Related papers: Structure-preserving numerical schemes for Lindbla…
In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent…
In this paper, we propose a general numerical framework to derive structure-preserving reduced order models for thermodynamically consistent PDEs. Our numerical framework has two primary features: (a) a systematic way to extract reduced…
This paper deals with the construction of numerical stable solutions of random mean square Fisher-KPP models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique…
For more than half a century, most of the plasma scientists have encountered a violation of the conservation laws of charge, momentum, and energy whenever they have numerically solve the first-principle equations of kinetic plasmas, such as…
A standard assumption in the study of logarithmic structures is "fineness", but this assumption is not preserved by intersections, fiber products, and more general limits. We explain how a coherent logarithmic scheme $X$ has a natural…
The stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability of a non-linear scheme in terms of its cor- responding scheme in…
We propose a structure-preserving finite difference scheme for the Cahn-Hilliard equation with a dynamic boundary condition using the discrete variational derivative method (DVDM). In this approach, it is important and essential how to…
A high-order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the $Q_k$ finite element with mass lumping on rectangular grids, the second-order…
We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variational principle. The method is based on the invariantization…
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…
We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow and an intermediate evolution law in an axisymmetric setting. The weak formulations are presented in terms of…
Two-fluid relativistic plasma flow equations combine the equations of relativistic hydrodynamics with Maxwell's equations for electromagnetic fields, which involve divergence constraints for the magnetic and electric fields. When developing…
Semi-Lagrangian schemes have proven to be very efficient to model advection problems. However most semi-Lagrangian schemes are not conservative. Here, a systematic method is introduced in order to enforce the conservative property on a…
We present a new numerical scheme for one dimensional dynamical systems. This is a modification of the discrete gradient method and keeps its advantages, including the stability and the conservation of the energy integral. However, its…
Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of…
We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e. pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
Emerging quantum hardware provides new possibilities for quantum simulation. While much of the research has focused on simulating closed quantum systems, the real-world quantum systems are mostly open. Therefore, it is essential to develop…
This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…
The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…