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

Geometric Numerical Integration

The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of numerical methods

Modelling laminar flame using simple chemical reacting system

The objective of my thesis work is to model laminar diffusion flame using simple chemical reacting system (SCRS) combustion model. This combustion model assumes that the chemical reactions are infinitely fast and take place via a global one-step without intermediate reactions. The detailed kinetics is considered unimportant as this model is concerned with the global nature of the combustion process and with the final major species concentration. The model is developed using C++ computer language. The algorithm used for solving Navier-stokes and mixture fraction equations is the fractional step method for compressible flow with low Mach number. Low Mach number approximation is used in simplifying the flow equations as flow speed is very low compared to speed of sound. By modelling diffusion flame through an SCRS, flame temperature and species concentration are retrieved from mixture fraction field. The thesis is divided into six chapters. Chapter 1 is an introductory chapter about objective, scope and justification of the work. In Chapter 2 the conservation laws of fluid motion are explained. In chapter 3, the discretization of the computational domain and discretization of different terms in the transport equations are explained. The fractional step method algorithm for incompressible flow and compressible flow with low Mach number are illustrated in chapter 4.In chapter 5, the code is verified for incompressible flow by the method of manufactured solution (MMS) and by comparing code results with benchmark solutions of driven cavity and differentially heated cavity for incompressible flow, while for compressible flow code result is compared with benchmark solution of differentially heated cavity with high temperature difference. In chapter 6 SCRS model is discussed and the simulation results for diluted methane diffusion flame are presented. The simulation results for the laminar diffusion flame show that the flame reaches its maximum temperature at the stoichiometric mixture fraction contour line where oxygen and fuel are completely consumed. The flame length is changed by altering fuel or oxidant streams velocities. Also changing the percentage of nitrogen gas in the fuel and oxidant stream affect both flame length and flame maximum temperature

