Now showing items 1-10 of 35
Numerical Solutions of Matrix Equations Arising in Model Reduction of Large-Scale Linear-Time-Invariant Systems
This thesis presents and analyzes new algorithms for matrix equations arising from model reduction of linear-time-invariant (LTI) systems. Such systems arise in a variety of areas, especially in circuit simulation. When ...
Adaptive Finite Element Methods for Linear-Quadratic Convection Dominated Elliptic Optimal Control Problems
The numerical solution of linear-quadratic elliptic optimal control problems requires the solution of a coupled system of elliptic partial differential equations (PDEs), consisting of the so-called state PDE, the adjoint ...
A C++ Class Supporting Adjoint-State Methods
The adjoint-state method is widely used for computing gradients in simulation- driven optimization problems. The adjoint-state evolution equation requires access to the entire history of the system states. There are ...
Sparse Signal Reconstruction via Iterative Support Detection
We present a novel sparse signal reconstruction method "ISD", aiming to achieve fast reconstruction and a reduced requirement on the number of measurements compared to the classical L1 minimization approach. ISD addresses ...
A Random Force is a Force, of Course, of Coarse: Decomposing Complex Enzyme Kinetics with Surrogate Models
The temporal autocorrelation (AC) function associated with monitoring order parameters characterizing conformational fluctuations of an enzyme is analyzed using a collection of surrogate models. The surrogates considered ...
Application of POD and DEIM to Dimension Reduction of Nonlinear Miscible Viscous Fingering in Porous Media
A Discrete Empirical Interpolation Method (DEIM) is applied in conjunction with Proper Orthogonal Decomposition (POD) to construct a nonlinear reduced-order model of finite difference discretized system used in the simulation ...
Accelerating the LSTRS Algorithm
In a recent paper [Rojas, Santos, Sorensen: ACM ToMS 34 (2008), Article 11] an efficient method for solvingthe Large-Scale Trust-Region Subproblem was suggested which is based on recasting it in terms of a parameter dependent ...
Time-Stepping Classes for Optimization (TSOpt)
This report introduces the "Time Stepping Package for Optimization", or TSOpt, which is an interface for time-stepping simulation written in C++. It packages a simulator together with its derivatives (\sensitivities") and ...
User's Guide for LMaFit: Low-rank Matrix Fitting
This User's Guide describes the functionality and basic usage of the Matlab package LMaFit for low-rank matrix optimization. It also briefly explains the formulations and algorithms used.
Dimension Reduction for Unsteady Nonlinear Partial Differential Equations via Empirical Interpolation Methods
This thesis evaluates and compares the efficiencies of techniques for constructing reduced-order models for finite difference (FD) and finite element (FE) discretized systems of unsteady nonlinear partial differential ...