Computing Interfaces in Diverse Applications
Mathematical models and computing methods for problems involving moving interfaces are considered. These occur in a great variety of applications, and mathematical models provide a unifying framework, facilitating interdisciplinary cooperation. We discuss and propose some generic numerical methods for problems involving moving interfaces. The level set method is used for interface capturing. A Cartesian and a finite element mesh are used simultaneously. This facilitates efficient local mesh refinement and derefinement for accurate computation of physical effects occurring at the interfaces, that move and may undergo topological change. The method has been implemented in three dimensions. We present examples from materials science (homogenization) and medical technology (wound healing).
Keywordsmoving interface level set method adaptive mesh refinement cut-cell method epidermal wound healing
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