On the Use of Compressed Polyhedral Quadrature Formulas in Embedded Interface Methods

The main idea of this paper is to apply a recent quadrature compression technique to algebraic quadrature formulas on complex polyhedra. The quadrature compression substantially reduces the number of integration points but preserves the accuracy of integration. The compression is easy to achieve since it is entirely based on the fundamental methods of numerical linear algebra. The resulting compressed formulas are applied in an embedded interface method to integrate the weak form of the Navier--Stokes equations. Simulations of flow past stationary and moving interface problems demonstrate that the compressed quadratures improve the efficiency of performing the weak form integration, while preserving accuracy and order of convergence

Algebraic cubature on polygonal elements with a circular edge

We compute low-cardinality algebraic cubature formulas on convex or concave polygonal elements with a circular edge, by subdivision into circular quadrangles, blending formulas via subperiodic trigonometric Gaussian quadrature and final compression via Caratheodory\u2013Tchakaloff subsampling of discrete measures. We also discuss applications to the VEM (Virtual Element Method) in computational mechanics problems

3D Capacitance Extraction With the Method of Moments

In this thesis, the Method of Moments has been applied to calculate capacitance between two arbitrary 3D metal conductors or a capacitance matrix for a 3D multi-conductor system. Capacitance extraction has found extensive use for systems involving sets of long par- allel transmission lines in multi-dielectric environment as well as integrated circuit package including three-dimensional conductors located on parallel planes. This paper starts by reviewing fundamental aspects of transient electro-magnetics followed by the governing dif- ferential and integral equations to motivate the application of numerical methods as Method of Moments(MoM), Finite Element Method(FEM), etc. Among these numerical tools, the surface-based integral-equation methodology - MoM is ideally suited to address the prob- lem. It leads to a well-conditioned system with reduced size, as compared to volumetric methods. In this dissertation, the MoM Surface Integral Equation (SIE)-based modeling approach is developed to realize electrostatic capacitance extraction for 3D geometry. MAT- LAB is employed to validate its e?ciency and e?ectiveness along with design of a friendly GUI. As a base example, a parallel-plate capacitor is considered. We evaluate the accu- racy of the method by comparison with FEM simulations as well as the corresponding quasi-analytical solution. We apply this method to the parallel-plate square capacitor and demonstrate how far could the undergraduate result 0C = A ? =d\u27 be from reality. For the completion of the solver, the same method is applied to the calculation of line capacitance for two- and multi-conductor 2D transmission lines

Drift-diffusion models for innovative semiconductor devices and their numerical solution

We present charge transport models for novel semiconductor devices which may include ionic species as well as their thermodynamically consistent finite volume discretization

Analysis of large antenna systems

The research presented in this thesis has been conducted within the framework of the Square Kilometre Array (SKA) project. SKA is a next generation radio telescope that will have a receiver sensitivity two orders of magnitude larger than the most sensitive radio telescope currently in operation. To meet the specifications, various low-cost low-noise actively beamformed receiving array antennas are being considered. A major problem in designing these systems is that the present-day commercially available electromagnetic solvers need an excessive amount of memory and simulation time to solve electrically large antenna problems. Moreover, it is essential to be able to analyze the receiver sensitivity of large antenna array systems to understand the sensitivity limiting factors. No dedicated commercial software tools exist that can analyze the receiver sensitivity of entire antenna systems specifically for radio astronomy. The thesis subject deals with two major challenges: (i) To accurately compute the impedance and radiation characteristics of realistically large and complex antenna arrays using only moderate computing power, particularly, of single and dual-polarized arrays of 100+ Tapered Slot Antenna (TSA) elements that are electrically interconnected. If the collection of these elements forms a subarray of a larger system, it is also of interest to analyze an array of disjoint subarrays. (ii) To characterize the system sensitivity of actively beamformed arrays of strongly coupled antenna elements. To address the above challenges, a conventional method-of-moments approach to solving an electric-field integral equation is enhanced using the Characteristic Basis Function Method (CBFM) to handle electrically large antenna problems. The generation of the associated reduced matrix equation is expedited by combining the CBFM with the Adaptive Cross Approximation (ACA) technique. Furthermore, because an overlapping domain decom270 Bibliography position technique is employed, Characteristic Basis Functions (CBFs) are generated that partially overlap to ensure the continuity of the current between adjacent subdomains that are electrically interconnected. While generating the CBFs, edge-singular currents are avoided by a post-windowing technique. Finally, a meshing strategy is proposed to optimally exploit the quasi-Toeplitz symmetry of the reduced moment matrix. The numerical accuracy and efficiency has been determined for numerous cases, among which a dual-polarized interconnected TSA array of 112 elements that has been fabricated and subsequently validated by measurements. The receiver system has been modeled by both a numerical and a semi-analytical method. The models account for a nonuniform brightness temperature distribution of the sky, mismatch effects, noise that emanates from amplifiers inputs and re-enters the system coherently through the mutually coupled antennas (noise coupling), beamformer weights, etc. Results are shown for a practical setup and design rules are derived which demonstrate that minimum receiver noise can be reached by noise matching the low-noise amplifiers to the active antenna reflection coefficient, rather than the passive one. Finally, it is demonstrated that the radiation efficiency of antennas is an important quantity that can degrade the system sensitivity severely. Nevertheless, a number of commercial software tools have shown to be inadequate as the computed efficiency exceeds 100%. A method is proposed which is numerically efficient and robust since it guarantees an efficiency below 100%

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

EFFICIENT INTEGRAL EQUATION METHOD FOR 2.5D MICROWAVE CIRCUITS IN LAYERED MEDIA

An efficient integral equation method based on a method of moment (MoM) discretization of the Mixed-Potential Integral Equation (MPIE) for the analysis of 2.5D or 3D planar microwave circuits is presented. The robust Discrete Complex Image Method (DCIM) is employed to approximate the Greens functions in layered media for horizontal and vertical sources of fields, where closed-form formulations of the z-integrations are derived in the spectral domain. Meanwhile, an efficient and accurate numerical integration technique based on the Khayat-Wilton transform is used to integrate functions with 1/R singularities and near singularities. The fast iterative solver - Quadrature Sampled Pre-Corrected Fast Fourier Transform (QSPCFFT) - is associated with the MoM formulation to analyze electrically large, dense and complex microwave circuits