A parallel algorithm for deformable contact problems

In the field of nonlinear computational solid mechanics, contact problems deal with the deformation of separate bodies which interact when they come in touch. Usually, these problems are formulated as constrained minimization problems which may be solved using optimization techniques such as penalty method, Lagrange multipliers, Augmented Lagrangian method, etc. This classical approach is based on node connectivities between the contacting bodies. These connectivities are created through the construction of contact elements introduced for the discretization of the contact interface, which incorporate the contact constraints in the global weak form. These methods are well known and widely used in the resolution of contact problems in engineering and science. As parallel computing platforms are nowadays widely available, solving large engineering problems on high performance computers is a real possibility for any engineer or researcher. Due to the memory and compute power that contact problems require and consume, they are good candidates for parallel computation. Industrial and scientific realistic contact problems involve different physical domains and a large number of degrees of freedom, so algorithms designed to run efficiently in high performance computers are needed. Nevertheless, the parallelization of the numerical solution methods that arises from the classical optimization techniques and discretization approaches presents some drawbacks which must be considered. Mainly, for general contact cases where sliding occurs, the introduction of contact elements requires the update of the mesh graph in a fixed number of time steps. From the point of view of the domain decomposition method for parallel resolution of numerical problems this is a major drawback due to its computational expensiveness, since dynamic repartitioning must be done to redistribute the updated mesh graph to the different processors. On the other hand, some of the optimization techniques modify dynamically the number of degrees of freedom in the problem, by introducing Lagrange multipliers as unknowns. In this work we introduce a Dirichlet-Neumann type parallel algorithm for the numerical solution of nonlinear frictional contact problems, putting a strong focus on its computational implementation. Among its main characteristics it can be highlighted that there is no need to update the mesh graph during the simulation, as no contact elements are used. Also, no additional degrees of freedom are introduced into the system, since no Lagrange multipliers are required. In this algorithm the bodies in contact are treated separately, in a segregated way. The coupling between the contacting bodies is performed through boundary conditions transfer at the contact zone. From a computational point of view, this feature allows to use a multi-code approach. Furthermore, the algorithm can be interpreted as a black-box method as it solves each body separately even with different computational codes. In addition, the contact algorithm proposed in this thesis can also be formulated as a general fixed-point solver for the solution of interface problems. This generalization gives us the theoretical basis to extrapolate and implement numerical techniques that were already developed and widely tested in the field of fluid-structure interaction (FSI) problems, especially those related to convergence ensurance and acceleration. We describe the parallel implementation of the proposed algorithm and analyze its parallel behaviour and performance in both validation and realistic test cases executed in HPC machines using several processors.En el ámbito de la mecánica de contacto computacional, los problemas de contacto tratan con la deformación que sufren cuerpos separados cuando interactúan entre ellos. Comunmente, estos problemas son formulados como problemas de minimización con restricciones, que pueden ser resueltos utilizando técnicas de optimización como la penalización, los multiplicadores de Lagrange, el Lagrangiano Aumentado, etc. Este enfoque clásico está basado en la conectividad de nodos entre los cuerpos, que se realiza a través de la construcción de los elementos de contacto que surgen de la discretización de la interfaz. Estos elementos incorporan las restricciones de contacto en forma débil. Debido al consumo de memoria y a los requerimientos de potencia de cálculo que los problemas de contacto requieren, resultan ser muy buenos candidatos para su paralelización computacional. Sin embargo, tanto la paralelización de los métodos numéricos que surgen de las técnicas clásicas de optimización como los distintos enfoques para su discretización, presentan algunas desventajas que deben ser consideradas. Por un lado, el principal problema aparece ya que en los casos más generales de la mecánica de contacto ocurre un deslizamiento entre cuerpos. Por este motivo, la introducción de los elementos de contacto vuelve necesaria una actualización del grafo de la malla cada cierto número de pasos de tiempo. Desde el punto de vista del método de descomposición de dominios utilizado en la resolución paralela de problemas numéricos, esto es una gran desventaja debidoa su coste computacional. En estos casos, un reparticionamiento dinámico debe ser realizado para redistribuir el grafo actualizado de la malla entre los diferentes procesadores. Por otro lado, algunas técnicas de optimización modifican dinámicamente el número de grados de libertad del problema al introducir multiplicadores de Lagrange como incógnitas. En este trabajo presentamos un algoritmo paralelo del tipo Dirichlet-Neumann para la resolución numérica de problemas de contacto no lineales con fricción, poniendo un especial énfasis en su implementación computacional. Entre sus principales características se puede destacar que no hay necesidad de actualizar el grafo de la malla durante la simulación, ya que en este algoritmo no se utilizan elementos de contacto. Adicionalmente, ningún grado de libertad extra es introducido al sistema, ya que los multiplicadores de Lagrange no son requeridos. En este algoritmo los cuerpos en contacto son tratados de forma separada, de una manera segregada. El acople entre estos cuerpos es realizado a través del intercambio de condiciones de contorno en la interfaz de contacto. Desde un punto de vista computacional, esta característica permite el uso de un enfoque multi-código. Además, este algoritmo puede ser interpretado como un método del tipo black-box ya que permite resolver cada cuerpo por separado, aún utilizando distintos códigos computacionales. Adicionalmente, el algoritmo de contacto propuesto en esta tesis puede ser formulado como un esquema de resolución de punto fijo, empleado de forma general en la solución de problemas de interfaz. Esta generalización permite extrapolar técnicas numéricas ya utilizadas en los problemas de interacción fluido-estructura e implementarlas en la mecánica de contacto, en especial aquellas relacionadas con el aseguramiento y aceleración de la convergencia. En este trabajo describimos la implementación paralela del algoritmo propuesto y analizamos su comportamiento y performance paralela tanto en casos de validación como reales, ejecutados en computadores de alta performance utilizando varios procesadores.Postprint (published version

Efficient algorithms for the fast computation of space charge effects caused by charged particles in particle accelerators

In this dissertation, a Poisson solver is improved with three parts: the efficient integrated Green's function; the discrete cosine transform of the efficient integrated Green's function values; the implicitly zero-padded fast Fourier transform for charge density. In addition, the high performance computing technology is utilized for the further improvement of efficiency, such as: OpenMP API, OpenMP+CUDA, MPI, and MPI+OpenMP parallelizations. The examples and simulation results are matched with the results of the commonly used Poisson solver to demonstrate the accuracy performance

Methods based on B-splines for model representation, numerical analysis and image registration

