中文摘要：

以曲面论为理论基础的高精度曲面建模模型（HASM）从理论上解决了曲面模拟的误差问题，但是计算量大，存储要求高。为了解决这一问题，应用多重网格法（MG法）来求解HASM模型离散得到的线性方程组。数值试验结果表明，MG法在保持求解精度的前提下大幅度提高了HASM模型的模拟速度，同时解决了HASM模型存储要求高等问题。

英文摘要：

High accuracy surface modeling （HASM） developed in terms of the fundamental theorem of surfaces has theoretically given a solution to the error problem. However, HASM had a huge computation cost and very large memory cost because it must solve a partial differential equation set for simulating each lattice of surface, which make HASM difficult to be widely applied. As multi-grid method is well known as a fastest solution for the elliptic partial differential equations, we apply multi-grid method in the process of HASM. Numerical tests show that multi-grid method is efficient for HASM whilst it keeping the accuracy of the solutions, and it solves the memory problem of HASM as well.