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Numerical safeguarded use of the implicit restarted Lanczos algorithm for solving nonlinear eigenvalue problems and its monotonicity analysis
In this thesis, we develop an efficient accurate numerical algorithm for evaluating a few of the smallest eigenvalues and their corresponding eigenvectors for large scale nonlinear eigenproblems. The entries of the matrices ...
Recovering elastic moduli of nonlinear anisotropic annular membranes from interior measurements of deformation and pressure
We investigate the problem of inferring elastic moduli of nonlinearly elastic membranes from interior measurements of deformation and pressure. We begin by formulating a model of membrane deformation under a vertical force ...
A comparison of finite difference stencils on two forms of the acoustic wave equation
In practice, two forms of the acoustic wave equation, the velocity-stress and pressure forms, are used to simulate seismic experiments. These equations in their discrete forms lead to two families of finite difference ...
Mixed finite element methods for flow in porous media
Mixed finite element discritizations for problems arising in flow in porous medium applications are considered. We first study second order elliptic equations which model single phase flow. We consider the recently introduced ...
The use of optimization techniques in the solution of partial differential equations from science and engineering
Optimal Control of systems governed by Partial Differential Equations is an applications-driven area of mathematics involving the formulation and solution of minimization problems. Given a physical phenomenon described by ...