Adaptive finite element methods for nonlinear inverse problems

ABSTRACT

Nonlinear inverse problems are usually formulated as optimization problems on function spaces constrained by partial differential equations. As a consequence, in realistic, three-dimensional cases, they become extraordinarily expensive to solve numerically, and advanced methods like adaptive mesh refinement become indispensible. In this contribution, we outline such an adaptive algorithm and demonstrate results using a realistic example from optical tomography.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations

Additional Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE

Keywords:
adaptive finite element methods, biomedical imaging