The primary objective of this thesis is to develop a fast and efficient computational framework for the nonlinear inverse problem of identifying a variable coefficient in a system of partial differential equation modelling the response of an incompressible elastic object under some known body forces and boundary traction. The main novelty of this contribution is to use, for the first time, of the so-called heavy ball with friction method for inverse problems. The heavy ball with friction dynamical system is a nonlinear oscillator with damping. The key idea is to pose the inverse problem as an optimization problem, derive its optimality system, and then seek the solution through a trajectory of a dynamical system. In this work, we will study four different optimization formulations for the nonlinear inverse problem and thoroughly compare their convergence and numerical performance. Since we use a second-order method, we also investigate a general second-order hybrid and a second-order adjoint method for an efficient computation of the hessian of the output least-squares formulation. The stability of the dynamical system approach with respect to the contamination in the data is thoroughly investigate in the context of a simpler elliptic partial differential equation. The mixed finite element approach is used to discretize the direct as well as the inverse problems.
Library of Congress Subject Headings
Elastography--Mathematics; Inverse problems (Differential equations); Differential equations, Partial; Mathematical optimization
Applied and Computational Mathematics (MS)
Department, Program, or Center
School of Mathematical Sciences (COS)
Eluyefa, Oladayo, "Heavy Ball with Friction Method for the Elastography Inverse Problem" (2015). Thesis. Rochester Institute of Technology. Accessed from
RIT – Main Campus