THESIS
2023
1 online resource (xiii, 59 pages) : illustrations (some color)
Abstract
The level set method is a numerical approach for interface computation that is widely
applied in various fields such as interface modeling, image processing, and inverse problems.
The original method represents the interface implicitly by considering the zero level set of
a level set function. However, when dealing with multiple interfaces, the original method
requires more than one level set function for computations. To address this issue, this
thesis introduces a multilayer level set method that extends the original method. This
new method enables the representation of multiple interfaces that are subject to different
motion laws using a single level set function. This provides a more compact way to express
complex geometries for computation. Numerical examples are given to illustrat...[
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The level set method is a numerical approach for interface computation that is widely
applied in various fields such as interface modeling, image processing, and inverse problems.
The original method represents the interface implicitly by considering the zero level set of
a level set function. However, when dealing with multiple interfaces, the original method
requires more than one level set function for computations. To address this issue, this
thesis introduces a multilayer level set method that extends the original method. This
new method enables the representation of multiple interfaces that are subject to different
motion laws using a single level set function. This provides a more compact way to express
complex geometries for computation. Numerical examples are given to illustrate the
application of the multilayer level set method in general interface motion problems and
Schrödinger inverse source problems.
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