论文标题
椭圆均质问题的有效在线途径方法
An Efficient Online-Offline Method for Elliptic Homogenization Problems
论文作者
论文摘要
我们提出了一种解决椭圆均质化问题的新数值方法。主要的想法是，缺少有效矩阵是通过在离线阶段求解局部最小二乘的重建的，该阶段应作为在线计算的输入数据。借助重建运算符的精制估计值分析了所提出方法的准确性。二维和三维数值测试证实了所提出的方法的效率，并说明这种在线办公策略可能会大大降低成本而不会损失准确性。
We present a new numerical method for solving the elliptic homogenization problem. The main idea is that the missing effective matrix is reconstructed by solving the local least-squares in an offline stage, which shall be served as the input data for the online computation. The accuracy of the proposed method are analyzed with the aid of the refined estimates of the reconstruction operator. Two dimensional and three dimensional numerical tests confirm the efficiency of the proposed method, and illustrate that this online-offline strategy may significantly reduce the cost without loss of accuracy.
