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An implicit boundary integral method for interfaces evolving by Mullins-Sekerka dynamics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0001-8441-3678
2017 (English)In: Springer Proceedings in Mathematics and Statistics, Springer New York LLC , 2017, p. 1-21Conference paper, Published paper (Refereed)
Abstract [en]

We present an algorithm for computing the nonlinear interface dynamics of the Mullins-Sekerka model for interfaces that are defined implicitly (e.g. by a level set function) using integral equations. The computation of the dynamics involves solving Laplace’s equation with Dirichlet boundary conditions on multiply connected and unbounded domains and propagating the interface using a normal velocity obtained from the solution of the PDE at each time step. Our method is based on a simple formulation for implicit interfaces, which rewrites boundary integrals as volume integrals over the entire space. The resulting algorithm thus inherits the benefits of both level set methods and boundary integral methods to simulate the nonlocal front propagation problem with possible topological changes. We present numerical results in both two and three dimensions to demonstrate the effectiveness of the algorithm.

Place, publisher, year, edition, pages
Springer New York LLC , 2017. p. 1-21
Keywords [en]
Boundary integral methods, Dendritic growth simulation, Free boundary problem, Implicit interface, Level set methods, Mullins-Sekerka, Boundary conditions, Drop breakup, Dynamics, Integral equations, Level measurement, Nonlinear equations, Dendritic growth, Free-boundary problems, Level Set method, Mullins, Numerical methods
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-222928DOI: 10.1007/978-3-319-66764-5_1Scopus ID: 2-s2.0-85034267821ISBN: 9783319667621 OAI: oai:DiVA.org:kth-222928DiVA, id: diva2:1193709
Conference
International Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015, 16 August 2015 through 18 August 2015
Note

QC 20180327

Available from: 2018-03-27 Created: 2018-03-27 Last updated: 2018-03-27Bibliographically approved

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Tsai, Yen-Hsi Richard

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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More styles
Language
  • de-DE
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  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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