This thesis describes two problem solving environments that integrate visualization and computational tools into a high level user interface. The objective of a problem solving environment is to provide scientists with a complete, usable, and integrated set of high level facilities for solving problems in a specific domain. Integrating visualization tools with computation tools encourages scientists to think in terms of the overall task of solving a problem, not simply using the visualization to view the results of the computation. This increases their productivity by allowing them to focus on the problem at hand rather than on general computation issues. Two problem solving environments based on this philosophy, but intended for different problem domains, are presented: VizCraft and WBCSim. VizCraft provides an integrated environment for aircraft designers working with multidimensional design spaces. The design problem currently being faced by aircraft designers, some approaches that have been taken in the past towards solving it, and how VizCraft provides a unique approach in helping the designer visualize the problem, are presented. WBCSim provides a Web-based framework for wood scientists conducting research on wood-based composite materials. It integrates legacy simulation codes with a graphical front end, an optimization tool, and a visualization tool. WBCSim serves as a prototype for the design, construction, and evaluation of larger scale problem solving (computing) environments. Several different wood-based composite material simulations are supported. / Master of Science

This thesis describes user interface and visualization components in the problem solving environment "Site-Specific System Simulator for Wireless System Design" (S4W) developed by CS and ECE faculty and students at Virginia Tech. S4W integrates visualization and computational tools with a high level user interface. The objective of this PSE is to improve the ability of wireless design engineers to design an indoor wireless system through the aid of various simulation and visualization components. S4W provides engineers with the facility of thinking in terms of the overall task of designing the system for optimal performance. They need not to worry about computation, data-management and connectivity issues. The choice of method for interaction between service logic within a PSE and its user is always a challenging issue. The selection of user interaction channel is mostly dictated by the characteristics of the problem domain. For S4W, we chose to build a graphical user interface as human interaction interface, which was connected to other components via a high speed Local Area Network (LAN). The other key form of user interaction in a PSE is the visual representations of the abstract data results of simulations, perceived as user interface for data. The Complex nature of data sets in the domain of wireless simulations calls for a customized set of visualization tools. To address the specific needs of visualizations for S4W, ad hoc visualization tools were developed and integrated into the graphical user interface. A comparison of the integrated PSE and an earlier collection of unintegrated tools and scripts is presented. / Master of Science

Boundary value problems (BVPs) are systems of ordinary differential equations (ODEs) with boundary conditions imposed at two or more distinct points. Such problems arise within mathematical models in a wide variety of applications. Numerically solving BVPs for ODEs generally requires the use of a series of complex numerical algorithms. Fortunately, when users are required to solve a BVP, they have a variety of BVP software packages from which to choose. However, all BVP software packages currently available implement a specific set of numerical algorithms and therefore function quite differently from each other. Users must often try multiple software packages on a BVP to find the one that solves their problem most effectively. This creates two problems for users. First, they must learn how to specify the BVP for each software package. Second, because each package solves a BVP with specific numerical algorithms, it becomes difficult to determine why one BVP package outperforms another. With that in mind, this thesis offers two contributions. <p> First, this thesis describes the development of the BVP component to the fully featured problem-solving environment (PSE) for the numerical solution of ODEs called pythODE. This software allows users to select between multiple numerical algorithms to solve BVPs. As a consequence, they are able to determine the numerical algorithms that are effective at each step of the solution process. Users are also able to easily add new numerical algorithms to the PSE. The effect of adding a new algorithm can be measured by making use of an automated test suite. <p> Second, the BVP component of pythODE is used to perform two research studies. In the first study, four known global-error estimation algorithms are compared in pythODE. These algorithms are based on the use of Richardson extrapolation, higher-order formulas, deferred corrections, and a conditioning constant. Through numerical experimentation, the algorithms based on higher-order formulas and deferred corrections are shown to be computationally faster than Richardson extrapolation while having similar accuracy. In the second study, pythODE is used to solve a newly developed one-dimensional model of the agglomerate in the catalyst layer of a proton exchange membrane fuel cell.

