SIAM Journal on Numerical Analysis, Volume 59, Issue 4, Page 2138-2162, January 2021.
The numerical integration over a planar domain that is cut by an implicitly defined boundary curve is an important problem that arises, for example, in unfitted finite element methods and in isogeometric analysis on trimmed computational domains. In this paper, we introduce a a very general version of the transport theorem for moving domains defined by implicitly defined curves and use it to establish an efficient and accurate quadrature rule for this class of domains. In numerical experiments it is shown that the method achieves high orders of convergence. Our approach is suited for high-order geometrically unfitted finite element methods as well as for high-order trimmed isogeometric analysis.

中文翻译：

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使用隐式定义的移动曲线的高阶传输定理在平面域上执行正交

SIAM Journal on Numerical Analysis，第 59 卷，第 4 期，第 2138-2162 页，2021
年1 月。 由隐式定义的边界曲线切割的平面域上的数值积分是一个重要问题，例如，在未拟合的有限元中方法和修剪计算域的等几何分析。在本文中，我们介绍了由隐式定义曲线定义的移动域的传输定理的一个非常通用的版本，并使用它为此类域建立有效且准确的求积规则。数值实验表明，该方法实现了高阶收敛。我们的方法适用于高阶几何未拟合有限元方法以及高阶修整等几何分析。