The thesis consists of inter-connected parts for modeling and analysis using newly developed isogeometric methods. The main parts are reproducing kernel triangular B-splines, extended isogeometric analysis for solving weakly discontinuous problems, collocation methods using superconvergent points, and B-spline basis in image registration applications. Each topic is oriented towards application of isogeometric analysis basis functions to ease the process of integrating the modeling and analysis phases of simulation. First, we develop reproducing a kernel triangular B-spline-based FEM for solving PDEs. We review the triangular B-splines and their properties. By definition, the triangular basis function is very flexible in modeling complicated domains. However, instability results when it is applied for analysis. We modify the triangular B-spline by a reproducing kernel technique, calculating a correction term for the triangular kernel function from the chosen surrounding basis. The improved triangular basis is capable to obtain the results with higher accuracy and almost optimal convergence rates. Second, we propose an extended isogeometric analysis for dealing with weakly discontinuous problems such as material interfaces. The original IGA is combined with XFEM-like enrichments which are continuous functions themselves but with discontinuous derivatives. Consequently, the resulting solution space can approximate solutions with weak discontinuities. The method is also applied to curved material interfaces, where the inverse mapping and the curved triangular elements are considered. Third, we develop an IGA collocation method using superconvergent points. The collocation methods are efficient because no numerical integration is needed. In particular when higher polynomial basis applied, the method has a lower computational cost than Galerkin methods. However, the positions of the collocation points are crucial for the accuracy of the method, as they affect the convergent rate significantly. The proposed IGA collocation method uses superconvergent points instead of the traditional Greville abscissae points. The numerical results show the proposed method can have better accuracy and optimal convergence rates, while the traditional IGA collocation has optimal convergence only for even polynomial degrees. Lastly, we propose a novel dynamic multilevel technique for handling image registration. It is application of the B-spline functions in image processing. The procedure considered aims to align a target image from a reference image by a spatial transformation. The method starts with an energy function which is the same as a FEM-based image registration. However, we simplify the solving procedure, working on the energy function directly. We dynamically solve for control points which are coefficients of B-spline basis functions. The new approach is more simple and fast. Moreover, it is also enhanced by a multilevel technique in order to prevent instabilities. The numerical testing consists of two artificial images, four real bio-medical MRI brain and CT heart images, and they show our registration method is accurate, fast and efficient, especially for large deformation problems

End-to-end drilling optimization using machine learning

Drilling costs occupy a significant portion of oil and gas project’s budget. Optimization of drilling - increasing speed, reducing vibrations, and minimizing borehole instability - can lead to significant savings and hence have been extensively studied. Currently, most drilling optimization tools (or models) only tackle a single drilling metric: they seek to optimize either the rate of penetration (ROP), torque on bit (TOB), mechanical specific energy (MSE) or drilling vibrations. Models are often built independent of other metrics (without coupling) and do not accurately represent downhole conditions since drilling metrics are interrelated. This may lead to over or underestimation of the metric optimized which can severely reduce the effect of optimization. The objective of this dissertation is to introduce techniques, strategies, and algorithms that can be used to build a fully coupled drilling optimization model. Drilling optimization is studied by first optimizing ROP– where models for ROP prediction and inference are constructed using machine learning. Strategies and algorithms for determining optimal drilling parameters using ROP models are discussed. The unique problem posed by data-driven models are solved using meta-heuristic algorithms. A coupled model is constructed by building ROP, TOB, and MSE models conjointly using the random forests algorithm. Drilling vibrations – axial, lateral, and torsional – are modeled using a machine learning classification algorithm. This classification algorithm used to restrict the optimization space, ensuring that optimal parameters do not induce vibrations ahead of the bit. This model is used to investigate the effect of optimizing ROP and MSE on field data. A workflow is introduced linking all the aforementioned models into an end-to-end drilling optimization tool. The tool can be used as a recommendation system where field-measured data are used to determine and implement optimal drilling parameters ahead of the bit. The dissertation illustrates the use of statistical (or machine) learning techniques to address the problems encountered in drilling optimizationPetroleum and Geosystems Engineerin

Fully-integrated mm-Wave Full-duplexing and MIMO Multi-beamforming Receiver Techniques for 5G and Beyond

