A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

Análise numérica e experimental do comportamento de fundações superficiais assentes em solo melhorado

O presente trabalho tem como objetivo estudar o comportamento de camadas superficiais de solo melhorado como base de fundações superficiais. Nesta pesquisa foram realizados ensaios de placa de 30 cm de diâmetro sobre camadas de solo residual compactado e de solo tratado com cimento (teor de 5% de cimento), ambas com 60 cm de espessura. O programa experimental também incluiu a retirada de amostras de campo das camadas de solo melhorado para a execução de ensaios triaxiais drenados (CID) com medida interna de deformações, a fim de obter parâmetros constitutivos para a realização de simulações numéricas. Uma comparação entre os resultados dos ensaios triaxiais com amostras retiradas em campo e moldadas em laboratório (Rohlfes Junior, 1996) é apresentada. A diferença entre os resultados dos ensaios triaxiais com amostras de campo e laboratório foi significativa para o caso das amostras de solo melhorado com cimento, tal fato é atribuído principalmente a dificuldade de mistura em campo. O Método dos Elementos Finitos foi utilizado para simular o comportamento carga x recalque das placas assentes sobre camadas de solo melhorado. O modelo Pseudo-Elástico Não Linear (Hiperbólico) foi empregado na análise numérica para modelar o comportamento dos novos materiais. Os resultados dos ensaios de placa sobre camadas de solo melhorado demonstraram que houve um aumento significativo da capacidade de suporte, além de uma redução considerável dos recalques, quando comparados ao comportamento carga x recalque do solo natural (Cudmani, 1994). A analise do comportamento de fundações superficiais assentes em solos estratificados, através de simulações numéricas, demonstrou ser eficiente para a previsão do comportamento carga x recalque das mesmas.

Desenvolvimento de antenas de microfita e antenas DRA Broadband

The search for ever smaller device and without loss of performance has been increasingly investigated by researchers involving applied electromagnetics. Antennas using ceramics materials with a high dielectric constant, whether acting as a substract element of patch radiating or as the radiant element are in evidence in current research, that due to the numerous advantages offered, such as: low profile, ability to reduce the its dimensions when compared to other devices, high efficiency of ratiation, suitability the microwave range and/or millimeter wave, low temperature coefficient and low cost. The reason for this high efficiency is that the dielectric losses of ceramics are very low when compared to commercially materials sold used in printed circuit boards, such as fiberglass and phenolite. These characteristics make ceramic devices suitable for operation in the microwave band. Combining the design of patch antennas and/or dielectric resonator antenna (DRA) to certain materials and the method of synthesis of these powders in the manufacture of devices, it s possible choose a material with a dielectric constant appropriate for the design of an antenna with the desired size. The main aim of this work is the design of patch antennas and DRA antennas on synthesis of ceramic powders (synthesis by combustion and polymeric precursors - Pe- chini method) nanostructured with applications in the microwave band. The conventional method of mix oxides was also used to obtain nanometric powders for the preparation of tablets and dielectric resonators. The devices manufactured and studied on high dielectric constant materials make them good candidates to have their small size compared to other devices operating at the same frequency band. The structures analyzed are excited by three different techniques: i) microstrip line, ii) aperture coupling and iii) inductive coupling. The efficiency of these techniques have been investigated experimentally and compared with simulations by Ansoft HFSS, used in the accurate analysis of the electromagnetic behavior of antennas over the finite element method (FEM). In this thesis a literature study on the theory of microstrip antennas and DRA antenna is performed. The same study is performed about the materials and methods of synthesis of ceramic powders, which are used in the manufacture of tablets and dielectric cylinders that make up the devices investigated. The dielectric media which were used to support the analysis of the DRA and/or patch antennas are analyzed using accurate simulations using the finite difference time domain (FDTD) based on the relative electrical permittivity (er) and loss tangent of these means (tand). This work also presents a study on artificial neural networks, showing the network architecture used and their characteristics, as well as the training algorithms that were used in training and modeling some parameters associated with the devices investigated

Análise e síntese de antenas e superfícies seletivas de frequência utilizando computação evolucionária e inteligência de enxames

