Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (6): 1479-1489.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 65M32
Trendmd