A spectral element algorithm for solution of the incompressible Navier-Stokes and heat transfer equations is developed, with an emphasis on extending the classical conforming Galerkin formulations to nonconforming spectral elements. The new algorithm employs both the Constrained Approximation Method (CAM), and the Mortar Element Method (MEM) for p-and h-type nonconforming elements. Detailed descriptions, and formulation steps for both methods, as well as the performance comparisons between CAM and MEM, are presented. This study fills an important gap in the literature by providing a detailed explanation for treatment of p-and h-type nonconforming interfaces. A comparative eigenvalue spectrum analysis of diffusion and convection operators is provided for CAM and MEM. Effects of consistency errors due to the nonconforming formulations on the convergence of steady and time dependent problems are studied in detail. Incompressible flow solvers that can utilize these nonconforming formulations on both p- and h-type nonconforming grids are developed and validated. Engineering use of the developed solvers are demonstrated by detailed parametric analyses of oscillatory flow forced convection heat transfer in two-dimensional channels.

In this work, we propose, implement and test two fully automated mesh adaptation methods for 1-D multigroup eigenproblems. The first method is the standard hp-adaptive refinement strategy and the second technique is a goal-oriented hp-adaptive refinement strategy. The hp-strategies deliver optimal guaranteed solutions obtained with exponential convergence rates with respect to the number of unknowns. The goal-oriented method combines the standard hp-adaptation technique with a goal-oriented adaptivity based on the simultaneous solution of an adjoint problem in order to compute quantities of interest, such as reaction rates in a sub-domain or point-wise fluxes or currents. These algorithms are tested for various multigroup 1-D diffusion problems and the numerical results confirm the optimal, exponential convergence rates predicted theoretically.

<p>This report is about a Thesis for Degree of Bachelor of Science at Linköping University. It describes design of equipment which makes it possible to measure signal and noise quality during data transmission via Asymmetric Digital Subscriber Line, ADSL. The measuring instrument is HP 4934A Transmission Impairment Measuring Set. The equipment was supposed to be used for testing of ADSL systems within Solectron Sweden AB. In fact, the equipment stands for virtual Plain Old Telephone Service, POTS. That is why it simulates all three states that may come up. The states are following:"on hook", ringing,"off hook"(speech transmission). There is a control unit in the design. It changes between different circuit connections to get one of the states. You have to use a computer for control of the equipment. The computer commands are sent to equipment via its serial port via RS232 to the control unit. The equipment is driven with 48 Vdc.</p>

Die vorliegende Arbeit befasst sich mit verschiedenen Aspekten der hp-FEM. Insbesondere werden hierbei folgende Punkte genauer untersucht: 1. Das effiziente Aufstellen der Steifigkeitsmatrix auf Referenzelementen, die keine Tensorproduktstruktur besitzen. 2. Eine lokale Konvergenzbetrachtung für die randkonzentrierte hp-FEM. 3. Ein Multilevel-Löser für die randkonzentrierte hp-FEM. 4. Eine Strategie für hp-Adaptivität.

The boundary concentrated finite element method is a variant of the hp-version of the FEM that is particularly suited for the numerical treatment of elliptic boundary value problems with smooth coefficients and boundary conditions with low regularity or non-smooth geometries. In this paper we consider the case of the discretization of a Dirichlet problem with exact solution $u \in H^{1+\delta}(\Omega)$ and investigate the local error in various norms. We show that for a $\beta > 0$ these norms behave as $O(N^{−\delta−\beta})$, where $N$ denotes the dimension of the underlying finite element space. Furthermore, we present a new Gauss-Lobatto based interpolation operator that is adapted to the case non-uniform polynomial degree distributions.

We present an $hp$-adaptive strategy that is based on estimating the decay of the expansion coefficients when a function is expanded in $L^2$-orthogonal polynomails on a triangle or a tetrahedron. This method is justified by showing that the decay of the coefficients is exponential if and only if the function is analytic. Numerical examples illustrate the performance of this approach, and we compare it with two other $hp$-adaptive strategies.

We analyze and compare different techniques to set up the stiffness matrix in the hp-version of the finite element method. The emphasis is on methods for second order elliptic problems posed on meshes including triangular and tetrahedral elements. The polynomial degree may be variable. We present a generalization of the Spectral Galerkin Algorithm of [7], where the shape functions are adapted to the quadrature formula, to the case of triangles/tetrahedra. Additionally, we study on-the-fly matrix-vector multiplications, where merely the matrix-vector multiplication is realized without setting up the stiffness matrix. Numerical studies are included.

The boundary concentrated finite element method is a variant of the hp-version of the finite element method that is particularly suited for the numerical treatment of elliptic boundary value problems with smooth coefficients and low regularity boundary conditions. For this method we present two multilevel preconditioners that lead to preconditioned stiffness matrices with condition numbers that are bounded uniformly in the problem size N. The cost of applying the preconditioners is O(N). Numerical examples illustrate the efficiency of the algorithms.

We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solidand fluidmechanics.For manyof these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model.Most notably, the use of least-squares principles leads to a variational unconstrained minimization problem where stability conditions such as inf-sup conditions (typically arising in mixed methods using weak form Galerkin finite element formulations) never arise. In addition, the least-squares based finite elementmodelalways yields a discrete system ofequations witha symmetric positive definite coeffcientmatrix.These attributes, amongst manyothers highlightedand detailed in this work, allow the developmentofrobust andeffcient finite elementmodels for problems of practical importance. The research documented herein encompasses least-squares based formulations for incompressible and compressible viscous fluid flow, the bending of thin and thick plates, and for the analysis of shear-deformable shell structures.

The reduction of fuel consumption and the reduction of toxic emissions are the main goals of research and development in the area of internal combustion engines. The use of exhaust gas recirculation (EGR) to come further in that direction is today an established method for diesel engines. EGR reduces the emissions of nitrogen oxides with a low penalty in fuel consumption. The increasingly hard regulations on emissions put high pressure on the manufacturers to improve these systems. The present work aims at increasing the knowledge in the area of EGR. Two of the main challenges when applying EGR are addressed, efficiency and mixing. The efficiency of the EGR-system is analyzed, focusing on keeping the fuel penalty low for a given EGR-rate. Different layouts of the EGR system are studied and compared regarding their stationary and transient properties. Exergy analysis is used to show the potential for improvement in different system components. In the same time, exergy analysis as a tool is introduced and compared to energy analysis of a system. The usefulness of exergy analysis of the entire gas exchange is shown by the example of a heavy-duty diesel engine. The problem of EGR and air mixing is approached by a detailed study of the mixing process in a heavy-duty diesel engine. Different methods for the measurement of EGR distribution are presented and compared. Additionally, the possibility to predict the mixing effects by 1-D and 3-D simulation is assessed. It is shown that the mixing between air and EGR is highly dependent on the pulsating nature of the flow. The EGR is shown to be transported in packets in the air flow. This leads to the conclusion that mixing not only at the mixing point, but also mixing in flow direction needs to be optimized, as the distribution of EGR between the cylinders is dependent on the timing between the passage of the EGR packets and the valve opening time. / <p>QC 20140203</p>