Related papers: New parallelizable schemes for integrating the Dis…
The equations of Lagrangian gas dynamics fall into the larger class of overdetermined hyperbolic and thermodynamically compatible (HTC) systems of partial differential equations. They satisfy an entropy inequality (second principle of…
Dissipative particle dynamics is a widely used mesoscale technique for the simulation of hydrodynamics (as well as immersed particles) utilizing coarse-grained molecular dynamics. While the method is capable of describing any fluid, the…
In this paper, we consider numerical approximations of a hydrodynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a…
In this paper, we generalize the idea in our previous work for the Vlasov-Amp\`{e}re (VA) system \cite{cheng_va} and develop energy-conserving discontinuous Galerkin (DG) methods for the Vlasov-Maxwell (VM) system. The VM system is a…
We introduce a framework for model reduction of chain models for dissipative particle dynamics (DPD) simulations, where the characteristic size of the chain, pressure, density, and temperature are preserved. The proposed methodology reduces…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known as aggregation-diffusion equations, in any dimension.…
Distributed point charge models (DCM) and their minimal variants (MDCM) have been integrated with tools widely used for condensed-phase simulations, including a virial-based barostat and a slow-growth algorithm for thermodynamic…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
In this work, we consider the error estimates and the long-time conservation or near-conservation of geometric structures, including energy, mass shell and phase-space volume, for four two-step symmetric methods applied to relativistic…
We are interested in the approximation of a steady hyperbolic problem. In some cases, the solution can satisfy an additional conservation relation, at least when it is smooth. This is the case of an entropy. In this paper, we show, starting…
Furihata and Matsuo proposed in 2010 an energy-conserving scheme for the Zakharov equations, as an application of the discrete variational derivative method (DVDM). This scheme is distinguished from conventional methods (in particular the…
We describe a modified form of Smoothed Particle Hydrodynamics (SPH) in which the specific thermal energy equation is based on a compatibly differenced formalism, guaranteeing exact conservation of the total energy. We compare the errors…
In this paper, we present a parallel numerical algorithm for solving the phase field crystal equation. In the algorithm, a semi-implicit finite difference scheme is derived based on the discrete variational derivative method. Theoretical…
The effectiveness of a new algorithm, parallel tempering, is studied for numerical simulations of biological molecules. These molecules suffer from a rough energy landscape. The resulting slowing down in numerical simulations is overcome by…
In this paper, we develop a novel, linearly implicit and local energy-preserving scheme for the sine-Gordon equation. The basic idea is from the invariant energy quadratization approach to construct energy stable schemes for gradient…
We present a parallel implicit-explicit time integration scheme for the advection-diffusion-reaction systems arising from the equations governing low-Mach number combustion with complex chemistry. Our strategy employs parallelization across…
A new scheme for numerical integration of the 1D2V relativistic Vlasov-Maxwell system is proposed. Assuming that all particles in a cell of the phase space move with the same velocity as that of the particle located at the center of the…
The use of explicit particle-in-cell (PIC) method for relativistic plasma simulations is restricted by numerical heating and instabilities that may significantly constrain the choice of time and space steps. To partially eliminate these…