Applications of Isogeometric Analysis Coupled with Finite Volume Method

In this thesis, a combination of Isogeometric Analysis (IGA) and Finite Volume Method (FVM) on geometries parameterized by Non-Uniform Rational Basis Splines (NURBS) is explored with applications in fluid flow, heat transfer, and shape optimization. An IGA framework supplemented with FVM is created in MATLAB® to solve problems defined over single patch domains with mesh refinement by node insertion. Additionally, a second-order finite difference method is developed using non-orthogonal curvilinear coordinates and a numerical Jacobian of the NURBS geometry. The examples include fully developed laminar flow through ducts, potential flow around a tilted ellipse, transient heat conduction, linear advection-diffusion, and a basic shape optimization example using a particle swarm technique. The numerical results are compared among the methods and verified with available analytical solutions

On the capture and representation of fonts

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The commercial need to capture, process and represent the shape and form of an outline has lead to the development of a number of spline routines. These use a mathematical curve format that approximates the contours of a given shape. The modelled outline lends itself to be used on, and for, a variety of purposes. These include graphic screens, laser printers and numerically controlled machines. The latter can be employed for cutting foil, metal. plastic and stone. One of the most widely used software design packages has been the lKARUS system. This, developed by URW of Hamburg (Gennany), employs a number of mathematical descriptions that facilitate the process of both modelling and representation of font characters. It uses a variety of curve formats, including Bezier cubics, general conics and parabolics. The work reported in this dissertation focuses on developing improved techniques, primarily. for the lKARUS system. This includes two algorithms which allow a Bezier cubic description, two for a general conic representation and, yet another, two for the parabolic case. In addition, a number of algorithms are presented which promote conversions between these mathematical forms; for example, Bezier cubics to a general conic form. Furthennore, algorithms are developed to assist the process of rasterising both cubic and quadratic arcs.This study was partly funded by the Science and Education Research Council (SERC)

Optimal control problems solved via swarm intelligence

Questa tesi descrive come risolvere problemi di controllo ottimo tramite swarm in telligence. Grande enfasi viene posta circa la formulazione del problema di controllo ottimo, in particolare riguardo a punti fondamentali come l’identificazione delle incognite, la trascrizione numerica e la scelta del risolutore per la programmazione non lineare. L’algoritmo Particle Swarm Optimization viene preso in considerazione e la maggior parte dei problemi proposti sono risolti utilizzando una formulazione differential flatness. Quando viene usato l’approccio di dinamica inversa, il problema di ottimo relativo ai parametri di trascrizione è risolto assumendo che le traiettorie da identificare siano approssimate con curve B-splines. La tecnica Inverse-dynamics Particle Swarm Optimization, che viene impiegata nella maggior parte delle applicazioni numeriche di questa tesi, è una combinazione del Particle Swarm e della formulazione differential flatness. La tesi investiga anche altre opportunità di risolvere problemi di controllo ottimo tramite swarm intelligence, per esempio usando un approccio di dinamica diretta e imponendo a priori le condizioni necessarie di ottimalitá alla legge di controllo. Per tutti i problemi proposti, i risultati sono analizzati e confrontati con altri lavori in letteratura. Questa tesi mostra quindi the algoritmi metaeuristici possono essere usati per risolvere problemi di controllo ottimo, ma soluzioni ottime o quasi-ottime possono essere ottenute al variare della formulazione del problema.This thesis deals with solving optimal control problems via swarm intelligence. Great emphasis is given to the formulation of the optimal control problem regarding fundamental issues such as unknowns identification, numerical transcription and choice of the nonlinear programming solver. The Particle Swarm Optimization is taken into account, and most of the proposed problems are solved using a differential flatness formulation. When the inverse-dynamics approach is used, the transcribed parameter optimization problem is solved assuming that the unknown trajectories are approximated with B-spline curves. The Inverse-dynamics Particle Swarm Optimization technique, which is employed in the majority of the numerical applications in this work, is a combination of Particle Swarm and differential flatness formulation. This thesis also investigates other opportunities to solve optimal control problems with swarm intelligence, for instance using a direct dynamics approach and imposing a-priori the necessary optimality conditions to the control policy. For all the proposed problems, results are analyzed and compared with other works in the literature. This thesis shows that metaheuristic algorithms can be used to solve optimal control problems, but near-optimal or optimal solutions can be attained depending on the problem formulation

