Related papers: Efficient algorithm for simulating particles in re…
Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
There is a class of problems that exhibit smooth behavior on macroscopic scales, where only a microscopic evolution law is known. Patch dynamics scheme of `equation-free multiscale modelling' is one of the techniques, which aims to extract…
Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
The quasicontinuum (QC) method, originally proposed by Tadmor, Ortiz and Phillips in 1996, is a computational technique that can efficiently handle regular atomistic lattices by combining continuum and atomistic approaches. In the present…
This work presents an efficient algorithm for generating statistically representative microstructures of particulate composites in periodic representative volume elements. The Swelling and Random Migration (SRM) algorithm combines…
A treatment of direct simulation Monte Carlo method (DSMC) as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived…
Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the…
We present fully nonlinear dissipative fluid dynamics simulations of a trapped two-dimensional Fermi gas at unitarity using a Lattice Boltzmann algorithm. We are able to simulate non-harmonic trapping potentials, temperature-dependent…
We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different velocity sets, i.e., higher- and lower-order lattices, are consistently and efficiently coupled, allowing us to use the…
The purpose of this paper is to propose a time-step-robust cell-to-cell integration of particle trajectories in 3-D unstructured meshes in particle/mesh Lagrangian stochastic methods. The main idea is to dynamically update the mean fields…
Warm dense matter--an exotic, highly compressed state on the boarder between solid and plasma phases is of high current interest, in particular for compact astrophysical objects, high pressure laboratory systems, and inertial confinement…
An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as…
The 3D quasi-static particle-in-cell (PIC) algorithm is a very efficient method for modeling short-pulse laser or relativistic charged particle beam-plasma interactions. In this algorithm, the plasma response to a non-evolving laser or…
In this paper, we address the problem of designing an experimental plan with both discrete and continuous factors under fairly general parametric statistical models. We propose a new algorithm, named ForLion, to search for locally optimal…
We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from $O(N^2)$ per time step to…
We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and…
We report on a lattice based algorithm, completely vectorized for molecular dynamics simulations. Its algorithmic complexity is of the order $O(N)$, where $N$ is the number of particles. The algorithm works very effectively when the…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…