A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

Influence of Crown Ferrule Heights and Dowel Material Selection on the Mechanical Behavior of Root-Filled Teeth: A Finite Element Analysis

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

Methods Used for Assessing Stresses in Buccomaxillary Prostheses: Photoelasticity, Finite Element Technique, and Extensometry

The authors describe a literature revision on assessing stresses in buccomaxillary prostheses photoelasticity, finite element technique, and extensometry. They describe the techniques and the importance for use of each method in buccomaxillary prostheses with implants and the need of accomplishing more studies in this scarce literary area.

A finite element free convection model for the side wall heated cavity

This paper presents a finite element numerical solution of free convection in a cavity with side walls maintained at constant but different temperatures. The predictions from the model and the method of solution were validated by comparison with the 'bench mark' solution and Vahl Davis' results and good agreement was found. The present model was used to obtain additional results over a wide range of Rayleigh number (10(3)-10(6)) and L/H ratios varying from 0.1 to 1.0. The predicted stream function patterns, temperature and velocity profiles as well as the mean Nusselt number were presented and discussed. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Finite element analysis of warpage in laminated aluminium alloy plates for machining of primary aeronautic parts

The aim of this paper consists in presenting a method of simulating the warpage in 7xxx series aluminium alloy plates. To perform this simulation finite element software MSC.Patran and MSC.Marc were used. Another result of this analysis will be the influence on material residual stresses induced on the raw material during the rolling process upon the warpage of primary aeronautic parts, fabricated through machining (milling) at Embraer. The method used to determinate the aluminium plate residual stress was Layer Removal Test. The numerical algorithm Modified Flavenot Method was used to convert layer removal and beam deflection in stress level. With such information about the level and profile of residual stresses become possible, during the step that anticipate the manufacturing to incorporate these values in the finite-element approach for modelling warpage parts. Based on that warpage parameter surely the products are manufactured with low relative vulnerability propitiating competitiveness and price. © 2007 American Institute of Physics.

Three-dimensional finite element analysis of stress distribution in retention screws of different crown-implant ratios

The retaining screw of the implant-supported dental prosthesis is the weakest point of the crown/implant system. Furthermore, crown height is another important factor that may increase the lever arm. Therefore, the aim of this study was to assess the stress distribution in implant prosthetic screws with different heights of the clinical crown of the prosthesis using the method of three-dimensional finite element analysis. Three models were created with implants (3.75 mm × 10 mm) and crowns (heights of 10, 12.5 and 15 mm). The results were visualised by means of von Mises stress maps that increased the crown heights. The screw structure exhibited higher levels of stresses in the oblique load. The oblique loading resulted in higher stress concentration when compared with the axial loading. It is concluded that the increase of the crown was damaging to the stress distribution on the screw, mainly in oblique loading. © 2013 Taylor & Francis.

Finite element evaluation of three methods of stable fixation of condyle base fractures

The surgical treatment of mandibular condyle fractures currently offers several possibilities for stable internal fixation. In this study, a finite element model evaluation was performed of three different methods for osteosynthesis of low subcondylar fractures: (1) two four-hole straight plates, (2) one seven-hole lambda plate, and (3) one four-hole trapezoidal plate. The finite element model evaluation considered a load applied to the first molar on the contralateral side to the fracture. Results showed that, although the three methods are capable of withstanding functional loading, the lambda plate displayed a more homogeneous stress distribution for both osteosynthesis material and bone and may be a better method when single-plate fixation is the option.

Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

Finite element models of coseismic deformation due to the 2009 L'Aquila (Italy) and 2008 Wenchuan(China) earthquakes

The topic of my Ph.D. thesis is the finite element modeling of coseismic deformation imaged by DInSAR and GPS data. I developed a method to calculate synthetic Green functions with finite element models (FEMs) and then use linear inversion methods to determine the slip distribution on the fault plane. The method is applied to the 2009 L’Aquila Earthquake (Italy) and to the 2008 Wenchuan earthquake (China). I focus on the influence of rheological features of the earth's crust by implementing seismic tomographic data and the influence of topography by implementing Digital Elevation Models (DEM) layers on the FEMs. Results for the L’Aquila earthquake highlight the non-negligible influence of the medium structure: homogeneous and heterogeneous models show discrepancies up to 20% in the fault slip distribution values. Furthermore, in the heterogeneous models a new area of slip appears above the hypocenter. Regarding the 2008 Wenchuan earthquake, the very steep topographic relief of Longmen Shan Range is implemented in my FE model. A large number of DEM layers corresponding to East China is used to achieve the complete coverage of the FE model. My objective was to explore the influence of the topography on the retrieved coseismic slip distribution. The inversion results reveals significant differences between the flat and topographic model. Thus, the flat models frequently adopted are inappropriate to represent the earth surface topographic features and especially in the case of the 2008 Wenchuan earthquake.

Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

Computer aided design and finite element modeling to predict bulk mechanical properties of bone scaffolds using triply periodic minimal surfaces (progettazione assistita al calcolatore ed analisi con il metodo degli elementi finiti per predire il comportamento meccanico di scaffolds ossei creati con l'uso di superfici minime periodiche in tre direzioni)

The aim of Tissue Engineering is to develop biological substitutes that will restore lost morphological and functional features of diseased or damaged portions of organs. Recently computer-aided technology has received considerable attention in the area of tissue engineering and the advance of additive manufacture (AM) techniques has significantly improved control over the pore network architecture of tissue engineering scaffolds. To regenerate tissues more efficiently, an ideal scaffold should have appropriate porosity and pore structure. More sophisticated porous configurations with higher architectures of the pore network and scaffolding structures that mimic the intricate architecture and complexity of native organs and tissues are then required. This study adopts a macro-structural shape design approach to the production of open porous materials (Titanium foams), which utilizes spatial periodicity as a simple way to generate the models. From among various pore architectures which have been studied, this work simulated pore structure by triply-periodic minimal surfaces (TPMS) for the construction of tissue engineering scaffolds. TPMS are shown to be a versatile source of biomorphic scaffold design. A set of tissue scaffolds using the TPMS-based unit cell libraries was designed. TPMS-based Titanium foams were meant to be printed three dimensional with the relative predicted geometry, microstructure and consequently mechanical properties. Trough a finite element analysis (FEA) the mechanical properties of the designed scaffolds were determined in compression and analyzed in terms of their porosity and assemblies of unit cells. The purpose of this work was to investigate the mechanical performance of TPMS models trying to understand the best compromise between mechanical and geometrical requirements of the scaffolds. The intention was to predict the structural modulus in open porous materials via structural design of interconnected three-dimensional lattices, hence optimising geometrical properties. With the aid of FEA results, it is expected that the effective mechanical properties for the TPMS-based scaffold units can be used to design optimized scaffolds for tissue engineering applications. Regardless of the influence of fabrication method, it is desirable to calculate scaffold properties so that the effect of these properties on tissue regeneration may be better understood.

Safety of Active Implantable Devices during MRI Examinations: A Finite Element Analysis of an Implantable Pump

The goal of this study was to propose a general numerical analysis methodology to evaluate the magnetic resonance imaging (MRI)-safety of active implants. Numerical models based on the finite element (FE) technique were used to estimate if the normal operation of an active device was altered during MRI imaging. An active implanted pump was chosen to illustrate the method. A set of controlled experiments were proposed and performed to validate the numerical model. The calculated induced voltages in the important electronic components of the device showed dependence with the MRI field strength. For the MRI radiofrequency fields, significant induced voltages of up to 20 V were calculated for a 0.3T field-strength MRI. For the 1.5 and 3.0T MRIs, the calculated voltages were insignificant. On the other hand, induced voltages up to 11 V were calculated in the critical electronic components for the 3.0T MRI due to the gradient fields. Values obtained in this work reflect to the worst case situation which is virtually impossible to achieve in normal scanning situations. Since the calculated voltages may be removed by appropriate protection circuits, no critical problems affecting the normal operation of the pump were identified. This study showed that the proposed methodology helps the identification of the possible incompatibilities between active implants and MR imaging, and can be used to aid the design of critical electronic systems to ensure MRI-safety

A patient-specific finite element methodology to predict damage accumulation in vertebral bodies under axial compression, sagittal flexion and combined loads

Due to the inherent limitations of DXA, assessment of the biomechanical properties of vertebral bodies relies increasingly on CT-based finite element (FE) models, but these often use simplistic material behaviour and/or single loading cases. In this study, we applied a novel constitutive law for bone elasticity, plasticity and damage to FE models created from coarsened pQCT images of human vertebrae, and compared vertebral stiffness, strength and damage accumulation for axial compression, anterior flexion and a combination of these two cases. FE axial stiffness and strength correlated with experiments and were linearly related to flexion properties. In all loading modes, damage localised preferentially in the trabecular compartment. Damage for the combined loading was higher than cumulated damage produced by individual compression and flexion. In conclusion, this FE method predicts stiffness and strength of vertebral bodies from CT images with clinical resolution and provides insight into damage accumulation in various loading modes.