The frequency selective surfaces, or FSS (Frequency Selective Surfaces), are structures consisting of periodic arrays of conductive elements, called patches, which are usually very thin and they are printed on dielectric layers, or by openings perforated on very thin metallic surfaces, for applications in bands of microwave and millimeter waves. These structures are often used in aircraft, missiles, satellites, radomes, antennae reflector, high gain antennas and microwave ovens, for example. The use of these structures has as main objective filter frequency bands that can be broadcast or rejection, depending on the specificity of the required application. In turn, the modern communication systems such as GSM (Global System for Mobile Communications), RFID (Radio Frequency Identification), Bluetooth, Wi-Fi and WiMAX, whose services are highly demanded by society, have required the development of antennas having, as its main features, and low cost profile, and reduced dimensions and weight. In this context, the microstrip antenna is presented as an excellent choice for communications systems today, because (in addition to meeting the requirements mentioned intrinsically) planar structures are easy to manufacture and integration with other components in microwave circuits. Consequently, the analysis and synthesis of these devices mainly, due to the high possibility of shapes, size and frequency of its elements has been carried out by full-wave models, such as the finite element method, the method of moments and finite difference time domain. However, these methods require an accurate despite great computational effort. In this context, computational intelligence (CI) has been used successfully in the design and optimization of microwave planar structures, as an auxiliary tool and very appropriate, given the complexity of the geometry of the antennas and the FSS considered. The computational intelligence is inspired by natural phenomena such as learning, perception and decision, using techniques such as artificial neural networks, fuzzy logic, fractal geometry and evolutionary computation. This work makes a study of application of computational intelligence using meta-heuristics such as genetic algorithms and swarm intelligence optimization of antennas and frequency selective surfaces. Genetic algorithms are computational search methods based on the theory of natural selection proposed by Darwin and genetics used to solve complex problems, eg, problems where the search space grows with the size of the problem. The particle swarm optimization characteristics including the use of intelligence collectively being applied to optimization problems in many areas of research. The main objective of this work is the use of computational intelligence, the analysis and synthesis of antennas and FSS. We considered the structures of a microstrip planar monopole, ring type, and a cross-dipole FSS. We developed algorithms and optimization results obtained for optimized geometries of antennas and FSS considered. To validate results were designed, constructed and measured several prototypes. The measured results showed excellent agreement with the simulated. Moreover, the results obtained in this study were compared to those simulated using a commercial software has been also observed an excellent agreement. Specifically, the efficiency of techniques used were CI evidenced by simulated and measured, aiming at optimizing the bandwidth of an antenna for wideband operation or UWB (Ultra Wideband), using a genetic algorithm and optimizing the bandwidth, by specifying the length of the air gap between two frequency selective surfaces, using an optimization algorithm particle swarm

Estudos e projetos de filtro interdigital em microfita para aplicação prática ao transponder do satélite ITASAT

This work shows a theoretical analysis together with numerical and experimental results of transmission characteristics from the microstrip bandpass filters with different geometries. These filters are built over isotropic dielectric substrates. The numerical analysis is made by specifical commercial softwares, like Ansoft Designer and Agilent Advanced Design System (ADS). In addition to these tools, a Matlab Script was built to analyze the filters through the Finite-Difference Time-Domain (FDTD) method. The filters project focused the development of the first stage of filtering in the ITASAT s Transponder receptor, and its integration with the others systems. Some microstrip filters architectures have been studied, aiming the viability of implementation and suitable practical application for the purposes of the ITASAT Project due to its lowspace occupation in the lower UHF frequencies. The ITASAT project is a Universityexperimental project which will build a satellite to integrate the Brazilian Data Collect System s satellite constellation, with efforts of many Brazilian institutes, like for example AEB (Brazilian Spatial Agency), ITA (Technological Institute of Aeronautics), INPE/CRN (National Institute of Spatial Researches/Northeastern Regional Center) and UFRN (Federal University of Rio Grande do Norte). Comparisons were made between numerical and experimental results of all filters, where good agreements could be noticed, reaching the most of the objectives. Also, post-work improvements were suggested.

A fully adaptive multiresolution scheme for shock computations

The scheme is based on Ami Harten's ideas (Harten, 1994), the main tools coming from wavelet theory, in the framework of multiresolution analysis for cell averages. But instead of evolving cell averages on the finest uniform level, we propose to evolve just the cell averages on the grid determined by the significant wavelet coefficients. Typically, there are few cells in each time step, big cells on smooth regions, and smaller ones close to irregularities of the solution. For the numerical flux, we use a simple uniform central finite difference scheme, adapted to the size of each cell. If any of the required neighboring cell averages is not present, it is interpolated from coarser scales. But we switch to ENO scheme in the finest part of the grids. To show the feasibility and efficiency of the method, it is applied to a system arising in polymer-flooding of an oil reservoir. In terms of CPU time and memory requirements, it outperforms Harten's multiresolution algorithm.The proposed method applies to systems of conservation laws in 1Dpartial derivative(t)u(x, t) + partial derivative(x)f(u(x, t)) = 0, u(x, t) is an element of R-m. (1)In the spirit of finite volume methods, we shall consider the explicit schemeupsilon(mu)(n+1) = upsilon(mu)(n) - Deltat/hmu ((f) over bar (mu) - (f) over bar (mu)-) = [Dupsilon(n)](mu), (2)where mu is a point of an irregular grid Gamma, mu(-) is the left neighbor of A in Gamma, upsilon(mu)(n) approximate to 1/mu-mu(-) integral(mu-)(mu) u(x, t(n))dx are approximated cell averages of the solution, (f) over bar (mu) = (f) over bar (mu)(upsilon(n)) are the numerical fluxes, and D is the numerical evolution operator of the scheme.According to the definition of (f) over bar (mu), several schemes of this type have been proposed and successfully applied (LeVeque, 1990). Godunov, Lax-Wendroff, and ENO are some of the popular names. Godunov scheme resolves well the shocks, but accuracy (of first order) is poor in smooth regions. Lax-Wendroff is of second order, but produces dangerous oscillations close to shocks. ENO schemes are good alternatives, with high order and without serious oscillations. But the price is high computational cost.Ami Harten proposed in (Harten, 1994) a simple strategy to save expensive ENO flux calculations. The basic tools come from multiresolution analysis for cell averages on uniform grids, and the principle is that wavelet coefficients can be used for the characterization of local smoothness.. Typically, only few wavelet coefficients are significant. At the finest level, they indicate discontinuity points, where ENO numerical fluxes are computed exactly. Elsewhere, cheaper fluxes can be safely used, or just interpolated from coarser scales. Different applications of this principle have been explored by several authors, see for example (G-Muller and Muller, 1998).Our scheme also uses Ami Harten's ideas. But instead of evolving the cell averages on the finest uniform level, we propose to evolve the cell averages on sparse grids associated with the significant wavelet coefficients. This means that the total number of cells is small, with big cells in smooth regions and smaller ones close to irregularities. This task requires improved new tools, which are described next.

