Diss. (sammanfattning) Uppsala : Univ., 2004. / Härtill 8 uppsatser.

Diss. ETH No. 14577. Eidgenöss. Techn. Hochsch., Diss.--Zürich, 2002.

Thesis (M.E.E.)--University of Delaware, 2007. / Principal faculty advisor: Dennis W. Prather, Dept. of Electrical & Computer Engineering. Includes bibliographical references.

Thesis (Ph.D.) - University of St Andrews, January 2008.

Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (p. 165-171).

Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Madhavan Swaminathan; Committee Member: Andrew F. Peterson; Committee Member: David C. Keezer; Committee Member: Saibal Mukhopadyay; Committee Member: Suresh Sitaraman.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Includes bibliographical references (p. 115-120).

Thesis (M.A.)--University of Toronto, 2007. / "PCA R&D Serial No. 3030." (cover)

The elastic wave equation describes the propagation of elastic disturbances produced by seismic events in the Earth or vibrations in plates and beams. The acoustic wave equation governs the propagation of sound. The description of the wave fields resulting from an initial configuration or time dependent forces is a valuable tool when gaining insight into the effects of the layering of the Earth, the propagation of earthquakes or the behavior of underwater sound. In the most general case exact solutions to both the elastic wave equation and the acoustic wave equation are impossible to construct. Numerical methods that produce approximative solutions to the underlaying equations now become valuable tools. In this thesis we construct numerical solvers for the elastic and acoustic wave equations with focus on stability, high order of accuracy, boundary conditions and geometric flexibility. The numerical solvers are used to study wave boundary interactions and effects of curved geometries. We also compare the methods that we have constructed to other methods for the simulation of elastic and acoustic wave motion.

We address in this thesis the numerical solution of state constrained optimal control problems for systems modeled by linear parabolic equations. For the unconstrained or control-constrained optimal control problem, the first order optimality condition can be obtained in a general way and the associated Lagrange multiplier has low regularity, such as in the L²(Ω). However, for state-constrained optimal control problems, additional assumptions are required in general to guarantee the existence and regularity of Lagrange multipliers. The resulting optimality system leads to difficulties for both the numerical solution and the theoretical analysis. The approach discussed here combines the alternating direction of multipliers (ADMM) with a conjugate gradient (CG) algorithm, both operating in well-chosen Hilbert spaces. The ADMM approach allows the decoupling of the state constraints and the parabolic equation, in which we need solve an unconstrained parabolic optimal control problem and a projection onto the admissible set in each iteration. It has been shown that the CG method applied to the unconstrained optimal control problem modeled by linear parabolic equation is very efficient in the literature. To tackle the issue about the associated Lagrange multiplier, we prove the convergence of our proposed algorithm without assuming the existence and regularity of Lagrange multipliers. Furthermore, a worst case O(1/k) convergence rate in the ergodic sense is established. For numerical purposes, we employ the finite difference method combined with finite element method to implement the time-space discretization. After full discretization, the numerical results we obtain validate the methodology discussed in this thesis.