相关论文: Exact Charge-Conserving Scatter-Gather Algorithm f…
We present a set of linear, second order, unconditionally energy stable schemes for the Allen-Cahn equation with nonlocal constraints that preserves the total volume of each phase in a binary material system. The energy quadratization…
We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulation uses flux reconstruction (FR) in the spatial dimension…
A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve…
The aim of this paper is to develop stable and accurate numerical schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting boundary…
We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our…
In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is proved that…
This paper outlines a conservative transport scheme for scalar tracers within a compatible finite element model for geophysical fluid equations. Instead of using the advective transport equation for a mixing ratio, a conservative transport…
We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal…
By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle-mesh scheme which allows for diffusion-free advection, satisfies mass and momentum conservation principles in a…
In this paper, several two-grid finite element algorithms for solving parabolic integro-differential equations (PIDEs) with nonlinear memory are presented. Analysis of these algorithms is given assuming a fully implicit time discretization.…
The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers,…
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…
A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using using both canonical and non-canonical Hamiltonian formulations. Our…
We propose a modified Trefftz Discontinuous Galerkin (TDG) method for approximating a time-harmonic acoustic scattering problem in an infinitely elongated waveguide. In the waveguide we suppose there is a bounded, penetrable and possibly…
We give a detailed review of construction of conserved quantities in extended theories of gravity for asymptotically maximally symmetric spacetimes and carry out explicit computations for various solutions. Our construction is based on the…
The proposed distributed dynamic clustering algorithm enables to group agents based on their pre-selected feature states. The clusters are determined by comparing the distance of the agents' current feature states with average estimates of…
We propose energy-conserving discontinuous Galerkin (DG) methods for symmetric linear hyperbolic systems on general unstructured meshes. Optimal a priori error estimates of order $k+1$ are obtained for the semi-discrete scheme in one…
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…
We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements,…
In this study I develop a novel action for lattice gauge theory for finite systems, which accommodates non-periodic boundary conditions, implements the proper integral form of Gauss' law and exhibits an inherently symmetric energy momentum…