61 research outputs found
A multi-sphere particle numerical model for non-invasive investigations of neuronal human brain activity
In this paper, a multi-sphere particle method is built-up in order to estimate the solution of the Poisson's equation with Neumann boundary conditions describing the neuronal human brain
activity. The partial differential equations governing the relationships
between neural current sources and the data produced by neuroimaging
technique, are able to compute the scalp potential and magnetic field
distributions generated by the neural activity. A numerical approach is proposed with current dipoles as current sources and going on in the
computation by avoiding the mesh construction. The current dipoles
are into an homogeneous spherical domain modeling the head and the
computational approach is extended to multilayered con¯guration with
different conductivities. A good agreement of the numerical results is
shown and, for the first time compared with the analytical ones
Aplicação do método de Galerkin descontínuo para a análise de guias fotônicos
Orientador: Hugo Enrique Hernández FigueroaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Um novo método de onda completo para realizar a análise modal em guias de onda é introduzido nesta dissertação. A ideia central por trás do método é baseada na discretização da equação de onda vetorial com o Método de Galerkin Descontínuo com Penalidade Interior (IPDG, do inglês Interior Penalty Discontinuous Galerkin). Com uma função de penalidade apropriada, um método de alta precisão e sem modos espúrios é obtido. A eficiência do método proposto é provada em vários guias de onda, incluindo complicados guias de ondas ópticos com modos vazantes e também em guias de onda plasmônicos. Os resultados foram comparados com os métodos do estado-da-arte descritos na literatura. Também é discutida a importância dessa nova abordagem. Além disso, os resultados indicam que o método é mais preciso do que abordagens anteriores baseadas em Elementos Finitos. As principais contribuições deste trabalho são: foi desenvolvido um novo método robusto e de alta precisão para a análise de guias de ondas arbitrários, uma nova função de penalidade para o IPDG foi proposta e aplicações práticas do método proposto são apresentadas. Adicionalmente, no apêndice é apresentado uma aplicação da análise modal em simulação eletromagnética 3D com um método de Galerkin DescontínuoAbstract: A novel full-wave method to perform mode analysis on waveguides is introduced in this dissertation. The core of the method is based on an Interior Penalty Discontinuous Galerkin (IPDG) discretization of the vector wave equation. With an appropriate penalty function a spurious-free and high accuracy method is achieved. The efficiency of the proposed method was proved in several waveguides, including intricate optical waveguides with leaky modes and also on plasmonic waveguides. The obtained results were compared with the state-of-the-art mode solvers described in the literature. Also, a discussion on the importance of this new approach is presented. Moreover, the results indicate that the proposed method is more accurate than the previous approaches based on Finite Elements Methods. The main contributions of this work are: the development of a novel robust and accurate method for the analysis of arbitrary waveguides, a new penalty function for the IPDG was proposed and practical applications of the methods are discussed. In addition, in the appendix an application of modal analysis on 3D electromagnetic simulations with a Discontinuous Galerkin method is detailedMestradoTelecomunicações e TelemáticaMestre em Engenharia ElétricaCAPE
JST-SPH: a total Lagrangian, stabilised meshless methodology for mixed systems of conservation laws in nonlinear solid dynamics
The combination of linear finite elements space discretisation with Newmark
family time-integration schemes has been established as the de-facto
standard for numerical analysis of fast solid dynamics. However, this set-up
suffers from a series of drawbacks: mesh entanglements and elemental distortion
may compromise results of high strain simulations; numerical issues,
such as locking and spurious pressure oscillations, are likely to manifest;
and stresses usually reach a reduced order of accuracy than velocities.
Meshless methods are a relatively new family of discretisation techniques
that may offer a solution to problems of excessive distortion experienced by
linear finite elements. Amongst these new methodologies, smooth particles
hydrodynamics (SPH) is the simplest in concept and the most straightforward
to numerically implement. Yet, this simplicity is marred by some
shortcomings, namely (i) inconsistencies of the SPH approximation at or near
the boundaries of the domain; (ii) spurious hourglass-like modes caused by
the rank deficiency associated with nodal integration, and (iii) instabilities
arising when sustained internal stresses are predominantly tensile.
To deal with the aforementioned SPH-related issues, the following remedies
are hereby adopted, respectively: (i) corrections to the kernel functions
that are fundamental to SPH interpolation, improving consistency at and
near boundaries; (ii) a polyconvex mixed-type system based on a new set
of unknown variables (p, F, H and J) is used in place of the displacementbased
equation of motion; in this manner, stabilisation techniques from
computational fluid dynamics become available; (iii) the analysis is set in a
total Lagrangian reference framework.
