Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting the correct topology of the domain. Furthermore, a geometry-based local error estimate is explored to guide the hierarchical subdivision and save the computation cost. Numerical experiments are presented to demonstrate the accuracy and the potential of the proposed method.

中文翻译：

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具有拓扑保证的隐式定义域上的数值积分

由于隐函数的拓扑变化，在隐定义域上的数值积分是具有挑战性的。在本文中，我们使用区间算法准确地确定了积分域的边界，从而获得了正确的域拓扑。此外，探索了基于几何的局部误差估计，以指导分层细分并节省计算成本。数值实验表明了该方法的准确性和潜力。