In recent years, the research community's interest in fully integrated mm-Wave wireless communication systems has increased significantly. With the standards for 5G NR now in place, the focus has shifted to actual deployment. Mm-Wave systems provide wider bandwidths, higher capacity, and lower latency than existing systems such as 4G. Higher path loss and shadowing, however, limit the network coverage at mm-Wave frequencies. The possibility of beamforming due to compact antenna size at mm-Wave and range-extending repeaters help mitigate challenges arising from path loss and relax link budget requirements. In the first part of the thesis, fully integrated scalable MIMO multi-beamforming phased-array to enable unit-tile based densely packed (lambda=2) large scale phased-arrays is demonstrated. Large scale arrays enhance Signal to Noise Ratio (SNR) and/or Effective Isotropically Radiated Power (EIRP) and help meet link budget. In the second part, mm-Wave Full-duplex (FD) receiver (RX) to implement Integrated Access and Backhaul (IAB) and repeaters in a spectrum efficient way is demonstrated. Dense deployment of IAB and repeaters enhances link robustness and range of connectivity. Two Integrated Chips (ICs) are fabricated and measured for demonstration. In the first IC, a 4-element MIMO RX array with multi-beamforming and simplified single wire intermediate frequency (IF) IO is presented. The evolution of mm-wave phased array receivers to MIMO RX promises multi-beamforming and improved capacity. Digital Beamforming (DBF) provides the highest flexibility for multibeamforming. However, it suffers from # of ADCs scaling with the # of elements and absence of spatial filtering prior to the ADCs. Mm-Wave MIMO arrays must also address the challenge of increased IO routing while supporting dense ll-factors with =2 antenna spacing. In this work, a MIMO multi-beamforming RX array architecture with simultaneous spatial filtering and single wire Frequency-domain Multiplexing (FDM) for 5G and beyond is presented. The proposed system preserves full MIMO field-of-view while ensuring a single IF interface. A 28 GHz 4-element RX prototype demonstrates the proposed functionality in 65-nm CMOS. The IC occupies only 3.4mm x 3.1mm for a four-element MIMO 28 GHz array and can form four independent beams with > 400MHz 3 dB BW and FDM on to a single IF interface. Mm-wave MIMO operation is demonstrated by concurrent reception of two wireless 28 GHz beams at 400 Mb/s (100 Msps, 16QAM) data rate. In the second IC, a 26-GHz fully integrated In-band Full-duplex (IBFD) Circulator receiver, which employs passive and active Self-interference Cancellation (SIC) techniques in the mm-Wave domain is presented. Coverage of wireless networks at mm-Wave frequencies can be enhanced by deploying a large number of base stations economically using wireless backhauling. Integrated access and backhaul nodes with spectrum reuse is an efficient way of wireless backhauling. To retain the channel capacity, IAB needs to be implemented using FD schemes that suffers from a strong Transmitter (TX) to RX leakage. This SI leakage can significantly impact the receiver sensitivity and increase the baseband/ADC dynamic range requirements. Canceling SI at mm-Wave applications is challenging given the high frequency of operation, wide bandwidths, and antenna (ANT) impedance sensitivity to the surroundings. Proposed mm-Wave RX with a shared ANT interface based on a Circulator with active SI cancelers provide ~53 dB SIC over 400MHz and ~40 dB SIC over 400MHz to meet the link budget requirements. Proposed architecture achieves SIC by (i) introducing a shared ANT interface based on a hybrid-coupler and a Non-reciprocal Transmission Line (NTL) that provides wideband SIC and additionally creating a SI replica (ii) subsequent active cancellation using SI replica along with variable gain and phase shifters to accommodate SI channel variations. Proposed 26-GHz RX consumes only ~111mW power. The system is implemented in 45nm SOI CMOS and has an active area of 4.54mm². Stand-alone RX NF is ~5.8 dB, and TX to ANT Insertion Loss (IL) is ~3.1 dB. Over-the-Air (OTA) measurements with modulated TX (128 QAM 2.1 Gb/s) and RX (128 QAM 4.2 Gb/s) signals show an EVM of 3.3% when PTX = PRX

Modelling of servo-controlled pneumatic drives: a generalised approach to pneumatic modelling and applications in servo-drive design

The primary objective of this research is to develop a general modelling facility for modular pneumatic servo-drives. The component-oriented approach has been adopted as the modelling technique to provide the flexibility of modelling a wide variety of components and the segmentation of the non-linear system to less complex uncoupled component modules. A significant part of the research work has been devoted to identify a series of component modules of the single axis linear pneumatic servomechanism with standardised linking variables. The mathematical models have been implemented in a simulation software which produces time domain responses for design evaluation purposes. Alternative components for different servomechanism design were modelled as mutually exclusive modules which could be selected for assembly as if they were real physical entities. The philosophy of the approach was validated by tests on prototype servo-drives with matching components. Design analysis could be performed by simulating and comparing the performance of alternative system structures. [Continues.