复杂地电模型的非结构多重网格剖分算法

AN UNSTRUCTURED GEOMETRIC MULTIGRID GENERATION ALGORITHM FOR ARBITRARY GEOELECTRIC MODEL

面对越来越多的观测数据、越来越复杂的地电模型,大地电磁法的高维正反演需要发展高效、稳定的正、反演计算新技术。多重网格法是求解椭圆型偏微分方程最优化的方法之一,近些年来被广泛地用作大规模、高精度方程求解的加速器。目前,多重网格法多基于矩形网格来构造粗细不同的层次网格组,但是矩形网格不能适应几何形状复杂的区域并且不支持局部加密细化从而限制了多重网格法的应用。文中提出一种采用Delaunay三角网的非结构化多重网格生成算法,该算法能够自动对复杂区域生成粗细不同的网格,并且每层网格单元具有良好的形状比和可控的尺寸大小。文中采用该算法实现了对复杂地电模型的非结构多重网格的自动生成,解决了大地电磁多重网格正反演计算中复杂模型离散化这一关键的技术问题。

With the growing number of observational data,increasingly complex geoelectric model,and high-dimensional magnetotelluric method,the efficient and stable forward and inversion technologies become more and more required. Multigrid method enables the asymptotically optimal approximate numerical solution to elliptic partial differential equations including the MT 2D forward modeling problem. Currently,the coarsening and refining operations are based on regular grid which is easy to understand and implement. However,when the geometry of a region is complex or the region needs local refinements,regular grid becomes not well applicable. Unstructured triangular grid has better geometrical adaptability than structured grid. The Delaunay triangulation ensures that each triangle is generated to be Delaunay. This property is particularly suitable for numerical interpolation and FEM calculation. Besides,the Delaunay triangulation has a strong mathematical theory foundation which makes it very convenient for local refinement and sparseness. The key to solve the complicated geoelectric model using multigrid method is the automatic generation of unstructured multi-level grids.In this paper,we present an algorithm for generating unstructured grid for Multigrid method based on Delaunay triangulation. The algorithm will automatically generate the coarse and fine grid for complex input region,and all the triangle elements abide by the Delaunay criteria which ensure numerical accuracy and high convergence rate.