Assuming polyconvex variables as the main unknowns of the set of first
order conservation laws helps to establish the existence and uniqueness
of analytical solutions. This is a key reassurance for a robust numerical
implementation of simulations. The resulting system of hyperbolic first
order conservation laws presents analogies to the Euler equations in fluid
dynamics. This allows the use of a well-proven stabilisation technique in
computational fluid dynamics, the Jameson Schmidt Turkel (JST) algorithm.
JST is very effective in damping numerical oscillations, and in capturing discontinuities
in the solution that would otherwise be impossible to represent.
Finally, we note that the JST-SPH scheme so defined is employed in a
battery of numerical tests, selected to check its accuracy, robustness, momentum
preservation capabilities, and its viability for solving larger scale,
industry-related problems
Application of PEEC modeling for the development of a novel multi-gigahertz test interface with fine pitch wafer level package
Ph.DDOCTOR OF PHILOSOPH
Meshless methods for Maxwell’s equations with applications to magnetotelluric modelling and inversion
The first part of thesis presents new meshless methods for solving time harmonic electromagnetic fields in closed two- or three-dimensional volumes containing heterogeneous
materials. This new methods will be used to simulate magnetotelluric experiments, when an Earth conductivity model is given in advanced. Normally, classical approximation methods like finite elements or finite differences are used to solve this task. The algorithms
here in this thesis, only need an unstructured point sampling in the modelling domain for the discretization and is able to gain a solution for the partial differential equation without a fixed mesh or grid. This is advantageous when complex model geometries have to be described, because no adapted mesh or grid need to be generated. The meshless methods, described here in this thesis, use a direct discretization technique in combination with a generalized approximation method. This allows to formulate the partial differential equations in terms of linear functionals, which can be approximated and directly form the discretization. For the two-dimensional magnetotelluric problem, a second-order accurate algorithm to solve the partial differential equations was developed and tested with several example calculations. The accuracy of the new meshless methods was compared to analytical solutions, and it was found, that a better accuracy can be achieved with less degrees of freedoms compared to previously published results. For the three-dimensional case, a meshless formulation was given and numerical calculations show the ability of the scheme to handle models with heterogeneous conductivity structures. In the second part of this thesis, the newly developed two-dimensional simulation method will be used in an inversion scheme. Here, the task is to recover the unknown Earth conductivity model with the help of data gained from a magnetotelluric experiment. Due to the previously developed meshless approximation algorithm, some numerical tasks during the inversion can be simplified by reusing the discretization defined on the point sampling from the
forward simulation. The newly developed meshless inversion algorithm will be tested with synthetic data to reconstruct known conductivity anomalies. It can be shown, that the inverse algorithm produces correct results, even in the presence of topography
Electrical analogous in viscoelasticity
In this paper, electrical analogous models of fractional hereditary materials are introduced.
Based on recent works by the authors, mechanical models of materials viscoelasticity
behavior are firstly approached by using fractional mathematical operators. Viscoelastic
models have elastic and viscous components which are obtained by combining springs
and dashpots. Various arrangements of these elements can be used, and all of these viscoelastic
models can be equivalently modeled as electrical circuits, where the spring and
dashpot are analogous to the capacitance and resistance, respectively. The proposed models
are validated by using modal analysis. Moreover, a comparison with numerical experiments
based on finite difference time domain method shows that, for long time
simulations, the correct time behavior can be obtained only with modal analysis. The
use of electrical analogous in viscoelasticity can better reveal the real behavior of fractional
hereditary materials
Meshless Direct Numerical Simulation of Turbulent Incompressible Flows
A meshless direct pressure-velocity coupling procedure is presented to perform Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent incompressible flows in regular and irregular geometries. The proposed method is a combination of several efficient techniques found in different Computational Fluid Dynamic (CFD) procedures and it is a major improvement of the algorithm published in 2007 by this author. This new procedure has very low numerical diffusion and some preliminary calculations with 2D steady state flows show that viscous effects become negligible faster that ever predicted numerically. The fundamental idea of this proposal lays on several important inconsistencies found in three of the most popular techniques used in CFD, segregated procedures, streamline-vorticity formulation for 2D viscous flows and the fractional-step method, very popular in DNS/LES. The inconsistencies found become important in elliptic flows and they might lead to some wrong solutions if coarse grids are used. In all methods studied, the mathematical basement was found to be correct in most cases, but inconsistencies were found when writing the boundary conditions. In all methods analyzed, it was found that it is basically impossible to satisfy the exact set of