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Randomized sampling for basis functions construction in generalized finite element methods

dc.contributor.author Chen, K
dc.contributor.author Li, Q
dc.contributor.author Lu, J
dc.contributor.author Wright, SJ
dc.date.accessioned 2018-02-14T23:46:14Z
dc.date.available 2018-02-14T23:46:14Z
dc.date.issued 2018-02-14
dc.identifier http://arxiv.org/abs/1801.06938v1
dc.identifier.uri https://hdl.handle.net/10161/16084
dc.description.abstract In the context of generalized finite element methods for elliptic equations with rough coefficients $a(x)$, efficiency and accuracy of the numerical method depend critically on the use of appropriate basis functions. This work explores several random sampling strategies for construction of basis functions, and proposes a quantitative criterion to analyze and compare these sampling strategies. Numerical evidence shows that the optimal basis functions can be well approximated by a random projection of generalized eigenvalue problem onto subspace of $a$-harmonic functions.
dc.publisher Society for Industrial & Applied Mathematics (SIAM)
dc.subject math.OC
dc.subject math.OC
dc.subject math.NA
dc.title Randomized sampling for basis functions construction in generalized finite element methods
dc.type Journal article
duke.contributor.id Lu, J|0598771
pubs.author-url http://arxiv.org/abs/1801.06938v1
pubs.organisational-group Chemistry
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Physics
pubs.organisational-group Trinity College of Arts & Sciences
duke.contributor.orcid Lu, J|0000-0001-6255-5165


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