数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1479-1489.

• 论文 • 上一篇    下一篇

重构山体表面的非线性多重网格有限元反演算法

窦以鑫|韩波   

  1. 哈尔滨工业大学 数学系 哈尔滨 150001
  • 收稿日期:2010-08-24 修回日期:2011-12-01 出版日期:2011-12-25 发布日期:2011-12-25
  • 基金资助:

    中央高校基本科研业务费专项资金(2009051)资助

A Nonlinear Multigrid-FEM Inversion Algorithm for Reconstruction of a Mountain Surface

 DOU Yi-Xin, HAN Bo   

  1. Department of Mathematics, Harbin Institute of Technology, Harbin 150001
  • Received:2010-08-24 Revised:2011-12-01 Online:2011-12-25 Published:2011-12-25
  • Supported by:

    中央高校基本科研业务费专项资金(2009051)资助

摘要:

山体重构模型是由两个过程构成:一个是山体内部的热对流扩散过程, 另一个是山体表面运动过程. 前者是描述三位空间中岩石温度变化规律, 后者则是描述二维空间中山体表面演变规律. 山体表面重构过程归结为求解该耦合方程的反演问题. 从数值计算的角度来讲, 求解该问题会遇到一些困难, 例如:优化非凸罚函数和大计算量的问题. 为了避免这些问题, 本文建议利用非线性多重网格有限元反演算法重构山体表面. 数值算例表明该算法具有很好的稳定性和收敛性.

关键词: 山体表面模型, 反问题, 非线性多重网格有限元

Abstract:

The modeling of reconstruction of a mountain surface is made  of two processes: a thermal convection diffusion process inside a mountain and a mountain surface moving process. The former one describes the change of temperature of rocks in three dimensional spatial domain, and the latter one explains the evolution of a mountain surface in two dimensional spatial domain. The reconstruction of a mountain surface comes down to solving the inverse problem for this coupled system. From the point of view of numerical computation,
the authors  shall experience some difficulties,  for example, solving optimization of a non-convex cost functional and huge computational cost. In order to circumvent the difficulties above, the authors  propose a nonlinear multigrid-FEM inversion algorithm to reconstruct a mountain surface. Numerical experiments show that this algorithm is efficient for this coupled system.

Key words: Modeling of Mountain Surface,  Inverse Problem, Nonlinear Multigrid-FEM Inversion Algorithm

中图分类号: 

  • 65M32