boundary conditions and all formulations use a reduced set, valid for parabolic flows only. For example, for segregated methods, boundary condition of normal derivative for pressure zero is valid only in parabolic flows. Additionally, the complete proposal for mass balance correction is right exclusively for parabolic flows. In the streamline-vorticity formulation, the boundary conditions normally used for the streamline function, violates the no-slip condition for viscous flow. Finally, in the fractional-step method, the boundary condition for pseudo-velocity implies a zero normal derivative for pressure in the wall (correct in parabolic flows only) and, when the flows reaches steady state, the procedure does not guarantee mass balance. The proposed procedure is validated in two cases of 2D flow in steady state, backward-facing step and lid-driven cavity. Comparisons are performed with experiments and excellent agreement was obtained in the solutions that were free from numerical instabilities. A study on grid usage is done. It was found that if the discretized equations are written in terms of a local Reynolds number, a strong criterion can be developed to determine, in advance, the grid requirements for any fluid flow calculation. The 2D-DNS on parallel plates is presented to study the basic features present in the simulation of any turbulent flow. Calculations were performed on a short geometry, using a uniform and very fine grid to avoid any numerical instability. Inflow conditions were white noise and high frequency oscillations. Results suggest that, if no numerical instability is present, inflow conditions alone are not enough to sustain permanently the turbulent regime. Finally, the 2D-DNS on a backward-facing step is studied. Expansion ratios of 1.14 and 1.40 are used and calculations are performed in the transitional regime. Inflow conditions were white noise and high frequency oscillations. In general, good agreement is found on most variables when comparing with experimental data
Development of Micro-Macro Continuum-Discontinuum Coupled Numerical Method
A micro-macro and continuum-discontinuum coupled model and corresponding computer codes are developed in this thesis for rock dynamics study. Firstly, a new micromechanical model for describing the elastic continuum based on the underlying microstructure of material is proposed. The model provides a more general description of material than linear elasticity. Then, a numerical model Distinct Lattice Spring Model (DLSM) is developed based on the RMIB theory. The new proposed model has the advantages of being meshless, and automatic continuum description through underlying discontinuum structure and directly using macroscopic elastic parameters. Following this, the multi-scale DLSM (m-DLSM) is proposed to combine DLSM and NMM. The proposed model uses a tri-layer structure and the macro model can be automatically released into micro model during calculation. Forth ward, the ability of DLSM on modeling dynamic failure is studied. A damage based micro constitutive law is developed. Relationships between the micro constitutive parameters and the macro mechanical parameters of material are provided. The micro parameters can directly be obtained from macro experimental results, i.e., tensile strength and fracture energy, through these equations. Moreover, the ability of DLSM on modeling wave propagation is enhanced and verified. Non-reflection boundary condition and methods to represent discontinuity in DLSM are developed. Finally, the parallelization of DLSM and 2D implicit DLSM are introduced. The main achievements of the whole PhD work and future research works are summarized and prospected in the conclusion part of the thesis
Implementation of a general algorithm for incompressible and compressible flows within the multi-physics code Kratos and preparation of fluid-structure coupling
This diploma thesis deals with the implementation of a fluid solver for incompressible and compressible flows within the multi-physics framework Kratos. The presentation of this environment based on the finite element method (FEM) and an introduction to multidisciplinary problems in general are the starting point of this work and help understanding the following steps more easily.
Originating from the basic conservation equations for mass, momentum and energy, the Euler equations for inviscid flow are derived. In this context some approximations are presented that avoid the solution of the energy equation and allow the use of a general approach for the simulation of incompressible, slightly compressible and barotropic flow. The implementation of the incompressible case is outlined step-by-step: Having discretized the continuous problem, a fractional step scheme is presented in order to uncouple pressure and velocity components by a split of the momentum equation. Emphasis is placed on the nodal implementation using an edge-based data structure. Moreover, the orthogonal subscale stabilization - necessary because of the finite element discretization - is explained very briefly.
Subsequently, the solver is extended to compressible regime mentioning the respective modifications. For validation purposes numerical examples of incompressible and compressible flows in two and three dimensions round of this first part.
In a second step, the implemented flow solver is prepared for the fluid-structure coupling. After presenting solving procedures for multi-disciplinary problems, the arbitrary Lagrangian Eulerian (ALE) formulation is introduced and the conservation equations are modified accordingly. Some preliminary tests are performed, particularly with regard to mesh motion and adjustment of the boundary conditions. Finally, expectations for the envisaged fluid-structure coupling are brought forward
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