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Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass…

Computational Engineering, Finance, and Science · Computer Science 2026-01-28 Tim Bürchner , Lars Radtke , Sascha Eisenträger , Alexander Düster , Ernst Rank , Stefan Kollmannsberger , Philipp Kopp

Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…

Numerical Analysis · Mathematics 2020-01-22 Rebecca Conley , Xiangmin Jiao , Tristan J. Delaney

Generalized Entity Matching (GEM), which aims at judging whether two records represented in different formats refer to the same real-world entity, is an essential task in data management. The prompt tuning paradigm for pre-trained language…

Computation and Language · Computer Science 2024-05-09 Yikuan Xia , Jiazun Chen , Xinchi Li , Jun Gao

We consider a large-scale quadratic eigenvalue problem (QEP), formulated using P1 finite elements on a fine scale reference mesh. This model describes damped vibrations in a structural mechanical system. In particular we focus on problems…

Numerical Analysis · Mathematics 2015-10-21 Axel Målqvist , Daniel Peterseim

Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv = \lambda v$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to…

Quantum Physics · Physics 2020-08-28 Jeffrey B. Parker , Ilon Joseph

Solving challenging problems in quantum chemistry is one of the most promising applications of quantum computers. Within the quantum algorithms proposed for problems in excited state quantum chemistry, subspace-based quantum algorithms,…

Variational calculations of excited electronic states are carried out by finding saddle points on the surface that describes how the energy of the system varies as a function of the electronic degrees of freedom. This approach has several…

Chemical Physics · Physics 2023-02-15 Yorick L. A. Schmerwitz , Gianluca Levi , Hannes Jónsson

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…

The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approaches that aim to maximize the classical Rayleigh quotient…

Optimization and Control · Mathematics 2025-07-04 Xiaozhi Liu , Yong Xia

In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use…

Numerical Analysis · Mathematics 2019-09-04 Shubin Fu , Robert Altmann , Eric T. Chung , Roland Maier , Daniel Peterseim , Sai-Mang Pun

Eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors of a regular linear matrix pencil. The complex moment acts as a filter for extracting…

Numerical Analysis · Mathematics 2021-09-22 Keiichi Morikuni

We propose Energy-based generator matching (EGM), a modality-agnostic approach to train generative models from energy functions in the absence of data. Extending the recently proposed generator matching, EGM enables training of arbitrary…

Machine Learning · Computer Science 2025-11-20 Dongyeop Woo , Minsu Kim , Minkyu Kim , Kiyoung Seong , Sungsoo Ahn

A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter $\varepsilon$, based on locally approximating the solution on each subdomain by solution of a…

Numerical Analysis · Mathematics 2024-07-25 Chupeng Ma , Jens Markus Melenk

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…

Numerical Analysis · Mathematics 2012-04-23 Xuefeng Liu , Shin'ichi Oishi

Work on generalizing the deflated, restarted GMRES algorithm, useful in lattice studies using stochastic noise methods, is reported. We first show how the multi-mass extension of deflated GMRES can be implemented. We then give a deflated…

High Energy Physics - Lattice · Physics 2009-11-10 Dean Darnell , Ronald B. Morgan , Walter Wilcox

A recent Letter~\cite{Borsanyi:2025dyp} employs lattice QCD calculations of the equation of state, combined with entropy-density contour analysis, to place a lower bound of $\mu_B \gtrsim 450$~MeV on the location of the QCD critical…

High Energy Physics - Lattice · Physics 2026-04-01 Roy A. Lacey

This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems…

Machine Learning · Statistics 2023-05-23 Benyamin Ghojogh , Fakhri Karray , Mark Crowley

New stochastic approaches for the computation of electronic excitations are developed within the many-body perturbation theory. Three approximations to the electronic self-energy are considered: $G_0W_0$, $G_0W_0^tc$, and…

Chemical Physics · Physics 2019-08-27 Vojtech Vlcek

The generalized pseudospectral method is employed to study the bound-state spectra of some of the exponentially screened Coulomb potentials, \emph{viz.}, the exponential cosine screened Coulomb (ECSC) and general exponential screened…

Quantum Physics · Physics 2013-04-26 Amlan K. Roy

In the previous paper I \cite{bhagwat20} we have shown that self-consistent Extended Thomas-Fermi (ETF) potentials and densities associated with a given finite-range interaction can be parametrized by generalized Fermi distributions. As a…

Nuclear Theory · Physics 2021-03-03 A. Bhagwat , M. Centelles , X. Viñas , P. Schuck