Dewetting dynamics of anisotropic particles: A level set numerical approach

Siddharth Gavhale; Karel Švadlenka

Applications of Mathematics (2022)

  • Volume: 67, Issue: 5, page 543-571
  • ISSN: 0862-7940

Abstract

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We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface implicitly, which supports natural implementation of topology changes, such as merging and splitting, and makes the approach attractive for applications in material science. The main tool in the new scheme are convolution kernels developed in previous studies that approximate the given anisotropy in a nonlocal way. We provide a detailed report on the numerical properties of the proposed algorithm.

How to cite

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Gavhale, Siddharth, and Švadlenka, Karel. "Dewetting dynamics of anisotropic particles: A level set numerical approach." Applications of Mathematics 67.5 (2022): 543-571. <http://eudml.org/doc/298482>.

@article{Gavhale2022,
abstract = {We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface implicitly, which supports natural implementation of topology changes, such as merging and splitting, and makes the approach attractive for applications in material science. The main tool in the new scheme are convolution kernels developed in previous studies that approximate the given anisotropy in a nonlocal way. We provide a detailed report on the numerical properties of the proposed algorithm.},
author = {Gavhale, Siddharth, Švadlenka, Karel},
journal = {Applications of Mathematics},
keywords = {interface evolution; anisotropic energy; weighted mean curvature; obstacle problem; thresholding method; convolution kernels; topology change; numerical analysis},
language = {eng},
number = {5},
pages = {543-571},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dewetting dynamics of anisotropic particles: A level set numerical approach},
url = {http://eudml.org/doc/298482},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Gavhale, Siddharth
AU - Švadlenka, Karel
TI - Dewetting dynamics of anisotropic particles: A level set numerical approach
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 5
SP - 543
EP - 571
AB - We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface implicitly, which supports natural implementation of topology changes, such as merging and splitting, and makes the approach attractive for applications in material science. The main tool in the new scheme are convolution kernels developed in previous studies that approximate the given anisotropy in a nonlocal way. We provide a detailed report on the numerical properties of the proposed algorithm.
LA - eng
KW - interface evolution; anisotropic energy; weighted mean curvature; obstacle problem; thresholding method; convolution kernels; topology change; numerical analysis
UR - http://eudml.org/doc/298482
ER -

References

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