Boundary value problems (BVPs) are systems of ordinary differential equations (ODEs) with boundary conditions imposed at two or more distinct points. Such problems arise within mathematical models in a wide variety of applications. Numerically solving BVPs for ODEs generally requires the use of a series of complex numerical algorithms. Fortunately, when users are required to solve a BVP, they have a variety of BVP software packages from which to choose. However, all BVP software packages currently available implement a specific set of numerical algorithms and therefore function quite differently from each other. Users must often try multiple software packages on a BVP to find the one that solves their problem most effectively. This creates two problems for users. First, they must learn how to specify the BVP for each software package. Second, because each package solves a BVP with specific numerical algorithms, it becomes difficult to determine why one BVP package outperforms another. With that in mind, this thesis offers two contributions. <p> First, this thesis describes the development of the BVP component to the fully featured problem-solving environment (PSE) for the numerical solution of ODEs called pythODE. This software allows users to select between multiple numerical algorithms to solve BVPs. As a consequence, they are able to determine the numerical algorithms that are effective at each step of the solution process. Users are also able to easily add new numerical algorithms to the PSE. The effect of adding a new algorithm can be measured by making use of an automated test suite. <p> Second, the BVP component of pythODE is used to perform two research studies. In the first study, four known global-error estimation algorithms are compared in pythODE. These algorithms are based on the use of Richardson extrapolation, higher-order formulas, deferred corrections, and a conditioning constant. Through numerical experimentation, the algorithms based on higher-order formulas and deferred corrections are shown to be computationally faster than Richardson extrapolation while having similar accuracy. In the second study, pythODE is used to solve a newly developed one-dimensional model of the agglomerate in the catalyst layer of a proton exchange membrane fuel cell.

This thesis describes a computing environment WBCSim and its experiment management component. WBCSim is a web-based simulation system used to increase the productivity of wood scientists conducting research on wood-based composite and material manufacturing processes. This experiment management component integrates a web-based graphical front end, server scripts, and a database management system to allow scientists to easily save, retrieve, and perform customized operations on experimental data. A detailed description of the system architecture and the experiment management component is presented, along with a typical scenario of usage. / Master of Science

A problem solving environment (PSE) is a computational system that provides a complete and convenient set of high level tools for solving problems from a specific domain. This thesis takes an in-depth look at the experiment management aspect of PSEs, which can be divided into three levels: 1) data management, 2) change management, and 3) execution management. At the data management level, anything related to an experiment (computer simulation) should be stored and documented. A database management system can be used to store the simulation runs for a PSE. Then various high level interfaces can be provided to allow users to save, retrieve, search, and compare these simulation runs. At the change management level, a scientist should only focus on how to solve a problem in the experiment domain. Aside from running experiments, a scientist may only consider how to define a new model, how to modify an existing model, and how to interpret an experiment result. By using XML to describe a simulation model and unify various implementation layers, changing an existing model in a PSE can be intuitive and fast. At the execution management level, how an experiment is executed is the main concern. By providing a computational steering capability, a scientist can pause, examine, and compare the intermediate results from a simulation. Contrasted with the traditional way of running a lengthy simulation to see the result at the end, computational steering can leverage the user's expert knowledge on the fly (during the simulation run) and provide new insights and new product design opportunities. This thesis illustrates these concepts and implementation by using WBCSim as an example. WBCSim is a PSE that increases the productivity of wood scientists conducting research on wood-based composite materials and manufacturing processes. It integrates Fortran 90 simulation codes with a Web based graphical front end, an optimization tool, and various visualization tools. The WBCSim project was begun in 1997 with support from United States Department of Agriculture, Department of Energy, and Virginia Tech. It has since been used by students in several wood science classes, by graduate students and faculty, and by researchers at several forest products companies. WBCSim also serves as a test bed for the design, construction, and evaluation of useful, production quality PSEs. / Ph. D.

Large scale, multidisciplinary, engineering designs are always difficult due to the complexity and dimensionality of these problems. Direct coupling between the analysis codes and the optimization routines can be prohibitively time consuming. One way of tackling this problem is by constructing computationally cheap(er) approximations of the expensive simulations, that mimic the behavior of the simulation model as closely as possible. This paper presents a data driven, surrogate based optimization algorithm that uses a trust region based sequential approximate optimization (SAO) framework and a statistical sampling approach based on design of experiment (DOE) arrays. The algorithm is implemented using techniques from the two packages SURFPACK and SHEPPACK that provide a collection of approximation algorithms to build the surrogates and three different DOE techniques: full factorial (FF), Latin hypercube sampling (LHS), and central composite design (CCD) are used to train the surrogates. The biggest concern in using the proposed methodology is the generation of the required database. This thesis proposes a data driven approach where an expensive simulation run is required if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations are performed. Results show that the response surface approximations constructed using design of experiments can be effectively managed by a SAO framework based on a trust region strategy. An interesting result is the significant reduction in the number of simulations for the subsequent runs of the optimization algorithm with a cumulatively growing simulation database. / Master of Science