标题： 一种求解二维不规则域椭圆方程的快速四阶切割单元法 显示英文标题

标题： A Fast Fourth-Order Cut Cell Method for Solving Elliptic Equations in Two-Dimensional Irregular Domains

摘要： 我们提出了一种快速的四阶切割网格方法，用于求解二维不规则域中的常系数椭圆型方程。在我们的方法中，处理不规则域的关键是生成有限体积插值模板的定位格点生成（PLG）算法。通过在生成的模板上进行最小二乘拟合，我们可以推导出椭圆算子的高阶离散化。然后，我们设计了一种新的几何多重网格方案来高效地求解由此产生的线性系统。最后，我们通过在不规则域中的各种数值测试展示了该方法的准确性和效率。 显示英文摘要

摘要： We propose a fast fourth-order cut cell method for solving constant-coefficient elliptic equations in two-dimensional irregular domains. In our methodology, the key to dealing with irregular domains is the poised lattice generation (PLG) algorithm that generates finite-volume interpolation stencils near the irregular boundary. We are able to derive high-order discretization of the elliptic operators by least squares fitting over the generated stencils. We then design a new geometric multigrid scheme to efficiently solve the resulting linear system. Finally, we demonstrate the accuracy and efficiency of our method through various numerical tests in irregular domains.