Related papers: Energy preserving moving mesh methods applied to t…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
I recently proposed a method of bosonization valid for systems of an even number of fermions whose partition function is dominated at low energy by bosonic composites. This method respects all symmetries, in particular fermion number…
`Dual composition', a new method of constructing energy-preserving discretizations of conservative PDEs, is introduced. It extends the summation-by-parts approach to arbitrary differential operators and conserved quantities. Links to…
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…
A basic leapfrog integrator and its energy-preserving and variational / symplectic variants are proposed and studied for the numerical integration of the equations of motion of relativistic charged particles in an electromagnetic field. The…
By employing the closest point method, we extend the applicability of minimizing movements to the surface PDE setting. The corresponding approximation methods are created, and their convergence is observed. The numerical methods are then…
As is known that wave equations have physically very important properties which should be respected by numerical schemes in order to predict correctly the solution over a long time period. In this paper, the long-time behaviour of momentum…
We present a novel positive kinetic scheme built on the efficient collide-and-stream algorithm of the lattice Boltzmann method (LBM) to address hyperbolic conservation laws. We focus on the compressible Euler equations with strong…
This paper deals with time stepping schemes for the Cahn--Hilliard equation with three different types of dynamic boundary conditions. The proposed schemes of first and second order are mass-conservative and energy-dissipative and -- as…
In this paper, we develop bound-preserving (BP) finite-volume schemes for hyperbolic conservation laws on adaptive moving meshes. For scalar conservative laws, we rewrite the conventional high-order discretization as a convex combination of…
This work presents new parallelizable numerical schemes for the integration of Dissipative Particle Dynamics with Energy conservation (DPDE). So far, no numerical scheme introduced in the literature is able to correctly preserve the energy…
In this paper, we develop a novel class of arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation. With the aid of the invariant energy quadratization approach, the Camassa-Holm equation is first reformulated into an…
We introduce a stochastic perturbation of the Camassa-Holm equation such that, unlike previous formulations, energy is conserved by the stochastic flow. We compare this to a complementary approach which preserves Casimirs of the Poisson…
The time-dependent Gross-Pitaevksii equation (GPE) is a nonlinear Schr\"odinger equation which is used in quantum physics to model the dynamics of Bose-Einstein condensates. In this work we consider numerical approximations of the GPE based…
We develop the number-conserving approach that has previously been used in a single component Bose-Einstein condensed dilute atomic gas, to describe consistent coupled condensate and noncondensate number dynamics, to an $n$-component…
We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is…
This work presents structure-preserving Lift & Learn, a scientific machine learning method that employs lifting variable transformations to learn structure-preserving reduced-order models for nonlinear partial differential equations (PDEs)…
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…
We study geometric properties of Krylov projection methods for large and sparse linear Hamiltonian systems. We consider in particular energy preservation. We discuss the connection to structure preserving model reduction. We illustrate the…
A kinetic approach to the Bose-Einstein condensates (BECs) is proposed, based on the Wigner-Moyal equation (WME). In the quasi-classical limit, the WME reduces to the particle number conservation equation. Two examples of application are:…