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An Object-oriented Approach to Semidefinite Programming
No full textAn object-oriented design and implementation of a primal-dual algorithm for solving the semidefinite programming problem is presented. The advantages of applying the object-oriented methodology to numerical computations, in particular to an interior point algorithm for semidefinite programming, or for solving other types of linear matrix inequalities are discussed. One object-oriented design of the primal-dual algorithm and its implementation using C++ is presented. The performance of the C++ implementation is compared with that of a procedural C implementation, and while the performance of the C++ implementation is comparable to that of the C implementation, the resulting code is easier to read, modify, and maintain
Convergence Theory of Probability-one Homotopies for Model Order Reduction
No full textThe optimal H-square model reduction problem is an inherently nonconvex problem and thus provides a nontrivial computational challenge. This paper systematically examines the requirements of probability-one homotopy methods to guarantee global convergence. Homotopy algorithms for nonlinear systems of equations construct a continuous family of systems, and solve the given system by tracking the continuous curve of solutions to the family. The main emphasis is on guaranteeing transversality for several homotopy maps based upon the pseudogramian formulation of the optimal projection equations and variations based upon canonical forms. These results are essential to the probability-one homotopy approach by guaranteeing good numerical properties in the computation- al implementation of the homotopy algorithms
Transforming Command-Line Driven Systems to Web Applications
No full textA method fo add a Web-based interface to a command-line driven system is presented. Without programming, Javamatic can generate a graphical user interface, then invokes commands in the legacy system transparently to the user. The user interface (UI) is automatically generated as a Java applet or stand-alone interface from a high-level description of the application, which is UI independent, using a set of UI mapping rules. The application is wrapped with an interface serverl thus multiple clients can use the legacy application through the Web
A New Adaptive GMRES Algorithm for Achieving High Accuracy
No full textGMRES(k) is widely used for solving nonsymmetric linear systems. However, it is inadequate either when it converges only for k close to the problem size or when numerical error in the modified Gram-Schmidt process used in the GMRES orthogonalization phase dramatically affects the algorithm performance. An adaptive version of GMRES(k) which tunes the restart value k based on criteria estimating the GMRES conversion rate for the given problem is proposed here. This adaptive GMRES(k) procedure outperforms standard GMRES(k), several other GMRES-like methods, and QMR on actual large scale sparse structural mechanics postbuckling and analog circuit simulation problems. There are some applications, such as homotopy methods for high Reynolds number viscous flows, solid mechanics postbuckling analysis, and analog circuit simulation, where very high accuracy in the linear system solutions is essential. In this context, the modified Gram-Schmidt process in GMRES can fail causing the entire GMRES iteration to fail. It is shown that the adaptive GMRES(k) with the orthogonalization performed by Householder transformations succeeds whenever GMRES(k) with the orthogonolization performed by the modified Gram-Schmidt process fails, and the extra cost of computing Householder transformations is justified for these applications
Wing Design for a High-Speed Civil Transport Using a Design of Experiments Methodology
No full textThe presence of numerical noise inhibits gradient-based optimization and therefore limits the practicality of performing aircraft multidisciplinary design optimization (MDO). To address this issue, a procedure has been developed to create noise free algebraic models of subsonic and supersonic aerodynamic performance for use in the MDO of high-speed civil transport (HSCT) configurations. This procedure employs methods from statistical design of experiments theory to select a set of HSCT wing designs (fuselage/tail/engine geometry fixed) for which numerous detailed aerodynamic analyses are performed. Polynomial approximations (i.e., response surface models) are created from the aerodynamic data to provide analytical models relating aerodynamic quantities (e.g., wave drag and drag-due-to-lift) to the variables which define the HSCT wing configuration. A multidisciplinary design optimization of the HSCT is then performed using the response surface models in lieu of the traditional, local gradient based design methods. The use of response surface models makes possible the efficient and robust application of MDO to the design of an aircraft system. Results obtained from five variable and ten variable wing design problems presented here demonstrate the effectiveness of this response surface modeling method
Improving Genetic Algorithm Efficiency and Reliability in the Design and Optimization of Composite Structures
No full textGenetic algorithms (GAs) often require many iterations for convergence. If the cost for the analysis of each laminate is high, then GA optimization becomes infeasible due to the large amount of CPU time required. A genetic algorithm's ability to find optimal laminate designs that have complicated stacking sequence patterns in an efficient manner may be improved if the GA takes greater advantage of all the information generated throughout the search scheme. In a standard GA procedure, an elitist method is typically implemented where the worst laminate from the chil population is replaced with the best laminate from the parent population. Valuable information that may exist in other laminates of the parent population is no longer utilized once the child population has been created. The present paper suggests new multiple elitist and variable elitist schemes where more than just the best laminate from the old population may be preserved in successive generations providing the GA with additional laminate designs with good performance. These additional designs may contain pieces of the stacking sequence pattern that are vital for achieving the optimal laminate and help the GA converge more rapidly. Results generated by utilizing the multiple elitist and variable elitist methods have shown to yield richer final populations and minor improvements in the computational cost, while maintaining a high level of reliability
Edge-Packing Planar Graphs by Cyclic Graphs
No full textMaximum G Edge-Packing is the problem of finding the maximum number of edge-disjoint isomorphic copies of a fixed guest graph G in a host graph H. This paper considers the cases where G and H are planar and G is cyclic. Recent work on the general problem is surveyed, inadequacies and limitations in these results are identified, and NP-completeness proofs for key cases are presented
Suitability of Optimization Packages for an MDO Environment
No full textAn examination of the performance of several optimization packages and their suitability for inclusion in a realistic multidisciplinary design optimization (MDO) environment is conducted. The packages are incorporated into a High-Speed Civil Transport (HSCT) aircraft design code and are used with both a response surface (RS) model and a more detailed, noisy model. While most packages converge to similar designs, there are large variations in CPU times and usability. Results are reported for a SGI workstation
Software Process Reuse in an Industrial Setting
No full textThis paper describes a method for creating reusable processes and our experience using them in an industrial environment. A notation and process for creating and tailoring reusable processes is described and applied to the building of a 120 process library at PRC Inc. Initial data collected on use of the library indicates large potential payoffs from process reuse such as a 10 to 1 improvement in the time to develop a project specific process