Beschreibung der Finite Elemente Software-Familie SPC-PM3-AdH-XX für: (S)cientific (P)arallel (C)omputing - (P)rogramm-(M)odul (3)D (ad)aptiv (H)exaederelemente. Für XX stehen die einzelnen Spezialvarianten, die in Teil 2 detailliert geschildert werden. Stand: Ende 2013

We consider high order discontinuous-Galerkin finite element methods for partial differential equations, with a focus on the neutron transport equation. We begin by examining a method for preprocessing block-sparse matrices, of the type that arise from discontinuous-Galerkin methods, prior to factorisation by a multifrontal solver. Numerical experiments on large two and three dimensional matrices show that this pre-processing method achieves a significant reduction in fill-in, when compared to methods that fail to exploit block structures. A discontinuous-Galerkin finite element method for the neutron transport equation is derived that employs high order finite elements in both space and angle. Parallel Krylov subspace based solvers are considered for both source problems and $k_{eff}$-eigenvalue problems. An a-posteriori error estimator is derived and implemented as part of an h-adaptive mesh refinement algorithm for neutron transport $k_{eff}$-eigenvalue problems. This algorithm employs a projection-based error splitting in order to balance the computational requirements between the spatial and angular parts of the computational domain. An hp-adaptive algorithm is presented and results are collected that demonstrate greatly improved efficiency compared to the h-adaptive algorithm, both in terms of reduced computational expense and enhanced accuracy. Computed eigenvalues and effectivities are presented for a variety of challenging industrial benchmarks. Accurate error estimation (with effectivities of 1) is demonstrated for a collection of problems with inhomogeneous, irregularly shaped spatial domains as well as multiple energy groups. Numerical results are presented showing that the hp-refinement algorithm can achieve exponential convergence with respect to the number of degrees of freedom in the finite element space

The tuning of optimization software is of key interest to researchers solving mixed integer programming (MIP) problems. The efficiency of the optimization software can be greatly impacted by the solver’s parameter settings and the structure of the MIP. A designed experiment approach is used to fit a statistical model that would suggest settings of the parameters that provided the largest reduction in the primal integral metric. Tuning exemplars of six and 59 factors (parameters) of optimization software, experimentation takes place on three classes of MIPs: survivable fixed telecommunication network design, a formulation of the support vector machine with the ramp loss and L1-norm regularization, and node packing for coding theory graphs. This research presents and demonstrates a framework for tuning a portfolio of MIP instances to not only obtain good parameter settings used for future instances of the same class of MIPs, but to also gain insights into which parameters and interactions of parameters are significant for that class of MIPs. The framework is used for benchmarking of solvers with tuned parameters on a portfolio of instances. A group screening method provides a way to reduce the number of factors in a design and reduces the time it takes to perform the tuning process. Portfolio benchmarking provides performance information of optimization solvers on a class with instances of a similar structure.

L’ Answer Set Programming (ASP) est un formalisme capable de représenter des connaissances en Intelligence Artificielle à l’aide d’un programme logique au premier ordre pouvant contenir des négations par défaut. En quelques années, plusieurs solveurs performants ont été proposés pour calculer les solutions d’un programme ASP que l’on nomme answer sets.Nous nous intéressons ici plus particulièrement au solveur ASPeRiX qui instancie les règles au premier ordre à la volée durant le calcul des answer sets. Pour réaliser cela, ASPeRiX applique un chaînage avant sur les règles à partir de littéraux précédemment déterminés.L’étude de ce solveur nous amène notamment à considérer la notion de justification dans le cadre d’une approche de calcul d’ answer sets basée sur les règles. Les justifications permettent d’expliquer pourquoi certaines propriétés sont vérifiées. Parmi celles-ci, nous nous concentrons particulièrement sur les raisons d’échecs qui justifient pourquoi certaines branches de l’arbre de recherche n’aboutissent pas à un answer set.Cela nous conduit à implémenter une version d’ ASPeRiX proposant du backjumping qui évite de parcourir systématiquement toutes les branches de l’arbre de recherche grâce aux informations fournies par les raisons d’échecs. / Answer set programming (ASP) is a formalism able to represent knowledge in Artificial Intelligence thanks to a first order logic program which can contain default negations. In recent years, several efficient solvers have been proposed to compute the solutions of an ASP program called answer sets. We are particularly interested in the ASPeRiX solver that instantiates the first order rules on the fly during the computation of answer sets. It applies a forward chaining of rules from literals previously determined. The study of this solver leads us to consider the concept of justification as part of a rule-based approach for computing answer sets. Justifications enable to explain why some properties are true or false. Among them, we focus particularly on the failure reasons which justify why some branches of the search tree does not result in an answer set. This encourages us to implement a version of ASPeRiX with backjumping in order to jump to the last choice point related to the failure in the search tree thanks to information provided by the failure reasons.

