Related papers: Eigenvalue Method for NEI Unit in FLASH Code
The rapid advancements in ultrafast laser technology have paved the way for pumping and probing the out-of-equilibrium dynamics of nuclei in crystals. However, interpreting these experiments is extremely challenging due to the complex…
Feature attribution (FA) methods are widely used in explainable AI (XAI) to help users understand how the inputs of a machine learning model contribute to its outputs. However, different FA models often provide disagreeing importance scores…
In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…
Conventional theoretical and computational approaches to fully coupled quantum molecular dynamics, i.e. when both the electrons and nuclei are treated as quantum-mechanical particles, are impractical for all but the smallest chemical…
The partial Schur factorization can be used to represent several eigenpairs of a matrix in a numerically robust way. Different adaptions of the Arnoldi method are often used to compute partial Schur factorizations. We propose here a…
We propose a modification of the Variational Quantum Eigensolver algorithm for electronic structure optimization using quantum computers, named non-unitary Variational Quantum Eigensolver (nu-VQE), in which a non-unitary operator is…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…
The exact factorization (EF) approach to coupled electron-ion dynamics recasts the time-dependent molecular Schr\"odinger equation as two coupled equations, one for the nuclear wavefunction and one for the conditional electronic…
In toroidally confined plasmas, the Grad-Shafranov equation, in general a non-linear PDE, describes the hydromagnetic equilibrium of the system. This equation becomes linear when the kinetic pressure is proportional to the poloidal magnetic…
We consider the numerical computation of resonances for metallic grating structures with dispersive media and small slit holes. The underlying eigenvalue problem is nonlinear and the mathematical model is multiscale due to the existence of…
We consider the approximation of eigenvalue problems for elasticity equations with interface. This kind of problems can be efficiently discretized by using immersed finite element method (IFEM) based on Crouzeix-Raviart P1-nonconforming…
This paper describes a new code for simulating astrophysical plasmas that solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal electron fluid (ITEF) [A. Schekochihin et al., Astrophys. J. Suppl. \textbf{182}, 310…
In magnetized plasmas of fusion devices the strong magnetic field leads to highly anisotropic physics where solution scales along field lines are much larger than perpendicular to it. Hence, regarding both accuracy and efficiency, a…
The weak imposition of essential boundary conditions is an integral aspect of unfitted finite element methods, where the physical boundary does not in general coincide with the computational domain. In this regard, the symmetric Nitsche's…
We develop a quantum-classical hybrid algorithm to calculate the analytical second-order derivative of the energy for the orbital-optimized variational quantum eigensolver (OO-VQE), which is a method to calculate eigenenergies of a given…
In this paper, we present a parallel numerical algorithm for solving the phase field crystal equation. In the algorithm, a semi-implicit finite difference scheme is derived based on the discrete variational derivative method. Theoretical…
In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method which is…
This work presents a novel framework for numerically simulating the depressurization of tanks and pipelines containing carbon dioxide (CO2). The framework focuses on efficient solution strategies for the coupled system of fluid flow…