Bound Constrained Partial DifferentialEquation Inverse Problem Solution by theSemi-Smooth Newton Method

Technical Report · Tue Feb 09 04:00:00 EST 2021

DOI:https://doi.org/10.2172/1765792· OSTI ID:1765792

Hartland, Tucker ^[1]; Petra, Cosmin G. ^[2]; Petra, Noemi ^[1]; Wang, Jingyi ^[2]

---

1. Univ. of California, Merced, CA (United States)
2. 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

Related Subjects

97 MATHEMATICS AND COMPUTING