Includes bibliographical references / In this thesis, the development of a strongly coupled, partitioned fluid-structure interactions (FSI) solver is outlined. Well established methods are analysed and new methods are proposed to provide robust, accurate and efficient FSI solutions. All the methods introduced and analysed are primarily geared towards the solution of incompressible, transient FSI problems, which facilitate the use of black-box sub-domain field solvers. In the first part of the thesis, radial basis function (RBF) interpolation is introduced for interface information transfer. RBF interpolation requires no grid connectivity information, and therefore presents an elegant means by which to transfer information across a non-matching and non-conforming interface to couple finite element to finite volume based discretisation schemes. The transfer scheme is analysed, with particular emphasis on a comparison between consistent and conservative formulations. The primary aim is to demonstrate that the widely used conservative formulation is a zero order method. Furthermore, while the consistent formulation is not provably conservative, it yields errors well within acceptable levels and converges within the limit of mesh refinement. A newly developed multi-vector update quasi-Newton (MVQN) method for implicit coupling of black-box partitioned solvers is proposed. The new coupling scheme, under certain conditions, can be demonstrated to provide near Newton-like convergence behaviour. The superior convergence properties and robust nature of the MVQN method are shown in comparison to other well-known quasi-Newton coupling schemes, including the least squares reduced order modelling (IBQN-LS) scheme, the classical rank-1 update Broyden's method, and fixed point iterations with dynamic relaxation. Partitioned, incompressible FSI, based on Dirichlet-Neumann domain decomposition solution schemes, cannot be applied to problems where the fluid domain is fully enclosed. A simple example often provided in the literature is that of balloon inflation with a prescribed inflow velocity. In this context, artificial compressibility (AC) will be shown to be a useful method to relax the incompressibility constraint, by including a source term within the fluid continuity equation. The attractiveness of AC stems from the fact that this source term can readily be added to almost any fluid field solver, including most commercial solvers. AC/FSI is however limited in the range of problems it can effectively be applied to. To this end, the combination of the newly developed MVQN method with AC/FSI is proposed. In so doing, the AC modified fluid field solver can continue to be treated as a black-box solver, while the overall robustness and performance are significantly improved. The study concludes with a demonstration of the modularity offered by partitioned FSI solvers. The analysis of the coupled environment is extended to include steady state FSI, FSI with free surfaces and an FSI problem with solid-body contact.

Prioritization of software requirements is an important part of the requirements engineering process within the industry of software development. There are many different methods for achieving the most optimal order of software requirements, a list that shows in what order the requirements should be implemented. This degree project utilizes the SMT-based solver Z3 for an interactive prioritization algorithm. Previous studies have shown good results with another SMT-based solver called Yices. With the newer Z3 from Microsoft, the results have been improved further, and the tool is based on Python, and the framework for Z3 is called Z3PY. Experiments have been conducted on a set of different software requirements derived from a project in the healthcare industry and show that the Z3 solution is, in general, improving the requirements prioritization compared to other mentioned solutions in the study that has been tested on the same set of requirements. Results show that the Z3 solution outperformed the other SMT-based solution Yices by 2-4% regarding disagreement and by 3% regarding average distance. The results are significantly improved based on an ANOVA test with a p-value <= 0.05.

Design of thermoelastic structures can be highly counterintuitive due to design-dependent loading and impact of geometric nonlinearity on the structural response. Thermal loading generates in-plane stresses in a restrained panel, but the presence of geometric nonlinearity creates an extension-bending coupling that results in considerable transverse displacement and variation in stiffness characteristics, and these affects are enhanced in post-bucking regimes. Herein a methodology for structural sizing of thermally stressed post-buckled stiffened panels is proposed and applied for optimization of the blade and hat stiffeners using a gradient-based optimizer. The stiffened panels are subjected to uniform thermal loading and optimized for minimum mass while satisfying stress and stability constraints. The stress constraints are used to avoid yielding of the structure, whereas the stability constraints are used to ensure static stability. Corrugation of the hat stiffeners is also studied through variation of its magnitude and position. A continuation solver has been validated to tackle the highly nonlinear nature of the thermoelastic problem, and formulations for the stability constraints have been derived and imposed to satisfy the static stability of the structure. The study confirms that geometric nonlinearity is an important aspect of sizing optimization and is needed for an accurate modeling of the structural behavior. The results also show that modeling of geometric nonlinearity adds extra complexity to the thermoelastic problem and requires a path-tracking solver. Finally, this work supports that corrugation enhances the stability features of the panel but requires a blending function to reduce stresses at the panel boundaries.

Artificial neural networks (ANN) have found extensive use in solving real-world problems in recent years, where their exceptional information processing is the main advantage. Facing increasingly complex problems, there is a need to improve their information processing. In this thesis, we explore new ways of synthesizing ANNs by reducing the synthesis problem to the Boolean satisfiability problem (SAT) that is, the problem of determining whether a given Boolean formula is satisfiable. Also known as the SAT problem, it aims to determine if there exists such a combination of Boolean variables in a propositional formula for which the formula evaluates to true. We derived a general formula in conjunctive normal form (CNF) representing the synthesis of a neural network. Given randomly generated datasets, we were able to construct CNF formulas whose satisfying assignments encode neural networks consistent with the datasets. These formulas were run through an off-the-shelf SAT solver, where the outputted models simulated the synthesis of neural networks consistent with the datasets. The experiments conducted in this thesis showed that our method had the ability to produce feed-forward neural networks of varying sizes consistent with randomly generated datasets of binary strings.

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<p> Novel scalar and full-vectorial mode solvers based on quadratic spline collocation (QSC) method have been developed in MATLAB for optical dielectric waveguide with arbitrary two-dimensional cross-section and refractive index profile.</p> <p> Compared with the conventional finite difference mode solver in the literature and a commercial mode solver, the QSC mode solvers are simple and easy to implement in MATLAB without losing the accuracy of the mode solutions. The scalar mode solver is fast for solving weakly guiding waveguides. Three typical rib waveguides are calculated by the QSC scalar mode solver and compared with the numerical results of a finite difference scalar mode solver in the literature. The full-vectorial mode solver is capable of solving both weakly and strongly guiding waveguides. Typical numerical examples are calculated by the full-vectorial QSC mode solver and the solver is verified by comparing the results to a commercial mode solver.</p> <p> At the end of the thesis, methods of calculating leaky and radiation modes of general dielectric waveguides and possible methods of increasing the accuracy of the QSC mode solvers are proposed.</p> / Thesis / Master of Applied Science (MASc)