High order unfitted finite element methods on level set domains using isoparametric mappings
High order unfitted finite element methods on level set domains using isoparametric mappings
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DOI：
10.1016/j.cma.2015.12.005
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
C. Lehrenfeld
中科院分区：
文献类型：
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作者：
C. Lehrenfeld
本文介绍了一类新的非拟合有限元方法，它在曲面和体积上具有高精度数值积分，而曲面和体积仅由水平集函数隐式定义。一个不适合的有限元方法，这是适合于分段平面接口的情况下，结合了参数映射的基本网格，从而在一个等参不适合的有限元方法。参数映射的构建方式使得分段平面界面重建的质量显着提高，从而允许（未拟合）域和表面积分的高阶精确计算。我们提出的方法，讨论实施方面，并提出数值例子，证明这种方法的质量和潜力。
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is suitable for the case of piecewise planar interfaces is combined with a parametric mapping of the underlying mesh resulting in an isoparametric unfitted finite element method. The parametric mapping is constructed in a way such that the quality of the piecewise planar interface reconstruction is significantly improved allowing for high order accurate computations of (unfitted) domain and surface integrals. We present the method, discuss implementational aspects and present numerical examples which demonstrate the quality and potential of this method.