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A target specific QBX method for the accurate computation of boundary integrals with nearly touching interfaces Siegel, Michael
Description
Boundary integral methods are among the most popular methods for computing interfacial fluid flow, and have the advantage that they can be made high-order accurate. Thus, they are useful for investigating phenomena that require high accuracy to resolve features, such as "pinching" or topological singularities that can occur on the interface. However, standard BI methods lose accuracy when two parts of an interface are near touching. In this talk, we present a new algorithm based on the QBX method of Klockner et al. for the accurate computation of boundary integrals with singular or nearly singular kernels in 3D. The QBX method is typically based on a spherical harmonics expansion which when truncated at $\mathcal{O}(p)$ has $\mathcal{O}(p^2)$ terms. This expansion can equivalently be written with $\mathcal{O}(p)$ terms, but paying the price that the expansion coefficients will depend on the target point. Based on this observation, we develop a target specific QBX method. We give error estimates for our method, and illustrate its performance in several examples. This work is joint with Anna-Karin Tornberg.
Item Metadata
Title |
A target specific QBX method for the accurate computation of boundary integrals with nearly touching interfaces
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-10-02T11:04
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Description |
Boundary integral methods are among the most popular methods for computing interfacial fluid flow, and have the advantage that they can be made high-order accurate. Thus, they are useful for investigating phenomena that require high accuracy to resolve features, such as "pinching" or topological singularities that can occur on the interface. However, standard BI methods lose accuracy when two parts of an interface are near touching. In this talk, we present a new algorithm based on the QBX method of Klockner et al. for the accurate computation of boundary integrals with singular or nearly singular kernels in 3D. The QBX method is typically based on a spherical harmonics expansion which when truncated at $\mathcal{O}(p)$ has $\mathcal{O}(p^2)$ terms. This expansion can equivalently be written with $\mathcal{O}(p)$ terms, but paying the price that the expansion coefficients will depend on the target point. Based on this observation, we develop a target specific QBX method. We give error estimates for our method, and illustrate its performance in several examples. This work is joint with Anna-Karin Tornberg.
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Extent |
31 minutes
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File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: New Jersey Institute of Technology
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Series | |
Date Available |
2018-04-13
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0365578
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International