528 research outputs found
A hp-like discontinuous Galerkin method for solving the 2D time-domain Maxwell's equations on non-conforming locally refined triangular meshes
This work is concerned with the design of a hp-like discontinuous Galerkin (DG) method for solving the 2D time-domain Maxwell's equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements of the mesh, with a leap-frog time integration scheme
Application of Helmholtz/Hodge Decomposition to Finite Element Methods for Two-Dimensional Maxwell\u27s Equations
In this work we apply the two-dimensional Helmholtz/Hodge decomposition to develop new finite element schemes for two-dimensional Maxwell\u27s equations. We begin with the introduction of Maxwell\u27s equations and a brief survey of finite element methods for Maxwell\u27s equations. Then we review the related fundamentals in Chapter 2. In Chapter 3, we discuss the related vector function spaces and the Helmholtz/Hodge decomposition which are used in Chapter 4 and 5. The new results in this dissertation are presented in Chapter 4 and Chapter 5. In Chapter 4, we propose a new numerical approach for two-dimensional Maxwell\u27s equations that is based on the Helmholtz/Hodge decomposition for divergence-free vector fields. In this approach an approximate solution for Maxwell\u27s equations can be obtained by solving standard second order scalar elliptic boundary value problems. This new approach is illustrated by a P1 finite element method. In Chapter 5, we further extend the new approach described in Chapter 4 to the interface problem for Maxwell\u27s equations. We use the extraction formulas and multigrid method to overcome the low regularity of the solution for the Maxwell interface problem. The theoretical results obtained in this dissertation are confirmed by numerical experiments
FDTD-based full wave co-simulation model for hybrid electromagnetic systems
In high-frequency ranges, the present electronic design automation software has limited capabilities to model electromagnetic (EM) systems where there are strong field effects influencing their characteristics. In this situation, a full-wave simulation tool is desired for the analysis and design of high-speed and non-linear EM systems. It is necessary to explore the interaction between the field and electronic components during a transient process when field effects are more significant. The finite-difference time-domain (FDTD) technique receives growing attention in the area of EM system analysis and simulation due to its simplicity, flexibility and robustness. It is a full-wave simulation method that solves the Maxwell\u27s equations in time domain directly. Decades of research and development and rapid growth in computer capability have built up a firm foundation for FDTD techniques to be applied to many practical problems.
Based on FDTD, this dissertation develops a stable CO-simulation method to perform a full-wave simulation of a hybrid EM system consisting of lumped elements and distributed structures. In this method, FDTD is used to solve the EM field problems associated with distributed structures, and a circuit simulator solves the response of lumped elements. A field-circuit model proposed in the dissertation serves as the interface between the two simulation tools. Compared with previous methods, the FDTD method based on this model is much more flexible and stable for linear and nonlinear lumped elements under both small and large signal conditions. Because of its flexibility and robustness, this model is a promising approach to integrate a field solver and a circuit simulator in the simulations of practical EM systems.
In order to improve the simulation accuracy, some problems related to FDTD simulation are studied. Based on the numerical dispersion in homogeneous media uniform grids, the FDTD numerical reflection and transmission on the boundary of media, which are discritized by a non-uniform grid, are investigated. This investigation provides for the first time an estimation of FDTD numerical error in inhomogeneous media and non-uniform grids. Perfectly matched layer (PML) was previously utilized the homogeneous media or uniform grids. This dissertation extends the PML boundary conditions to handle the inhomogeneous media and non-uniform grid. Techniques extracting S parameters from FDTD simulation are also discussed.
Two and three-dimensional CO-simulation software, written in C++, has be derived, developed and verified in this dissertation. The simulation results agree well with results from other simulation methods, like SPICE, for many test circuits. Taking data sampling and interpolation into account, simulation results generally fit well to measurement and other simulation results for complicated three-dimensional structures.
With further improvements of the FDTD technique and circuit simulation, field-circuit CO-simulation model will widen its application to general EM systems
Advanced techniques in scientific computing: application to electromagnetics
Mención Internacional en el tÃtulo de doctorDurante los últimos años, los componentes de radiofrecuencia que
forman parte de un sistema de comunicaciones necesitan simulaciones
cada vez más exigentes desde el punto de vista de recursos computacionales.
Para ello, se han desarrollado diferentes técnicas con el método de
los elementos finitos (FEM) como la conocida como adaptatividad hp,
que consiste en estimar el error en el problema electromagnético para
generar mallas de elementos adecuadas al problema que obtienen una
aproximación de forma más efectiva que las mallas estándar; o métodos
de descomposición de dominios (DDM), basado en la división del problema
original en problemas más pequeños que se pueden resolver en
paralelo. El principal problema de las técnicas de adaptatividad es que
ofrecen buenas prestaciones para problemas bidimensionales, mientras
que en tres dimensiones el tiempo de generación de las mallas adaptadas
es prohibitivo. Por otra parte, DDM se ha utilizado satisfactoriamente
para la simulación de problemas eléctricamente muy grandes y de gran
complejidad, convirtiéndose en uno de los temas más actuales en la comunidad
de electromagnetismo computacional.
