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Partition of unity extension of functions on complex domains
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, p. 57-79Article in journal (Refereed) Published
Abstract [en]

We introduce an efficient algorithm, called partition of unity extension or PUX, to construct an extension of desired regularity of a function given on a complex multiply connected domain in 2D. Function extension plays a fundamental role in extending the applicability of boundary integral methods to inhomogeneous partial differential equations with embedded domain techniques. Overlapping partitions are placed along the boundaries, and a local extension of the function is computed on each patch using smooth radial basis functions; a trivially parallel process. A partition of unity method blends the local extrapolations into a global one, where weight functions impose compact support. The regularity of the extended function can be controlled by the construction of the partition of unity function. We evaluate the performance of the PUX method in the context of solving the Poisson equation on multiply connected domains using a boundary integral method and a spectral solver. With a suitable choice of parameters the error converges as a tenth order method down to 10−14.

Place, publisher, year, edition, pages
Academic Press Inc. , 2018. Vol. 375, p. 57-79
Keywords [en]
Boundary integral method, Embedded domain, Function extension, Linear elliptic partial differential equation, Partition of unity, Radial basis function
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-236548DOI: 10.1016/j.jcp.2018.08.012ISI: 000450907600003Scopus ID: 2-s2.0-85052310129OAI: oai:DiVA.org:kth-236548DiVA, id: diva2:1266154
Funder
Swedish Research Council, 2015-04998
Note

Funding text: This work has been supported by the Swedish Research Council under Grant No. 2015-04998 and by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine and is gratefully acknowledged. QC 20181127

Available from: 2018-11-27 Created: 2018-11-27 Last updated: 2018-12-11Bibliographically approved

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Lehto, ErikTornberg, Anna-Karin

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Fryklund, FredrikLehto, ErikTornberg, Anna-Karin
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