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DOE OSTI · 1765792

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

Hartland, Tucker·Petra, Cosmin G.·Petra, Noemi·Wang, Jingyi
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Abstract

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.

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97 MATHEMATICS AND COMPUTING

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Hartland, Tucker, Petra, Cosmin G., Petra, Noemi, Wang, Jingyi. 2021-02-09. Bound Constrained Partial DifferentialEquation Inverse Problem Solution by theSemi-Smooth Newton Method. https://doi.org/10.2172/1765792

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