Large degree-of-freedom real-time adaptive optics (AO) control requires reconstruction algorithms that are computationally efficient and readily parallelized for hardware implementation. In particular, we find the wave-front reconstruction for the Hudgin and Fried geometry can be cast into a form of the well-known Sylvester equation using the Kronecker product properties of matrices. We derive ...

In this dissertation, we investigate the parabolic mixed derivative diffusion equation modeling the viscous and viscoelastic effects in a non-Newtonian viscoelastic fluid. The model is analytically considered using Fourier and Laplace transformations. The main focus of the dissertation, however, is the implementation of the Peaceman-Rachford Alternating Direction Implicit method. The one-dimens...

We present a highly efficient parallelization of the computation of the price of exotic cross-currency interest rate derivatives with path-dependent features via a Partial Differential Equation (PDE) approach. In particular, we focus on the parallel pricing on Graphics Processing Unit (GPU) clusters of long-dated foreign exchange (FX) interest rate derivatives, namely Power-Reverse Dual-Currenc...

In this article, the focus is mainly on gaining optimal control for unstable power system models and stabilizing them through Riccati-based feedback stabilization process with sparsity-preserving techniques. We are to find solution of Continuous-time Algebraic Riccati Equations (CAREs) governed from derived Brazilian Inter-Connected Power System (BIPS) models, which large-scale sparse index-1 d...

We present an alternating direction implicit method solving numerically the TV-H−1 flow which shows good performance when applied to various imaging problems. Some stability issues depending on the regularization of the total variation may appear, thus explicit terms need to be controlled. A primal-dual approach and its possible applications to such problems is presented as well. 1 Higher order...

We study a spline wavelet alternative direction implicit (SW-ADI) algorithm for solving two-dimensional reaction diffusion equations. This algorithm is based on a collocation method for PDEs with a specially designed spline wavelet for the Sobolev space H 2(I ) on a closed interval I. By using the tensor product nature of adaptive wavelet meshes, we propose a SW-ADI method for two-dimensional p...

Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-impli...