce a Lagrangian nodal discontinuous Galerkin (DG) cell-centered hydrodynamics method for solving multi-dimensional hyperbolic systems. By incorporating an adaptation of Zalesak's flux-corrected transport algorithm, we combine a…

In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for scalar hyperbolic conservation laws in multidimensions. Compared with previous work for linear hyperbolic equations \cite{guo2016transport,…

The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great difficulties in numerical simulation. To tackle this…

We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…

The elucidation of many physical problems in science and engineering is subject to the accurate numerical modelling of complex wave propagation phenomena. Over the last decades, high-order numerical approximation for partial differential…

We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations…

In this paper, we propose an accurate numerical means built upon a spectral-Galerkin method in spatial discretization and an enriched multi-step spectral-collocation approach in temporal direction, for Maxwell equations in Cole-Cole…

In this paper we study the finite element approximation of systems of second-order nonlinear hyperbolic equations. The proposed numerical method combines a $hp$-version discontinuous Galerkin finite element approximation in the time…

We consider the one-dimensional shallow water equations (SW) in a finite channel with variable bottom topography. We pose several initial-boundary-value problems for the SW system, including problems with transparent (characteristic)…

We present a fast spectral Galerkin scheme for the discretization of boundary integral equations arising from two-dimensional Helmholtz transmission problems in multi-layered periodic structures or gratings. Employing suitably parametrized…

Conductor moving in magnetic field is quite common in electrical equipment. The numerical simulation of such problem is vital in their design and analysis of electrical equipment. The Galerkin finite element method (GFEM) is a commonly…

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order…

We investigate numerically spherically symmetric collapse of a scalar field in the semi-classical approximation. We first verify that our code reproduces the critical phenomena (the Choptuik effect) in the classical limit and black hole…

This paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with triangular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial…

A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron-molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic…

Although Galerkin discretizations have been intensively employed in the IgA context, an efficient implementation requires special numerical quadrature rules when constructing the system of equations. To avoid this issue, isogeometric…

We propose a new discontinuous Galerkin Isogeometric Analysis (IgA) technique for the numerical solution of elliptic diffusion problems in computational domains decomposed into volumetric patches with non-matching interfaces. Due to an…

We present and analyze a methodology for numerical homogenization of spatial networks, modelling e.g. diffusion processes and deformation of mechanical structures. The aim is to construct an accurate coarse model of the network. By solving…

A new computational algorithm, the discrete singular convolution (DSC), is introduced for computational electromagnetics. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied.…