This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields. The singularities are described by eigenpairs of a corresponding operator pencil on a subdomain of the sphere. The solution approach is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear forms and a skew-...

Abstract. Numerical solutions of exact controllability problems for linear and semilinear 2-d wave equations with distributed controls are studied. Exact controllability problems can be solved by the corresponding optimal control problems. The optimal control problem is reformulated as a system of equations (an optimality system) that consists of an initial value problem for the underlying (lin...

Adjoint Algorithms are a powerful way to obtain the gradients that are needed in Scientific Computing. Automatic Differentiation can build Adjoint Algorithms automatically by source transformation of the direct algorithm. The specific structure of Adjoint Algorithms strongly relies on reversal of the sequence of computations made by the direct algorithm. This reversal problem is at the same tim...

We present a multigrid algorithm for the solution of distributed parameter inverse problems constrained by variable-coefficient linear parabolic partial differential equations. We consider problems in which the inversion variable is a function of space only; for stability we use an L2 Tikhonov regularization. The main feature of our algorithm is that its convergence rate is mesh-independent—eve...

‎In this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎The equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎Such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

an enhamced scheme is introduced for the solution of two dimensional umsteady euler equations. the finite- volume method of jameson et al. is modified by devicing a pnessune sensor in cell flux calculations. then the discretized gorerning equations ane relaxed in time until na steady state is reached. an appropriate model for the artificial dissipation was also employed. several tests wene cond...

This paper introduces and analyzes a new parallel-in-time gradient type method for the solution of convex linear-quadratic discrete-time optimal control (DTOC) problems. Each iteration of the classical gradient method requires the solution of the forward-in-time state equation followed by the solution of the backward-in-time adjoint equation to compute the gradient. To introduce parallelism, th...

We analyze the use of fast solvers as preconditioners for the discretized pressure equation arising in reservoir simulation. Under proper conditions on the permeability functions and the source term, we show that the number of iterations for the Conjugate Gradient method is bounded independently of both the lower bound of the permeability and the discretization parameter h. Such results are obt...

OPTIMAL SHAPE DESIGN OF AERODYNAMIC CONFIGURATIONS: A NEWTON-KRYLOV APPROACH Marian Nemec Doctor of Philosophy Graduate Department of Aerospace Science and Engineering University of Toronto 2003 Optimal shape design of aerodynamic configurations is a challenging problem due to the nonlinear effects of complex flow features such as shock waves, boundary layers, ...

This paper presents a Receding Horizon Optimal Control (RHOC) scheme with zero terminal constraint, to guarantee the stability of linear 2x2 hyperbolic systems with boundary control. The boundary control problem is first reformulated into the abstract form in which the existence and the explicit formulation of the optimal control were established in the literature. These results are then applie...