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<p>This thesis concerns the approximation of optimally controlled partial differential equations for applications in optimal design and reconstruction. Such optimal control problems are often ill-posed and need to be regularized to obtain good approximations. We here use the theory of the corresponding Hamilton-Jacobi-Bellman equations to construct regularizations and derive error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method where the first, analytical, step is to regularize the Hamiltonian. Next its stationary Hamiltonian system, a nonlinear partial differential equation, is computed efficiently with the Newton method using a sparse Jacobian. An error estimate for the difference between exact and approximate objective functions is derived, depending only on the difference of the Hamiltonian and its finite dimensional regularization along the solution path and its<em> L</em>² projection, i.e. not on the difference of the exact and approximate solutions to the Hamiltonian systems. In the thesis we present solutions to applications such as optimal design and reconstruction of conducting materials and elastic structures.</p>

In this paper matrix compression techniques in the context of wavelet Galerkin schemes for boundary integral equations are developed and analyzed that exhibit optimal complexity in the following sense. The fully discrete scheme produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that is proven to stay proportional to the number of unknowns. Key issues are the second compression, that reduces the near field complexity significantly, and an additional a-posteriori compression. The latter one is based on a general result concerning an optimal work balance, that applies, in particular, to the quadrature used to compute the compressed stiffness matrix with sufficient accuracy in linear time. The theoretical results are illustrated by a 3D example on a nontrivial domain.

Using data from the Drug Use Forecasting (DUF) and the Arrestee Drug Abuse Monitoring (ADAM) programs collected by the National Institute of Justice the question whether the drug estimates of DUF, using a non-probability sample, and the drug use estimates of ADAM, using a probability sample, yield substantially different results will be explored. The following main questions will be addressed using equivalence analysis: Are there substantial differences in the DUF and ADAM samples with regard to the drug use information obtained from arrestees at nine sites across the United States? The analysis suggests that the drug use information contained in DUF and ADAM is not substantially different for marijuana, cocaine, and opiates for all sites analyzed together. Additionally, there are no substantial differences for seven of the nine sites. The implications of these findings are discussed.

In this study, I examine the influence of construals (interpretations) and mindsets on professional skepticism in auditors. Auditors have been criticized lately for not displaying enough professional skepticism, particularly in their audits of complex estimates (PCAOB 2008). Regulators speculate about and academic research shows a correlation between low professional skepticism and both audit failures and audit malpractice claims (Beasley et al. 2001; Anderson and Wolfe 2002). I hypothesize that prolonging the deliberative mindset in the audit judgment and decision-making process can increase professional skepticism in auditors. Experienced auditors take part in a 1 x 3 between-participants experiment in which they play the role of a senior auditor charged with evaluating a client's fair value estimate. I manipulate the type of mindset (deliberative or implemental) invoked by the evidence documentation instructions and have a third condition in which participants do not have to document audit evidence. Using multiple measures of professional skepticism, I find that auditors in the deliberative mindset condition display higher professional skepticism than both auditors in the implemental mindset condition and auditors in the no documentation condition. I further analyze the types of textual responses entered by the auditors and offer direction for future research in this area.

Range disclosures of estimates, whether in an expanded auditor’s report or by managers, would be intended to communicate measurement uncertainty to investors. Knowing this information should enhance investors’ ability to identify aggressive reporting, thereby possibly increasing investor actions taken against managers. In a laboratory experiment, I find that students in a managerial reporting role (hereafter, managers) report less aggressive estimates of an asset’s value when ranges of possible estimates accompany their point estimates reported to students in an investor role (hereafter, investors), such that investor actions against managers do not increase when ranges are disclosed. However, this decline in aggressiveness is concentrated in managers with a greater degree of association with one or more of the following personalities: psychopathy, narcissism, and Machiavellianism (collectively deemed the “Dark Triad” in psychology). Notably, this result occurs because, in a regime of no range disclosure, these managers report relatively aggressive estimates to investors, irrespective of their private information about the asset’s true value, while managers exhibiting low association with any of these personalities report estimates that more accurately reflect their private information. Range disclosure disciplines the former group of managers, which suggests that requiring range disclosure would discipline the reporting of the managers who are the most prone to take advantage of investors absent the communication of this information. / text

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The American Society of Civil Engineers (ASCE) Standard 41-06 Supplement No.1 (2007) assists engineers in modeling and evaluating the non-linear behavior of structures till collapse. Different levels of conservatism were used throughout the standard to produce modeling parameters for different structural elements, which leads to inconsistencies at the system level. Task to update current ASCE 41-06 provisions pertaining to RC structures is now handled by ACI (American Concrete Institute) committee 369 entitled “Seismic Repair and Rehabilitation”. This study is a part of ACI 369 committee’s effort. Existing provisions for non-linear analysis are re-assessed in this study for both rectangular and circular reinforced concrete columns. A database of 490 column tests was compiled for this project. Median rather than conservative estimates of non-linear modeling parameters were produced to achieve “best” estimates of structural behavior. Proposed modeling parameters show improved fit with experimental data over existing parameters. Data necessary for selection of acceptance criteria are provided. / text

Storm surge, the pileup of seawater occurring as a result of high surface stresses and strong currents generated by extreme storm events such as hurricanes, is known to cause greater loss of life than these storms' associated winds. For example, inland flooding from the storm surge along the Gulf Coast during Hurricane Katrina killed hundreds of people. Previous storms produced even larger death tolls. Simultaneously, dune, barrier island, and channel erosion taking place during a hurricane leads to the removal of major flow controls, which significantly affects inland inundation. Also, excessive sea bed scouring around pilings can compromise the structural integrity of bridges, levees, piers, and buildings. Modeling these processes requires tightly coupling a bed morphology equation to the shallow water equations (SWE). Discontinuous Galerkin finite element methods (DGFEMs) are a natural choice for modeling this coupled system, given the need to solve these problems on large, complicated, unstructured computational meshes, as well as the desire to implement hp-adaptivity for capturing the dynamic features of the solution. Comprehensive modeling of these processes in the coastal zone presents several challenges and open questions. Most existing hydrodynamic models use a fixed-bed approach; the bottom is not allowed to evolve in response to the fluid motion. With respect to movable-bed models, there is no single, generally accepted mathematical model in use. Numerical challenges include coupling models of processes that exhibit disparate time scales during fair weather, but possibly similar time scales during intense storms. The main goals of this dissertation include implementing a robust, efficient, tightly-coupled morphological model using the local discontinuous Galerkin (LDG) method within the existing Advanced Circulation (ADCIRC) modeling framework, performing systematic code and model verification (using test cases with known solutions, proven convergence rates, or well-documented physical behavior), analyzing the stability and accuracy of the implemented numerical scheme by way of a priori error estimates, and ultimately laying some of the necessary groundwork needed to simultaneously model storm surges and bed morphodynamics during extreme storm events. / text

published_or_final_version / abstract / toc / Real Estate and Construction / Master / Master of Science in Construction Project Management