Zobrazeno 1 - 10
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pro vyhledávání: '"Galkowski A."'
We discuss parallel (additive) and sequential (multiplicative) variants of overlapping Schwarz methods for the Helmholtz equation in $\mathbb{R}^d$, with large real wavenumber and smooth variable wave speed. The radiation condition is approximated by
Externí odkaz:
http://arxiv.org/abs/2408.16580
We prove sharp wavenumber-explicit error bounds for first- or second-type-N\'ed\'elec-element (a.k.a. edge-element) conforming discretisations, of arbitrary (fixed) order, of the variable-coefficient time-harmonic Maxwell equations posed in a bounded
Externí odkaz:
http://arxiv.org/abs/2408.04507
We study overlapping Schwarz methods for the Helmholtz equation posed in any dimension with large, real wavenumber and smooth variable wave speed. The radiation condition is approximated by a Cartesian perfectly-matched layer (PML). The domain-decomp
Externí odkaz:
http://arxiv.org/abs/2404.02156
We show that for the Lindblad evolution defined using (at most) quadratically growing classical Hamiltonians and (at most) linearly growing classical jump functions (quantized into jump operators assumed to satisfy certain ellipticity conditions and
Externí odkaz:
http://arxiv.org/abs/2403.09345
Autor:
Galkowski, Jeffrey, Zworski, Maciej
Motivated by the study of flat bands in models of twisted bilayer graphene (TBG), we give abstract conditions which guarantee the existence of a discrete set of parameters for which periodic Hamiltonians exhibit flat bands. As an application, we show
Externí odkaz:
http://arxiv.org/abs/2307.04896
Autor:
Baikie, Tomi K., Calado, Philip, Galkowski, Krzysztof, Andaji-Garmaroudi, Zahra, Chin, Yi-Chun, Luke, Joel, Henderson, Charlie, Dunlop, Tom, McGettrick, James, Kim, Ji-Seon, Rao, Akshay, Nelson, Jenny, Stranks, Samuel D., Barnes, Piers R. B.
Metal halide perovskite solar cells have gained widespread attention due to their high efficiency and high defect tolerance. The absorbing perovskite layer is as a mixed electron-ion conductor that supports high rates of ion and charge transport at r
Externí odkaz:
http://arxiv.org/abs/2305.14942
For $h$-FEM discretisations of the Helmholtz equation with wavenumber $k$, we obtain $k$-explicit analogues of the classic local FEM error bounds of [Nitsche, Schatz 1974], [Wahlbin 1991], [Demlow, Guzm\'an, Schatz 2011], showing that these bounds ho
Externí odkaz:
http://arxiv.org/abs/2304.14737
Autor:
Galkowski, Jeffrey, Wunsch, Jared
In this article, we study propagation of defect measures for Schr\"odinger operators, $-h^2\Delta_g+V$, on a Riemannian manifold $(M,g)$ of dimension $n$ with $V$ having conormal singularities along a hypersurface $Y$ in the sense that derivatives al
Externí odkaz:
http://arxiv.org/abs/2302.08154
Autor:
Galkowski, Jeffrey, Spence, Euan A.
In the analysis of the $h$-version of the finite-element method (FEM), with fixed polynomial degree $p$, applied to the Helmholtz equation with wavenumber $k\gg 1$, the $\textit{asymptotic regime}$ is when $(hk)^p C_{\rm sol}$ is sufficiently small a
Externí odkaz:
http://arxiv.org/abs/2301.03574
Let $(M,g)$ be a Zoll manifold, i.e., a smooth, compact, Riemannian manifold without boundary all of whose geodesics are closed with a minimal common period $T$. The positive definite Laplace-Beltrami operator has eigenvalues $\{\lambda_j^2\}_j$ whic
Externí odkaz:
http://arxiv.org/abs/2211.09644