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We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…

Numerical Analysis · Mathematics 2024-03-19 Fernando Henríquez , José Pinto

Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are…

Optimization and Control · Mathematics 2023-07-26 Olga Yufereva , Michael Persiianov , Pavel Dvurechensky , Alexander Gasnikov , Dmitry Kovalev

This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…

Quantum Physics · Physics 2026-05-29 Uditnarayan Kouskiya , Caglar Oskay

We propose an efficient residual minimization technique for the nonlinear model-order reduction of parameterized hyperbolic partial differential equations. Our nonlinear approximation space is a span of snapshots evaluated on a shifted…

Numerical Analysis · Mathematics 2021-01-21 Neeraj Sarna , Sara Grundel

We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…

Numerical Analysis · Mathematics 2015-06-23 Remi Abgrall , David Amsallem

We present the reduced basis method as a tool for developing emulators for equations with tunable parameters within the context of the nuclear many-body problem. The method uses a basis expansion informed by a set of solutions for a few…

Nuclear Theory · Physics 2022-11-30 Edgard Bonilla , Pablo Giuliani , Kyle Godbey , Dean Lee

Inspired by the idea of mimicking the measurement on a quantum system through a decoherence process to target specific eigenstates based on Born's law, i.e. the hiearchy of probabilities instead of the hierarchy of eigenvalues, we transform…

Quantum Physics · Physics 2017-09-06 Oliver Furtmaier , Miller Mendoza

In this contribution we are concerned with efficient model reduction for multiscale problems arising in lithium-ion battery modeling with spatially resolved porous electrodes. We present new results on the application of the reduced basis…

Numerical Analysis · Mathematics 2019-10-30 Mario Ohlberger , Stephan Rave , Felix Schindler

Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…

Quantum Physics · Physics 2023-01-12 Karen J. Morenz Korol , Kenny Choo , Antonio Mezzacapo

In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing…

Superconductivity · Physics 2023-04-19 Virgil V. Baran , Denis R. Nichita

Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively…

Numerical Analysis · Mathematics 2023-07-04 Jun Sur Richard Park , Xueyu Zhu

This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…

Numerical Analysis · Mathematics 2021-01-01 Donsub Rim , Benjamin Peherstorfer , Kyle T. Mandli

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…

In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…

Numerical Analysis · Mathematics 2024-10-14 Michael Kartmann , Tim Keil , Mario Ohlberger , Stefan Volkwein , Barbara Kaltenbacher

A new electronic structure model is developed in which the ground state energy of a molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set…

Chemical Physics · Physics 2014-02-11 Dimitri N. Laikov

Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on linear…

Numerical Analysis · Mathematics 2022-03-02 Francesco Romor , Giovanni Stabile , Gianluigi Rozza

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

Numerical Analysis · Mathematics 2019-04-15 Roland Pulch

A slow decaying Kolmogorov n-width of the solution manifold of a parametric partial differential equation precludes the realization of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the…

Numerical Analysis · Mathematics 2023-08-08 Francesco Romor , Giovanni Stabile , Gianluigi Rozza

Reduced basis methods for approximating the solutions of parameter-dependant partial differential equations (PDEs) are based on learning the structure of the set of solutions - seen as a manifold ${\mathcal S}$ in some functional space -…

Numerical Analysis · Mathematics 2024-07-08 Christophe Prud'Homme , Yvon Maday , Hassan Ballout

This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving…

Numerical Analysis · Mathematics 2026-02-03 Jan S. Hesthaven , Benjamin Peherstorfer , Benjamin Unger