Related papers: Lattice Discrete Particle Model (LDPM): Comparison…
Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
It is well-known that in fluid dynamics an alternative to customary direct solution methods (based on the discretization of the fluid fields) is provided by so-called \emph{particle simulation methods}. Particle simulation methods rely…
The material point method (MPM) is frequently used to simulate large deformations of nearly incompressible materials such as water, rubber, and undrained porous media. However, MPM solutions to nearly incompressible materials are…
It is well-known that molecular dynamics integrators, which are used for lattice quantum chromodynamics (QCD), suffer from instabilities and possess a rather low order of the accuracy. Hence, it is highly desirable to construct a new class…
The Discrete Particle Method (DPM) is used to model granular flows down an inclined chute. We observe three major regimes: static piles, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes…
Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…
The discrete dipole approximation (DDA) is a widely used and versatile numerical method for solving electromagnetic scattering by arbitrarily shaped objects. Despite its popularity, quantitative comparisons between independent…
This paper explores the embedding of lattice structures $L \subseteq \mathbb{R}^n$ into smooth manifolds $M \subseteq \mathbb{R}^n$ through a rigorous mathematical framework. Building upon the foundational results established in "Embedding…
The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…
In this work, a recently developed fracture modeling method called localizing gradient damage method (LGDM) is implemented in MATLAB. MATLAB is well-known in the computational research community for its simple and easy-to-learn coding…
Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…
This article introduces a novel framework for developing quantum algorithms for the Lattice Boltzmann Method (LBM) applied to the advection-diffusion equation. We formulate the collision-streaming evolution of the LBM as a compact…
We study parallel particle-in-cell (PIC) methods for low-temperature plasmas (LTPs), which discretize kinetic formulations that capture the time evolution of the probability density function of particles as a function of position and…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
The Landau collision integral is often considered the gold standard in the context of kinetic plasma simulation due to its conservative properties, despite challenges involved in its discretization. The primary challenge when implementing…
Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a "lumped" element representative of the physical scales of the modeled system. For systems where the definition of a…
Discrete choice models (DCMs) have been widely utilized in various scientific fields, especially economics, for many years. These models consider a stochastic environment influencing each decision maker's choices. Extensive research has…
The interpolated bounce-back scheme and the immersed boundary method are the two most popular algorithms in treating a no-slip boundary on curved surfaces in the lattice Boltzmann method. While those algorithms are frequently implemented in…
This paper presents a new adaptive multiscale homogenization scheme for the simulation of damage and fracture in concrete structures. A two-scale homogenization method, coupling meso-scale discrete particle models to macro- scale finite…