Bound Constrained Partial DifferentialEquation Inverse Problem Solution by theSemi-Smooth Newton Method
- Univ. of California, Merced, CA (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
We present the mathematical derivation, software implementation details, and computational results for a semi-smooth Newton method applied to two inverse problems governed by partial differential equations with bound constraints. The two problems share mathematical structural similarities to density-based topology optimization problems. The semi-smooth Newton method provides a mesh independent solution computation for the two test problems. A key step is that the complementarity part of the necessary optimality conditions are reformulated with the use of a complementarity functionφsuch that the complementarity conditions are satisfied if and only if a zero of a nonsmooth function has been obtained. The modular finite element package MFEM is utilized for the software implementation. In addition we constructed a matrix-free Operator to enable the use of efficient Krylov subspace IterativeSolver of MFEM for the solution of our two target problems.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1765792
- Report Number(s):
- LLNL--TR-819385; 1030420
- Country of Publication:
- United States
- Language:
- English
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