A high frequency $hp$ boundary element method for scattering by convex polygons

In this paper we propose and analyze a hybrid $hp$ boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods.

A finite element-spherical harmonics model for radiative transfer in inhomogeneous clouds. Part II. some applications

EVENT has been used to examine the effects of 3D cloud structure, distribution, and inhomogeneity on the scattering of visible solar radiation and the resulting 3D radiation field. Large eddy simulation and aircraft measurements are used to create realistic cloud fields which are continuous or broken with smooth or uneven tops. The values, patterns and variance in the resulting downwelling and upwelling radiation from incident visible solar radiation at different angles are then examined and compared to measurements. The results from EVENT confirm that 3D cloud structure is important in determining the visible radiation field, and that these results are strongly influenced by the solar zenith angle. The results match those from other models using visible solar radiation, and are supported by aircraft measurements of visible radiation, providing confidence in the new model.

A high frequency boundary element method for scattering by a class of nonconvex obstacles

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom N increases, and that to achieve any desired accuracy it is sufficient to increase N in proportion to the square of the logarithm of the frequency as the frequency increases (standard BEMs require N to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary ‘breakwater’ problem of propagation through an aperture in an infinite sound-hard screen.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

Estudo do efeito de substratos metamateriais em parâmetros de antenas de microfita

Microstrip antennas are subject matter in several research fields due to its numerous advantages. The discovery, at 1999, of a new class of materials called metamaterials - usually composed of metallic elements immersed in a dielectric medium, have attracted the attention of the scientific community, due to its electromagnetic properties, especially the ability to use in planar structures, such as microstrip, without interfering with their traditional geometry. The aim of this paper is to analyze the effects of one and bidimensional metamaterial substrates in microstrip antennas, with different configurations of resonance rings, SRR, in the dielectric layer. Fractal geometry is applied to these rings, in seeking to verify a multiband behavior and to reduce the resonance frequency of the antennas. The results are then given by commercial software Ansoft HFSS, used for precise analysis of the electromagnetic behavior of antennas by Finite Element Method (FEM). To reach it, this essay will first perform a literature study on fractal geometry and its generative process. This paper also presents an analysis of microstrip antennas, with emphasis on addressing different types of substrates as part of its electric and magnetic anisotropic behavior. It s performed too an approach on metamaterials and their unique properties

Finite Element Modeling for Development and Optimization of a Bone Plate for Mandibular Fracture in Dogs

This study aimed to develop a plate to treat fractures of the mandibular body in dogs and to validate the project using finite elements and biomechanical essays. Mandible prototypes were produced with 10 oblique ventrorostral fractures (favorable) and 10 oblique ventrocaudal fractures (unfavorable). Three groups were established for each fracture type. Osteosynthesis with a pure titanium plate of double-arch geometry and blocked monocortical screws offree angulanon were used. The mechanical resistance of the prototype with unfavorable fracture was lower than that of the fcworable fracture. In both fractures, the deflection increased and the relative stiffness decreased proportionally to the diminishing screw number The finite element analysis validated this plate study, since the maximum tension concentration observed on the plate was lower than the resistance limit tension admitted by the titanium. In conclusion, the double-arch geometry plate fixed with blocked monocortical screws has sufficient resistance to stabilize oblique,fractures, without compromising mandibular dental or neurovascular structures. J Vet Dent 24 (7); 212 - 221, 2010

Stress Analysis in Platform-Switching Implants: A 3-Dimensional Finite Element Study

The aim of this study was to evaluate the influence of the platform-switching technique on stress distribution in implant, abutment, and pen-implant tissues, through a 3-dimensional finite element study. Three 3-dimensional mandibular models were fabricated using the Solid Works 2006 and InVesalius software. Each model was composed of a bone block with one implant 10 mm long and of different diameters (3.75 and 5.00 mm). The UCLA abutments also ranged in diameter from 5.00 mm to 4.1 mm. After obtaining the geometries, the models were transferred to the software FEMAP 10.0 for pre- and postprocessing of finite elements to generate the mesh, loading, and boundary conditions. A total load of 200 N was applied in axial (0 degrees), oblique (45 degrees), and lateral (90) directions. The models were solved by the software NeiNastran 9.0 and transferred to the software FEMAP 10.0 to obtain the results that were visualized through von Mises and maximum principal stress maps. Model A (implants with 3.75 mm/abutment with 4.1 mm) exhibited the highest area of stress concentration with all loadings (axial, oblique, and lateral) for the implant and the abutment. All models presented the stress areas at the abutment level and at the implant/abutment interface. Models B (implant with 5.0 mm/abutment with 5.0 mm) and C (implant with 5.0 mm/abutment with 4.1 mm) presented minor areas of stress concentration and similar distribution pattern. For the cortical bone, low stress concentration was observed in the pen-implant region for models B and C in comparison to model A. The trabecular bone exhibited low stress that was well distributed in models B and C. Model A presented the highest stress concentration. Model B exhibited better stress distribution. There was no significant difference between the large-diameter implants (models B and C).

