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pro vyhledávání: '"35J05"'
In this paper, we study the Vlasov-Poisson system with massless electrons (VPME) near quasineutrality and with uncertainties. Based on the idea of reformulation on the Poisson equation by [P. Degond et.al., $\textit{Journal of Computational Physics}$
Externí odkaz:
http://arxiv.org/abs/2412.05663
We present a matrix-free parallel scalable multilevel deflation preconditioned method for heterogeneous time-harmonic wave problems. Building on the higher-order deflation preconditioning proposed by Dwarka and Vuik (SIAM J. Sci. Comput. 42(2):A901-A
Externí odkaz:
http://arxiv.org/abs/2412.04980
Let $\Omega\subset\mathbb{R}^n$ with $n\ge 2$ be a bounded Lipschitz domain with outer unit normal $\nu$. For $\alpha\in\mathbb{R}$ let $R_\Omega^\alpha$ be the Laplacian in $\Omega$ with the Robin boundary condition $\partial_\nu u+\alpha u=0$, and
Externí odkaz:
http://arxiv.org/abs/2412.04061
Autor:
Yovel, Rachel, Treister, Eran
We present a novel block-preconditioner for the elastic Helmholtz equation, based on a reduction to acoustic Helmholtz equations. Both versions of the Helmholtz equations are challenging numerically. The elastic Helmholtz equation is larger, as a sys
Externí odkaz:
http://arxiv.org/abs/2411.15897
Autor:
Dias, Manuel, Tewodrose, David
The symmetrized Asymptotic Mean Value Laplacian $\tilde{\Delta}$, obtained as limit of approximating operators $\tilde{\Delta}_r$, is an extension of the classical Euclidean Laplace operator to the realm of metric measure spaces. We show that, as $r
Externí odkaz:
http://arxiv.org/abs/2411.10202
Autor:
Kuijpers, Safiere, Scarabosio, Laura
We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then extend our re
Externí odkaz:
http://arxiv.org/abs/2410.23100
The truncated Floquet-Bloch transform can be used to characterise the spectral properties of finite periodic and aperiodic large systems of resonators. This paper aims to provide for the first time the mathematical foundations of this transform.
Externí odkaz:
http://arxiv.org/abs/2410.17597
In this paper, we examine some shape functionals, introduced by P\'olya and Makai, involving the torsional rigidity and the first Dirichlet-Laplacian eigenvalue for bounded, open and convex sets of $\mathbb{R}^n$. We establish new quantitative bounds
Externí odkaz:
http://arxiv.org/abs/2410.06858
In this paper we prove discrete to continuum convergence rates for Poisson Learning, a graph-based semi-supervised learning algorithm that is based on solving the graph Poisson equation with a source term consisting of a linear combination of Dirac d
Externí odkaz:
http://arxiv.org/abs/2407.06783
Autor:
Eberle-Blick, Sarah, Pohjola, Valter
We derive a linearized version of the monotonicity method for shape reconstruction using time harmonic elastic waves. The linearized method provides an efficient version of the method, drastically reducing computation time. Here we show that the line
Externí odkaz:
http://arxiv.org/abs/2409.20339