Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods For Elliptic Inverse Problems, Widodo Samyono
Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods For Elliptic Inverse Problems, Widodo Samyono
Mathematics & Statistics Theses & Dissertations
This study focuses on the solution of inverse problems for elliptic systems. The inverse problem is constructed as a PDE-constrained optimization, where the cost function is the L2 norm of the difference between the measured data and the predicted state variable, and the constraint is an elliptic PDE. Particular examples of the system considered in this stud, are groundwater flow and radiation transport. The inverse problems are typically ill-posed due to error in measurements of the data. Regularization methods are employed to partially alleviate this problem. The PDE-constrained optimization is formulated as the minimization of a Lagrangian functional, formed …