Title page for ETD etd-03292011-175733


Type of Document Dissertation
Author Alexe, Mihai
URN etd-03292011-175733
Title Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems
Degree PhD
Department Computer Science
Advisory Committee
Advisor Name Title
Sandu, Adrian Committee Chair
Borggaard, Jeffrey T. Committee Member
Cao, Yang Committee Member
De Sturler, Eric Committee Member
Ribbens, Calvin J. Committee Member
Keywords
  • Inverse problems
  • Adjoint Method
  • Adaptive Mesh Refinement
  • Automatic Differentiation
Date of Defense 2011-03-18
Availability restricted
Abstract
Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in science and engineering require the

solution of inverse problems where parameters for a given model are estimated based on available measurement information. In contrast to forward (regular) simulations, inverse problems have not extensively benefited from the adaptive solver technology. Previous research in inverse problems has focused mainly on the continuous approach to calculate sensitivities, and has typically employed fixed time and space meshes in the solution process. Inverse problem solvers that make exclusive use of uniform or static meshes avoid complications such as the differentiation of mesh motion equations, or inconsistencies in the sensitivity equations between subdomains with different refinement levels. However, this comes at the cost of low computational efficiency. More efficient computations are possible through judicious use of adaptive mesh refinement, adaptive time steps, and the discrete adjoint method. This dissertation develops a complete framework for fully discrete adjoint sensitivity analysis and inverse problem solutions, in the context of time dependent, adaptive mesh, and adaptive step models. The discrete framework addresses all the necessary ingredients

of a state–of–the–art adaptive inverse solution algorithm: adaptive mesh and time step refinement, solution grid transfer operators, a priori and a posteriori error analysis and estimation, and discrete adjoints for sensitivity analysis of flux–limited numerical algorithms.

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