Related papers: Efficient energy-preserving methods for charged-pa…
A method for constructing first integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The method can be used with both finite difference and partition of unity approaches,…
We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the…
We present a set of linear, second order, unconditionally energy stable schemes for the Allen-Cahn equation with nonlocal constraints that preserves the total volume of each phase in a binary material system. The energy quadratization…
This paper presents models for renewable energy systems with storage, and considers its optimal operation. We model and simulate wind and solar power production using stochastic differential equations as well as storage of the produced…
A recently introduced particle-based model for fluid dynamics with effective excluded volume interactions is analyzed in detail. The interactions are modeled by means of stochastic multiparticle collisions which are biased and depend on…
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…
The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. Here, a novel, implicit, particle-in-cell based…
Dissipative particle dynamics (DPD) does not conserve energy and this precludes its use in the study of thermal processes in complex fluids. We present here a generalization of DPD that incorporates an internal energy and a temperature…
Classical molecular dynamics simulations have recently become a standard tool for the study of electrochemical systems. State-of-the-art approaches represent the electrodes as perfect conductors, modelling their responses to the charge…
An improved Boris algorithm for simulating the motion of charged particles in electromagnetic fields has been developed. This enhancement addresses the issue of inaccurate fast-scale cyclotron phase calculations present in the original…
Data preservation is a mandatory specification for any present and future experimental facility and it is a cost-effective way of doing fundamental research by exploiting unique data sets in the light of the continuously increasing…
We analyze a category of problems that is of interest in many physical situations, including those encountered in introductory physics classes: systems with two well-delineated parts that exchange energy, eventually reaching a shared…
We present new linear energy-stable numerical schemes for numerical simulation of complex polymer-solvent mixtures. The mathematical model proposed by Zhou, Zhang and E (Physical Review E 73, 2006) consists of the Cahn-Hilliard equation…
When nonconforming discontinuous Galerkin methods are implemented for hyperbolic equations using quadrature, exponential energy growth can result even when the underlying scheme with exact integration does not support such growth. Using…
We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete…
This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations (PDEs). The vast majority of energy-preserving…
It is shown that the well-known disparity in classical electrodynamics between the power radiated in electromagnetic fields and the power-loss, as calculated from the radiation reaction on a charge undergoing a non-uniform motion, is…
The recently developed energy conserving semi-implicit method (ECsim) for PIC simulation is applied to multiple scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
The interrelationship between energy and probability conservation is explored from the point of view of statistical physics and non-relativistic quantum mechanics. The simultaneous validity of the law of conservation of energy and the…