Zobrazeno 1 - 10
of 111
pro vyhledávání: '"GILLETTE, ANDREW"'
Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods in
Externí odkaz:
http://arxiv.org/abs/2404.03586
Autor:
Gillette, Andrew, Rand, Alexander
Interpolation error estimates in terms of geometric quality measures are established for harmonic coordinates on polytopes in two and three dimensions. First we derive interpolation error estimates over convex polygons that depend on the geometric qu
Externí odkaz:
http://hdl.handle.net/10150/621355
http://arizona.openrepository.com/arizona/handle/10150/621355
http://arizona.openrepository.com/arizona/handle/10150/621355
In this work, we revisit the marking decisions made in the standard adaptive finite element method (AFEM). Experience shows that a na\"{i}ve marking policy leads to inefficient use of computational resources for adaptive mesh refinement (AMR). Conseq
Externí odkaz:
http://arxiv.org/abs/2207.06339
Autor:
Gillette, Andrew, Kur, Eugene
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the dens
Externí odkaz:
http://arxiv.org/abs/2203.05685
Autor:
Crum, Justin, Cheng, Cyrus, Ham, David A., Mitchell, Lawrence, Kirby, Robert C., Levine, Joshua A., Gillette, Andrew
Publikováno v:
ACM Transactions on Mathematical Software 48(1):8:1-8:19 (2022)
We present an implementation of the trimmed serendipity finite element family, using the open source finite element package Firedrake. The new elements can be used seamlessly within the software suite for problems requiring $H^1$, \hcurl, or \hdiv-co
Externí odkaz:
http://arxiv.org/abs/2104.12986
Publikováno v:
Computer-Aided Design 114 (2019) 64-72
Fractional partial differential equations (FDEs) are used to describe phenomena that involve a "non-local" or "long-range" interaction of some kind. Accurate and practical numerical approximation of their solutions is challenging due to the dense mat
Externí odkaz:
http://arxiv.org/abs/1905.00992
Autor:
GILLETTE, ANDREW1 gillette7@llnl.gov, KUR, EUGENE2 kur1@llnl.gov
Publikováno v:
ACM Transactions on Mathematical Software. Dec2024, Vol. 50 Issue 4, p1-21. 21p.
Many conforming finite elements on squares and cubes are elegantly classified into families by the language of finite element exterior calculus and presented in the Periodic Table of the Finite Elements. Use of these elements varies, based principall
Externí odkaz:
http://arxiv.org/abs/1806.00031
We propose two general operations on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of "nonstandard" convergent methods. The first operation, called DoF-transfer, moves edge degrees of free
Externí odkaz:
http://arxiv.org/abs/1804.04390
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