Related papers: Comparing Mass-Preserving Numerical Methods for th…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…
The traditional explicit electrostatic momentum-conserving Particle-in-cell algorithm requires strict resolution of the electron Debye length to deliver numerical accuracy. The explicit electrostatic energy-conserving Particle-in-Cell…
An industrial scheme, to simulate the two compressible phase flow in porous media, consists in a finite volume method together with a phase-by-phase upstream scheme. The implicit finite volume scheme satisfies industrial constraints of…
This paper presents a data-driven finite volume method for solving 1D and 2D hyperbolic partial differential equations. This work builds upon the prior research incorporating a data-driven finite-difference approximation of smooth solutions…
We evaluate the practical performance of the zero-multiple summation method (ZMM), a method for approximately calculating electrostatic interactions in molecular dynamics simulations. The performance of the ZMM is compared with that of the…
In this article, we derive a general form of local volume-averaging theory and apply it to a model of zinc-air conversion batteries. Volume-averaging techniques are frequently used for the macroscopic description of micro-porous electrodes.…
Constant potential method molecular dynamics simulation (CPM MD) enables the accurate modelling of atomistic electrode charges when studying the electrode-electrolyte interface at the nanoscale. Here we extend the theoretical framework of…
Incorporating conservation laws explicitly into matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used…
The Stochastic Weighted Particle Method (SWPM) is a Monte Carlo technique developed by Rjasanow and Wagner that generalizes Bird's Direct Simulation Monte Carlo (DSMC) method for solving the Boltzmann equation. To reduce computational cost…
In simulations of partial differential equations using particle-in-cell (PIC) methods, it is often advantageous to resample the particle distribution function to increase simulation accuracy, reduce compute cost, and/or avoid numerical…
We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws. The proposed algorithms combine finite volume spatio-temporal approximations with Monte Carlo and multi-level Monte Carlo…
We provide a mathematically proven parallelization scheme for particle methods on distributed-memory computer systems. Particle methods are a versatile and widely used class of algorithms for computer simulations and numerical predictions…
The Energy Conserving semi-implicit method (ECsim), presented by Lapenta in 2017, is a Particle in Cell (PIC) algorithm for the simulation of plasmas. Energy conservation is achieved within a semi-implicit formulation that does not require…
Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic method which allows to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a…
Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…
In this paper, we compare the performance of two scenario-based numerical methods to solve stochastic optimal control problems: scenario trees and particles. The problem consists in finding strategies to control a dynamical system perturbed…
An application for high-performance computing (HPC) is shown that is relevant in the field of battery development. Simulations of electrolyte wetting and flow are conducted using pore network models (PNM) and the lattice Boltzmann method…
Conventional model compression techniques for LLMs address high memory consumption and slow inference challenges but typically require computationally expensive retraining to preserve accuracy. In contrast, one-shot compression methods…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
Rechargeable battery electrodes have highly complex microstructures, consisting of nonuniform electrode particles, tortuous electrolyte channels, and irregular particle-electrolyte interfaces. Moreover, the electrochemical processes involve…