Related papers: Eigenvalue Method for NEI Unit in FLASH Code
Standard Virtual Element Methods (VEM) are based on polynomial projections and require a stabilization term to evaluate the contribution of the non-polynomial component of the discrete space. However, the stabilization term is not uniquely…
Multiple equilibrium states arise in many physical systems, including various types of liquid crystal structures. Having the ability to reliably compute such states enables more accurate physical analysis and understanding of experimental…
The solid electrolyte interphase SEI critically dictates the cyclability and Coulombic efficiency of sodium-metal batteries, yet its dynamic formation mechanisms and atomic-scale evolution during electrochemical cycling remain elusive due…
Nonlinear eigenvalue equations arise naturally in quantum information theory, particularly in the variational quantification of entanglement. In this work, we present a hybrid analytical and numerical framework for evaluating the geometric…
We show that the algorithm based on the weighted essentially nonoscillatory (WENO) scheme with anti-diffusive flux corrections can be used as a solver of the radiative transfer equations. This algorithm is highly stable and robust for…
Calculations of the photonic band structure, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The…
This paper describes the effects of electronic nonequilibrium in a simulation of ultrafast laser irradiation of materials. The simulation scheme based on tight-binding molecular dynamics, in which the electronic populations are traced with…
Numerical studies of ionic motion through solid electrolytes commonly involve static nudged-elastic band (NEB) methods or costly \emph{ab initio} molecular dynamics (AIMD). Building on a time-local model of current carrier-electrolyte…
Magnetic flux emergence has been shown to be a key mechanism for unleashing a wide variety of solar phenomena. However, there are still open questions concerning the rise of the magnetized plasma through the atmosphere, mainly in the…
We propose NEP_MiniMax, a novel computational method for solving nonlinear eigenvalue problems (NEPs) $T(\lambda)\mathbf{u}= 0$ on compact continua $\Omega \subset \mathbb{C}$. The method combines two key components: (1) a rational minimax…
Understanding the dynamics of the solar chromosphere is crucial to understanding energy transport across the solar atmosphere. The chromosphere is optically thick at many wavelengths and described by non-local thermodynamic equilibrium…
With only a few exceptions, the numerical simulation of cosmic and laboratory hydromagnetic dynamos has been carried out in the framework of the differential equation method. However, the integral equation method is known to provide robust…
In recent years, increasing aerospace safety requirements have intensified the demand for reliable structural damage detection. This work presents an Operational Modal Analysis approach for accurate modal parameter estimation, with an…
Three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a…
Nuclear quantum effects are essential for correctly describing hydrogen-rich materials at high pressures. Superconducting hydrides and ice are prime examples of such systems, requiring the inclusion of lattice anharmonicity and nuclear…
We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…
Average atom (AA) models allow one to efficiently compute electronic and optical properties of materials over a wide range of conditions and are often employed to interpret experimental data. However, at high pressure, predictions from AA…
Traditionally, classical numerical schemes have been employed to solve partial differential equations (PDEs) using computational methods. Recently, neural network-based methods have emerged. Despite these advancements, neural network-based…
In this article, we present a new unified finite element method (UFEM) for simulation of general Fluid-Structure interaction (FSI) which has the same generality and robustness as monolithic methods but is significantly more computationally…