A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows

This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier-Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110: 171-186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199-210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions. Copyright (c) 2006 John Wiley & Sons, Ltd.

Finite-Element Analysis of Stress on Dental Implant Prosthesis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamic stationary response of reinforced plates by the boundary element method

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state ( membrane) and for the out-of-plane state ( bending). These uncoupled systems are joined to formamacro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).

Influence of Cusp Inclination on Stress Distribution in Implant-Supported Prostheses. A Three-Dimensional Finite Element Analysis

Purpose: The aim of this study was to assess the influence of cusp inclination on stress distribution in implant-supported prostheses by 3D finite element method.Materials and Methods: Three-dimensional models were created to simulate a mandibular bone section with an implant (3.75 mm diameter x 10 mm length) and crown by means of a 3D scanner and 3D CAD software. A screw-retained single crown was simulated using three cusp inclinations (10 degrees, 20 degrees, 30 degrees). The 3D models (model 10d, model 20d, and model 30d) were transferred to the finite element program NeiNastran 9.0 to generate a mesh and perform the stress analysis. An oblique load of 200 N was applied on the internal vestibular face of the metal ceramic crown.Results: The results were visualized by means of von Mises stress maps. Maximum stress concentration was located at the point of application. The implant showed higher stress values in model 30d (160.68 MPa). Cortical bone showed higher stress values in model 10d (28.23 MPa).Conclusion: Stresses on the implant and implant/abutment interface increased with increasing cusp inclination, and stresses on the cortical bone decreased with increasing cusp inclination.

A marker-and-cell approach to free surface 2-D multiphase flows

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

MATHEMATICA notebook for computing tetrahedral finite element shape functions and matrices for the Helmholtz equation

A MATHEMATICA notebook to compute the elements of the matrices which arise in the solution of the Helmholtz equation by the finite element method (nodal approximation) for tetrahedral elements of any approximation order is presented. The results of the notebook enable a fast computational implementation of finite element codes for high order simplex 3D elements reducing the overheads due to implementation and test of the complex mathematical expressions obtained from the analytical integrations. These matrices can be used in a large number of applications related to physical phenomena described by the Poisson, Laplace and Schrodinger equations with anisotropic physical properties.

Finite element analysis and fracture resistance testing of a new intraradicular post

Objectives: The objective of the present study was to evaluate a prefabricated intraradicular threaded pure titanium post, designed and developed at the Sao Jose dos Campos School of Dentistry - UNESP, Brazil. This new post was designed to minimize stresses observed with prefabricated post systems and to improve cost-benefits. Materials and and methods: Fracture resistance testing of the post/core/root complex, fracture analysis by microscopy and stress analysis by the finite element method were used for post evaluation. The following four prefabricated metal post systems were analyzed: group 1, experimental post; group 2, modification of the experimental post; group 3, Flexi Post, and group 4, Para Post. For the analysis of fracture resistance, 40 bovine teeth were randomly assigned to the four groups (n=10) and used for the fabrication of test specimens simulating the situation in the mouth. The test specimens were subjected to compressive strength testing until fracture in an EMIC universal testing machine. After fracture of the test specimens, their roots were sectioned and analyzed by microscopy. For the finite element method, specimens of the fracture resistance test were simulated by computer modeling to determine the stress distribution pattern in the post systems studied. Results: The fracture test presented the following averages and standard deviation: G1 (45.63 +/- 8.77), G2 (49.98 +/- 7.08), G3 (43.84 +/- 5.52), G4 (47.61 +/- 7.23). Stress was homogenously distributed along the body of the intraradicular post in group 1, whereas high stress concentrations in certain regions were observed in the other groups. These stress concentrations in the body of the post induced the same stress concentration in root dentin. Conclusions: The experimental post (original and modified versions) presented similar fracture resistance and better results in the stress analysis when compared with the commercial post systems tested (08/2008PA/CEP).

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier B.V. All rights reserved.