Related papers: High-order energy-conserving Line Integral Methods…
There are many interesting physical processes which involve the generation of high density plasmas in large volumes. However, when modeling these systems numerically, the large densities and volumes present a significant computational…
In this note we discuss the construction of high order asymptotic preserving numerical schemes for the Boltzmann equation. The methods are based on the use of Implicit-Explicit (IMEX) Runge-Kutta methods combined with a penalization…
In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation in three dimensions. Based on the idea of the scalar…
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…
We introduce a class of high order accurate, semi-implicit Runge-Kutta schemes in the general setting of evolution equations that arise as gradient flow for a cost function, possibly with respect to an inner product that depends on the…
The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution…
This article considers non-relativistic charged particle dynamics in both static and non-static electromagnetic fields, which are governed by nonseparable, possibly time-dependent Hamiltonians. For the first time, explicit symplectic…
Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been…
We present a novel method for guaranteeing linear momentum in learned physics simulations. Unlike existing methods, we enforce conservation of momentum with a hard constraint, which we realize via antisymmetrical continuous convolutional…
We present a new molecular-dynamics algorithm for integrating the equations of motion for a system of particles interacting with mixed continuous/impulsive forces. This method, which we call Impulsive Verlet, is constructed using operator…
We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. We modify the classical algorithm by introducing a new…
A novel reduced-order model (ROM) formulation for incompressible flows is presented with the key property that it exhibits non-linearly stability, independent of the mesh (of the full order model), the time step, the viscosity, and the…
The study of the long time conservation for numerical methods poses interesting and challenging questions from the point of view of geometric integration. In this paper, we analyze the long time energy and magnetic moment conservations of…
In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…
Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
We are concerned in designing a suitable numerical scheme based on the equal-order hybrid high-order (HHO) method for the linear parabolic integro-differential equations. The spatial discretization is made using the equal-order HHO method…
The existing discrete variational derivative method is only second-order accurate and fully implicit. In this paper, we propose a framework to construct an arbitrary high-order implicit (original) energy stable scheme and a second-order…
Time-reversible symplectic methods, which are precisely compatible with Liouville's phase-volume-conservation theorem, are often recommended for computational simulations of Hamiltonian mechanics. Lack of energy drift is an apparent…
We address the problem of constructing numerical integrators for nonholonomic Lagrangian systems that enjoy appropriate discrete versions of the geometric properties of the continuous flow, including the preservation of energy. Building on…