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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 …
An Implicit Level Set Model For Firespread, Pallop Huabsomboon
An Implicit Level Set Model For Firespread, Pallop Huabsomboon
Mathematics & Statistics Theses & Dissertations
The level set method is a mathematical and computational, technique for tracking a moving interface over time. It can naturally handle topological changes such as merging or breaking interfaces. Intrinsic geometric properties of the interface, such as curvature and normal direction, are easily determined from the level set function &phis;. There are many applications of the level set method, including kinetic crystal growth, epitaxial growth of thin films, image restoration, vortex dominated flows, and so forth. Most applications described in the growing literature on the applications of level sets advance the level set equation with explicit time integration. Hence, small …