Algebraic level sets for CAD/CAE integration and moving boundary problems

Boundary representation (B-rep) of CAD models obtained from solid modeling kernels are commonly used in design, and analysis applications outside the CAD systems. Boolean operations between interacting B-rep CAD models as well as analysis of such multi-body systems are fundamental operations on B-rep geometries in CAD/CAE applications. However, the boundary representation of B-rep solids is, in general, not a suitable representation for analysis operations which lead to CAD/CAE integration challenges due to the need for conversion from B-rep to volumetric approximations. The major challenges include intermediate mesh generation step, capturing CAD features and associated behavior exactly and recurring point containment queries for point classification as inside/outside the solid. Thus, an ideal analysis technique for CAD/CAE integration that can enable direct analysis operations on B-rep CAD models while overcoming the associated challenges is desirable. ^ Further, numerical surface intersection operations are typically necessary for boolean operations on B-rep geometries during the CAD and CAE phases. However, for non-linear geometries, surface intersection operations are non-trivial and face the challenge of simultaneously satisfying the three goals of accuracy, efficiency and robustness. In the class of problems involving multi-body interactions, often an implicit knowledge of the boolean operation is sufficient and explicit intersection computation may not be needed. Such implicit boolean operations can be performed by point containment queries on B-rep CAD models. However, for complex non-linear B-rep geometries, the point containment queries may involve numerical iterative point projection operations which are expensive. Thus, there is a need for inexpensive, non-iterative techniques to enable such implicit boolean operations on B-rep geometries. ^ Moreover, in analysis problems with evolving boundaries (ormoving boundary problems), interfaces or cracks, blending functions are used to enrich the underlying domain with the known behavior on the enriching entity. The blending functions are typically dependent on the distance from the evolving boundaries. For boundaries defined by free form curves or surfaces, the distance fields have to be constructed numerically. This may require either a polytope approximation to the boundary and/or an iterative solution to determine the exact distance to the boundary. ^ In this work a purely algebraic, and computationally efficient technique is described for constructing signed distance measures from Non-Uniform Rational B-Splines (NURBS) boundaries that retain the geometric exactness of the boundaries while eliminating the need for iterative and non-robust distance calculation. The proposed technique exploits the NURBS geometry and algebraic tools of implicitization. Such a signed distance measure, also referred to as the Algebraic Level Sets, gives a volumetric representation of the B-rep geometry constructed by purely non-iterative algebraic operations on the geometry. This in turn enables both the implicit boolean operations and analysis operations on B-rep geometries in CAD/CAE applications. Algebraic level sets ensure exactness of geometry while eliminating iterative numerical computations. Further, a geometry-based analysis technique that relies on hierarchical partition of unity field compositions (HPFC) theory and its extension to enriched field modeling is presented. The proposed technique enables direct analysis of complex physical problems without meshing, thus, integrating CAD and CAE. The developed techniques are demonstrated by constructing algebraic level sets for complex geometries, geometry-based analysis of B-rep CAD models and a variety of fracture examples culminating in the analysis of steady state heat conduction in a solid with arbitrary shaped three-dimensional cracks. ^ The proposed techniques are lastly applied to investigate the risk of fracture in the ultra low-k (ULK) dies due to copper (Cu) wirebonding process. Maximum damage induced in the interlayer dielectric (ILD) stack during the process steps is proposed as an indicator of the reliability risk. Numerical techniques based on enriched isogeometric approximations are adopted to model damage in the ULK stacks using a cohesive damage description. A damage analysis procedure is proposed to conduct damage accumulation studies during Cu wirebonding process. Analysis is carried out to identify weak interfaces and potential sites for crack nucleation as well as damage nucleation patterns. Further, the critical process condition is identified by analyzing the damage induced during the impact and ultrasonic excitation stages. Also, representative ILD stack designs with varying Cu percentage are compared for risk of fracture

The Hyper Suprime-Cam Software Pipeline

In this paper, we describe the optical imaging data processing pipeline developed for the Subaru Telescope's Hyper Suprime-Cam (HSC) instrument. The HSC Pipeline builds on the prototype pipeline being developed by the Large Synoptic Survey Telescope's Data Management system, adding customizations for HSC, large-scale processing capabilities, and novel algorithms that have since been reincorporated into the LSST codebase. While designed primarily to reduce HSC Subaru Strategic Program (SSP) data, it is also the recommended pipeline for reducing general-observer HSC data. The HSC pipeline includes high level processing steps that generate coadded images and science-ready catalogs as well as low-level detrending and image characterizations.Comment: 39 pages, 21 figures, 2 tables. Submitted to Publications of the Astronomical Society of Japa

An efficient neural-network and finite-difference hybrid method for elliptic interface problems with applications

A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across the interface, when applying finite difference discretization to this problem, an additional treatment accounting for the jump discontinuities must be employed. Here, we aim to elevate such an extra effort to ease our implementation by machine learning methodology. The key idea is to decompose the solution into singular and regular parts. The neural network learning machinery incorporating the given jump conditions finds the singular solution, while the standard finite difference method is used to obtain the regular solution with associated boundary conditions. Regardless of the interface geometry, these two tasks only require supervised learning for function approximation and a fast direct solver for Poisson equation, making the hybrid method easy to implement and efficient. The two- and three-dimensional numerical results show that the present hybrid method preserves second-order accuracy for the solution and its derivatives, and it is comparable with the traditional immersed interface method in the literature. As an application, we solve the Stokes equations with singular forces to demonstrate the robustness of the present method