中文摘要：

为了对不均匀介质中物理场进行更有效的多尺度模拟，提出一种称为有限点集-网格元法的数值方法（finite point-grid element method，FPGEM）．FPGEM是对传统有限元方法的改造，它把网格与节点分离成独立的两套覆盖，采用离散的有限点集对物理场进行多尺度逼近，同时采用网格剖分作为介质分布的几何载体；点集和网格各自扮演不同的角色，发挥不同的功能．FPGEM主要的优点是：由于其节点和网格分离，对场的非均匀性及介质非均匀分布具有双重的多尺度模拟的优势，为一些地球物理问题中的多尺度模拟提供了一种更加灵活、自然的计算框架．

英文摘要：

To implement a more effective multi-scale calculation method adapted to modeling the distribution of physical fields in heterogeneous media, we have developed a numerical method named the Finite Point-Grid Element Method （FPGEM）. It was formulated from the traditional finite element method. In FPGEM the nodes （finite points） and grids perform different funetions in numerical simulation： the finite points approach the physical field with a multi-scale solution, and the grids describe the distribution of media parameters. Then we present some examples of resistivity modeling. The results show that FPGEM is good at implementing double modeling for heterogeneous fields and media by separating nodes from grids. It provides a more flexible and natural calculation frame for multi-scale numerical simulations in some geophysical problems.