Related papers: On the Cholesky Decomposition for electron propaga…
Particle in Cell (PIC) simulations are a widely used tool for the investigation of both laser- and beam-driven plasma acceleration. It is a known issue that the beam quality can be artificially degraded by numerical Cherenkov radiation…
Many important real-world applications, such as System Identification with Gaussian Processes, involve solving linear systems with symmetric positive-definite matrices. The iterative CG method and direct solvers based on the Cholesky…
We benchmark and analyze the error of energy conservation (EC) scheme for Particle in cell/Monte-Carlo Couple (PIC/MCC) algorithms by a radio frequency discharging simulation. The plasma heating behaviors and electron distributing functions…
The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…
The particular symmetry of the random-phase-approximation (RPA) matrix has been utilized in the past to reduce the RPA eigenvalue problem into a symmetric-matrix problem of half the dimension. The condition of positive definiteness of at…
We propose a class of Particle-In-Cell (PIC) methods for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on the motion of particles in the plane orthogonal to the…
Conducting Polymer Dendrites (CPD) are truly inspiring for unconventional electronics that shapes topological circuitries evolving upon an application. Driven by electrochemical processes, an electrochemical impedance rules signal…
The Cholesky decomposition plays an important role in finding the inverse of the correlation matrices. As it is a fast and numerically stable for linear system solving, inversion, and factorization compared to singular valued decomposition…
We review our recently developed electronic structure calculation methods used for the dynamics of large-scale solids or liquids with an efficient algorithm for large scale simultaneous linear equations. The electronic structure calculation…
As a multi-purpose Particle-In-Cell (PIC) code, Smilei gathers many different features in a single software. Combining some of them is challenging. In particular, spectral solvers and patch based load balancing have a priori non compatible…
We propose a new microscopy simulation system that can depict atomistic models in a micrograph visual style, similar to results of physical electron microscopy imaging. This system is scalable, able to represent simulation of electron…
Estimation of large sparse covariance matrices is of great importance for statistical analysis, especially in the high-dimensional settings. The traditional approach such as the sample covariance matrix performs poorly due to the high…
Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…
Molecular-scale diodes made from self-assembled monolayers (SAMs) could complement silicon-based technologies with smaller, cheaper, and more versatile devices. However, advancement of this emerging technology is limited by insufficient…
Parametric two-electron reduced-density-matrix (p-2RDM) methods have enjoyed much success in recent years; the methods have been shown to exhibit accuracies greater than coupled cluster with single and double substitutions (CCSD) for both…
We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham…
We propose that the Matrix Profile data structure, conventionally applied to large scale time-series data mining, is applicable to the analysis and suppression of cyclical error in electromechanical systems, paving the way for an…
While the coherent potential approximation (CPA) is the prevalent method for the study of disordered electronic systems, it fails to capture non-local correlations and Anderson localization. To incorporate such effects, we extend the dual…
A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…
In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczy\'{n}ski and…