El principal objetivo de este trabajo es estudiar la viabilidad de algoritmos
escalables (en términos de paralelización) combinando DDM no
conformes y adaptatividad automática en tres dimensiones. Esto permitir
Ãa la ejecución de algoritmos de adaptatividad independiente en cada
subdominio de DDM. En este trabajo se presenta y discute un prototipo
que combina técnicas de adaptatividad y DDM, que aún no se han tratado en detalle en la comunidad cientÃfica. Para ello, se implementan
tres bloques fundamentales: i) funciones de base para los elementos finitos
que permitan órdenes variables dentro de la misma malla; ii) DDM no
conforme y sin solapamiento; y iii) algoritmos de adaptatividad en tres
dimensiones. Estos tres bloques se han implementado satisfactoriamente
en un código FEM mediante un método sistemático basado en el método
de las soluciones manufacturadas (MMS). Además, se ha llevado a cabo
una paralelización a tres niveles: a nivel de algoritmo, con DDM; a nivel
de proceso, con MPI (Message Passing Interface); y a nivel de hebra, con
OpenMP; todo en un código modular que facilita el mantenimiento y la
introducción de nuevas caracterÃsticas.
Con respecto al primer bloque fundamental, se ha desarrollado una
familia de funciones base con un enfoque sistemático que permite la
expansión correcta del espacio de funciones. Por otra parte, se han introducido
funciones de base jerárquicas de otros autores (con los que el
grupo al que pertenece el autor de la tesis ha colaborado estrechamente
en los últimos años) para facilitar la introducción de diferentes órdenes
de aproximación en el mismo mallado.
En lo relativo a DDM, se ha realizado un estudio cuantitativo del
error generado por las disconformidades en la interfaz entre subdominios,
incluidas las discontinuidades generadas por un algoritmo de adaptatividad.
Este estudio es fundamental para el correcto funcionamiento
de la adaptatividad, y no ha sido evaluado con detalle en la comunidad
cientÃfica.
Además, se ha desarrollado un algoritmo de adaptatividad con prismas
triangulares, haciendo especial énfasis en las peculiaridades debidas
a la elección de este elemento. Finalmente, estos tres bloques básicos
se han utilizado para desarrollar, y discutir, un prototipo que une las
técnicas de adaptatividad y DDM.In the last years, more and more accurate and demanding simulations
of radiofrequency components in a system of communications are
requested by the community. To address this need, some techniques have
been introduced in finite element methods (FEM), such as hp adaptivity
(which estimates the error in the problem and generates tailored meshes
to achieve more accuracy with less unknowns than in the case of uniformly
refined meshes) or domain decomposition methods (DDM, consisting
of dividing the whole problem into more manageable subdomains
which can be solved in parallel). The performance of the adaptivity techniques
is good up to two dimensions, whereas for three dimensions the
generation time of the adapted meshes may be prohibitive. On the other
hand, large scale simulations have been reported with DDM becoming a
hot topic in the computational electromagnetics community.
The main objective of this dissertation is to study the viability of
scalable (in terms of parallel performance) algorithms combining nonconformal
DDM and automatic adaptivity in three dimensions. Specifically,
the adaptivity algorithms might be run in each subdomain independently.
This combination has not been detailed in the literature
and a proof of concept is discussed in this work. Thus, three building
blocks must be introduced: i) basis functions for the finite elements
which support non-uniform approximation orders p; ii) non-conformal
and non-overlapping DDM; and iii) adaptivity algorithms in 3D. In this
work, these three building blocks have been successfully introduced in a FEM code with a systematic procedure based on the method of manufactured
solutions (MMS). Moreover, a three-level parallelization (at the
algorithm level, with DDM; at the process level, with message passing
interface (MPI), and at the thread level, with OpenMP) has been developed
using the paradigm of modular programming which eases the
software maintenance and the introduction of new features.
Regarding first building block, a family of basis functions which follows
a sound mathematical approach to expand the correct space of
functions is developed and particularized for triangular prisms. Also,
to ease the introduction of different approximation orders in the same
mesh, hierarchical basis functions from other authors are used as a black
box. With respect to DDM, a thorough study of the error introduced
by the non-conformal interfaces between subdomains is required for the
adaptivity algorithm. Thus, a quantitative analysis is detailed including
non-conformalities generated by independent refinements in neighbor
subdomains. This error has not been assessed with detail in the literature
and it is a key factor for the adaptivity algorithm to perform properly.
An adaptivity algorithm with triangular prisms is also developed and
special considerations for the implementation are explained. Finally, on
top of these three building blocks, the proof of concept of adaptivity
with DDM is discussed.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Daniel Segovia Vargas.- Secretario: David Pardo Zubiaur.- Vocal: Romanus Dyczij-Edlinge
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Mini-Workshop: Analytical and Numerical Treatment of Singularities in PDE
[no abstract available
Numerical EEG Forward Modeling with Dipolar Sources: H(div) Approach
The objective of this master's thesis project is to study forward electroencephalography (EEG) modeling with divergence conforming, finite element sources. EEG is a method for measuring electric potentials on human head, caused by neural activity in the brain. The main goals were to implement previously studied H(div) - source types to a C++ based toolbox DUNE (Distributed and Unified Numerics Environment), and also to numerically analyze the influence of the element patch size on modeling accuracy. Moreover, an adaptive version of the previously studied H(div) approach is evaluated. The numerical analysis was conducted with a spherical mesh.
The results of the numerical experiments revealed that the divergence conforming source models produce relatively accurate results near the outer gray matter layer boundary. For deeper sources that are located further away from the gray matter boundary, the reference method St. Venant gave more precise results. Moreover, the modeling accuracy for the H(div) source model improved as the size of the element patch grew. Nevertheless, for sources near the gray matter boundary, there were no significant increases in modeling precision detected after taking more than four elements in source configuration. In addition, the adaptive style did not bring any remarkable advantage to the resulting accuracy
Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers
Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method
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