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This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…

Numerical Analysis · Mathematics 2025-07-24 Michał Wichrowski

The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's…

Numerical Analysis · Mathematics 2015-12-29 Matthew G. Knepley , Jaydeep P. Bardhan

A major challenge in the molecular simulation of electric double layer capacitors (EDLCs) is the choice of an appropriate model for the electrode. Typically, in such simulations the electrode surface is modeled using a uniform fixed charge…

Computational Physics · Physics 2015-06-22 Zhenxing Wang , Yang Yang , David L. Olmsted , Mark Asta , Brian B. Laird

Ab initio modeling of electrochemical systems is becoming a key tool for understanding and predicting electrochemical behavior. Development and careful benchmarking of computational electrochemical methods are essential to ensure their…

Chemical Physics · Physics 2017-03-01 Ravishankar Sundararaman , Kathleen Schwarz

This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration…

Systems and Control · Computer Science 2014-12-09 Ross Drummond , David A. Howey , Stephen R. Duncan

Bounded plasmas are characterized by a rapid but smooth transition from quasi-neutrality in the volume to electron depletion close to the electrodes and chamber walls. The thin non-neutral region, the boundary sheath, comprises only a small…

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the…

Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries…

Numerical Analysis · Mathematics 2025-06-06 Vinamra Agrawal , Brandon Runnels

We present a hybrid method for the simulation of colloidal systems, that combines molecular dynamics (MD) with the Lattice-Boltzmann (LB) scheme. The LB method is used as a model for the solvent in order to take into account the…

Soft Condensed Matter · Physics 2009-11-11 Apratim Chatterji , Juergen Horbach

The demand for lithium ion batteries (LIBs) on the market has gradually risen, with production increasing every year. To meet industrial needs, the development of digital twins designed to optimize LIB manufacturing processes is essential.…

We present a novel scheme for modelling quantum plasmas in the warm dense matter (WDM) regime via a hybrid smoothed particle hydrodynamic - molecular dynamic treatment, here referred to as 'Bohm SPH'. This treatment is founded upon Bohm's…

Owing to the trade-off between the accuracy and efficiency, machine-learning-potentials (MLPs) have been widely applied in the battery materials science, enabling atomic-level dynamics description for various critical processes. However,…

In this paper, a generalized macromodeling approach is presented to simulate complex electromagnetic (EM) surfaces consisting of unit cells with connected conductors. Macromodels of each unit cell are produced by applying the equivalence…

Numerical Analysis · Mathematics 2022-08-17 Reza Gholami , Parinaz Naseri , Piero Triverio , Sean V. Hum

The simulation of chemistry is among the most promising applications of quantum computing. However, most prior work exploring algorithms for block-encoding, time-evolving, and sampling in the eigenbasis of electronic structure Hamiltonians…

Porous electrodes composed of multiphase active materials are widely used in Li-ion batteries, but their dynamics are poorly understood. Two-phase models are largely empirical, and no models exist for three or more phases. Using a modified…

Chemical Physics · Physics 2014-02-07 Todd R. Ferguson , Martin Z. Bazant

We present a broad family of high-order finite element algorithms for simulating the flow of electroneutral electrolytes. The governing partial differential equations that we solve are the electroneutral…

Numerical Analysis · Mathematics 2026-03-31 Aaron Baier-Reinio , Patrick E. Farrell , Charles W. Monroe

In this work we consider how surface-adherent bacterial biofilm communities respond in flowing systems. We simulate the fluid-structure interaction and separation process using the immersed boundary method. In these simulations we model and…

Numerical Analysis · Mathematics 2013-02-18 Jason F. Hammond , Elizabeth J. Stewart , John G. Younger , Michael J. Solomon , David M. Bortz

We present a framework for atomistic simulations of surface catalysis under electrochemical bias. The framework makes use of extended Lagrangian Born-Oppenheimer quantum-based molecular dynamics (XL-BOMD) simulations, which provide the…

In this contribution we are concerned with efficient model reduction for multiscale problems arising in lithium-ion battery modeling with spatially resolved porous electrodes. We present new results on the application of the reduced basis…

Numerical Analysis · Mathematics 2019-10-30 Mario Ohlberger , Stephan Rave , Felix Schindler