Related papers: Discrete line integral method for the Lorentz forc…

This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving method to construct reduced-order models. This allows to…

A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Non-ideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and…

We present a novel methodology for constructing arbitrarily high-order structure-preserving methods tailored for damped Hamiltonian systems. This method combines the idea of exponential integrator and energy-preserving collocation methods,…

This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…

In this work, we propose a structure-preserving discretisation for the recently studied Cahn-Hilliard-Biot system using conforming finite elements in space and problem-adapted explicit-implicit Euler time integration. We prove that the…

We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…

We propose an entropic Fourier method for the numerical discretization of the Boltzmann collision operator. The method, which is obtained by modifying a Fourier Galerkin method to match the form of the discrete velocity method, can be…

We revisit force evaluation methodologies on rigid solid particles suspended in a viscous fluid and simulated via lattice Boltzmann method (LBM). We point out the non-commutativity of streaming and collision operators in the force…

We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions,…

We determine properties of the lattice Boltzmann method for semiclassical fluids, which is based on the Boltzmann equation and the equilibrium distribution function is given either by the Bose-Einstein or the Fermi-Dirac ones. New…

A semi-classical approach to the study of the evolution of anyonic excitations--elementary particles with fractional statistics, complementing bosons and fermions--is through the Boltzmann equation for anyons. This work reviews a…

We propose a new deterministic numerical scheme, based on the discontinuous Galerkin method, for solving the Boltzamnn equation for rarefied gases. The new scheme guarantees the conservation of the mass, momentum and energy. We avoid any…

It is well known, thanks to Lax-Wendroff theorem, that the local conservation of a numerical scheme for a conservative hyperbolic system is a simple and systematic way to guarantee that, if stable, a scheme will provide a sequence of…

This contribution presents an integration method based on the Simpson quadrature. The integrator is designed for finite-dimensional nonlinear mechanical systems that derive from variational principles. The action is discretized using…

We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…

We propose an explicit particle method for the Vlasov-Fokker-Planck equation that conserves energy at the fully discrete level. The method features two key components: a deterministic and conservative particle discretization for the…

In this paper, we propose a first order energy stable linear semi-implicit method for solving the Allen-Cahn-Ohta-Kawasaki equation. By introducing a new nonlinear term in the Ohta-Kawasaki free energy functional, all the system forces in…

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…

We consider a non-linear extension of Biot's model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. We perform an implicit discretization in time (backward Euler) and propose two…

In the presence of an inhomogeneous oscillatory electric field, charged particles experience a net force, averaged over the oscillatory timescale, known as the ponderomotive force. We derive a one-dimensional Hamiltonian model which…