Related papers: Solving the Schrodinger Poisson System using the c…

Stochastic version of alternating direction method of multiplier (ADMM) and its variants (linearized ADMM, gradient-based ADMM) plays a key role for modern large scale machine learning problems. One example is the regularized empirical risk…

This paper describes an angular adaptivity algorithm for Boltzmann transport applications which for the first time shows evidence of $\mathcal{O}(n)$ scaling in both runtime and memory usage, where $n$ is the number of adapted angles. This…

Hybrid quantum/molecular mechanics (QM/MM) models play a pivotal role in molecular simulations. These models provide a balance between accuracy, surpassing pure MM models, and computational efficiency, offering advantages over pure QM…

This work introduces a moving anchor acceleration technique to extragradient algorithms for smooth structured minimax problems. The moving anchor is introduced as a generalization of the original algorithmic anchoring framework, i.e. the…

We consider X-ray coherent scatter imaging, where the goal is to reconstruct momentum transfer profiles (spectral distributions) at each spatial location from multiplexed measurements of scatter. Each material is characterized by a unique…

We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the…

The solution of conservation laws with parametrized shock waves presents challenges for both high-order numerical methods and model reduction techniques. We introduce an r-adaptivity scheme based on optimal transport and apply it to develop…

In this paper, we consider the Anderson acceleration method for solving the contractive fixed point problem, which is nonsmooth in general. We define a class of smoothing functions for the original nonsmooth fixed point mapping, which can…

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Numerous renowned algorithms for tackling the compressed sensing problem…

We study relaxation-based approaches for conserving mass and energy in the numerical solution of Schr\"odinger-Poisson (SP) type systems. Relaxation-based methods offer a general approach that can be applied as post-time step processing to…

We study the stochastic nonlinear Schr\"odinger equations with additive stochastic forcing. By using the dispersive estimate, we present a simple argument, constructing a unique local-in-time solution with rougher stochastic forcing than…

We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…

This paper presents an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems. The heuristic to choose the shooting points is based on separating the effects of drift and diffusion terms and comparing the…

Adaptive mesh refinement (AMR) offers a practical solution to reduce the computational cost and memory requirement of numerical simulations that use computational meshes. In this work, we introduce a novel smart methodology for adaptive…

In this paper, we examine the properties of the solutions obtained by the Schwinger-Dyson equation (SDE). As a simple example, we consider a two-dimensional model including four-fermion interaction. It is shown that when this model is…

The inverse problems of particle neutral transport models have many important engineering and medical applications. Safety protocols, quality control procedures, and optical medical solutions can be developed based on inverse transport…

The cost and accuracy of simulating complex physical systems using the Finite Element Method (FEM) scales with the resolution of the underlying mesh. Adaptive meshes improve computational efficiency by refining resolution in critical…

Here we present exact, stationary, parametric solutions to the Schr\"odinger--Poisson system. We confront two images: on one hand, we draw on the homotopy analysis method which leads us to a nonlinear integral scheme. Indeed, this approach…

The analytical solutions of the N-dimensional Schrodinger equation with position-dependent mass for a general class of central potentials is obtained via the series expansion method. The position-dependent mass is expanded in series about…

Adaptive Multilevel Splitting (AMS for short) is a generic Monte Carlo method for Markov processes that simulates rare events and estimates associated probabilities. Despite its practical efficiency, there are almost no theoretical results…