Passivity Versus Unilateral Angular Misfit: Evaluation of Stress Distribution on Implant-Supported Single Crowns: Three-Dimensional Finite Element Analysis

The aim of this study was to evaluate the effect of unilateral angular misfit of 100 Km on stress distribution of implant-supported single crowns with ceramic veneering and gold framework by three-dimensional finite element analysis. Two three-dimensional models representing a maxillary section of premolar region were constructed: group 1 (control)-crown completely adapted to the implant and group 2-crown with unilateral angular misfit of 100 Km. A vertical force of 100 N was applied on 2 centric points of the crown. The von Mises stress was used as an analysis criterion. The stress values and distribution in the main maps (204.4 MPa for group 1 and 205.0 MPa for group 2) and in the other structures (aesthetic veneering, framework, retention screw, implant, and bone tissue) were similar for both groups. The highest stress values were observed between the first and second threads of the retention screw. Considering the bone tissue, the highest stress values were exhibited in the peri-implant cortical bone. The unilateral angular misfit of 100 Km did not influence the stress distribution on the implant-supported prosthesis under static loading.

Comparison of Single-Standing or Connected Implants on Stress Distribution in Bone of Mandibular Overdentures: A Two-Dimensional Finite Element Analysis

This study aimed to compare the influence of single-standing or connected implants on stress distribution in bone of mandibular overdentures by means of two-dimensional finite element analysis. Two finite element models were designed using software (ANSYS) for 2 situations: bar-clip (BC) group-model of an edentulous mandible supporting an overdenture over 2 connected implants with BC system, and o'ring (OR) group-model of an edentulous mandible supporting an overdenture over 2 single-standing implants with OR abutments. Axial loads (100 N) were applied on either central (L1) or lateral (L2) regions of the models. Stress distribution was concentrated mostly in the cortical bone surrounding the implants. When comparing the groups, BC (L1, 52.0 MPa and L2, 74.2 MPa) showed lower first principal stress values on supporting tissue than OR (L1, 78.4 MPa and L2, 76.7 MPa). Connected implants with BC attachment were more favorable on stress distribution over peri-implant-supporting tissue for both loading conditions.

Effect of Passive Fit Absence in the Prosthesis/Implant/Retaining Screw System: A Two-Dimensional Finite Element Analysis

The misfit between prostheses and implants is a clinical reality, but the level that can be accepted without causing mechanical or biologic problem is not well defined. This study investigates the effect of different levels of unilateral angular misfit prostheses in the prosthesis/implant/retaining screw system and in the surrounding bone using finite element analysis. Four models of a two-dimensional finite element were constructed: group I (control), prosthesis that fit the implant; groups 2 to 4, prostheses with unilateral angular misfit of 50, 100, and 200 mu m, respectively. A load of 133 N was applied with a 30-degree angulation and off-axis at 2 mm from the long axis of the implant at the opposite direction of misfit on the models. Taking into account the increase of the angular misfit, the stress maps showed a gradual increase of prosthesis stress and uniform stress in the implant and trabecular bone. Concerning the displacement, an inclination of the system due to loading and misfit was observed. The decrease of the unilateral contact between prosthesis and implant leads to the displacement of the entire system, and distribution and magnitude alterations of the stress also occurred.

Platform Switching: Biomechanical Evaluation Using Three-Dimensional Finite Element Analysis

Purpose: The objective of this study was to evaluate, using three-dimensional finite element analysis (3D FEA), the stress distribution in peri-implant bone tissue, implants, and prosthetic components of implant-supported single crowns with the use of the platform-switching concept. Materials and Methods: Three 3D finite element models were created to replicate an external-hexagonal implant system with peri-implant bone tissue in which three different implant-abutment configurations were represented. In the regular platform (RP) group, a regular 4.1-mm-diameter abutment (UCLA) was connected to regular 4.1-mm-diameter implant. The platform-switching (PS) group was simulated by the connection of a wide implant (5.0 mm diameter) to a regular 4.1-mm-diameter UCLA abutment. In the wide-platform (WP) group, a 5.0-mm-diameter UCLA abutment was connected to a 5.0-mm-diameter implant. An occlusal load of 100 N was applied either axially or obliquely on the models using ANSYS software. Results: Both the increase in implant diameter and the use of platform switching played roles in stress reduction. The PS group presented lower stress values than the RP and WP groups for bone and implant. In the peri-implant area, cortical bone exhibited a higher stress concentration than the trabecular bone in all models and both loading situations. Under oblique loading, higher intensity and greater distribution of stress were observed than under axial loading. Platform switching reduced von Mises (17.5% and 9.3% for axial and oblique loads, respectively), minimum (compressive) (19.4% for axial load and 21.9% for oblique load), and maximum (tensile) principal stress values (46.6% for axial load and 26.7% for oblique load) in the peri-implant bone tissue. Conclusion: Platform switching led to improved biomechanical stress distribution in peri-implant bone tissue. Oblique loads resulted in higher stress concentrations than axial loads for all models. Wide-diameter implants had a large influence in reducing stress values in the implant system. INT J ORAL MAXILLOFAC IMPLANTS 2011;26:482-491