A simple non-linear global-local finite element methodology for composite structures

A simple non-linear global-local finite element methodology is presented. A global coarse model, using 2-D shell elements, is solved non-linearly and the displacements and rotations around a region of interest are applied, as displacement boundary conditions, to a refined local 3-D model using Kirchhoff plate assumptions. The global elements' shape functions are used to interpolate between nodes. The local model is then solved non-linearly with an incremental scheme independent of that used for the global model.

Dose, dose-rate and field size effects on cell survival following exposure to non-uniform radiation fields

For the delivery of intensity-modulated radiation therapy (IMRT), highly modulated fields are used to achieve dose conformity across a target tumour volume. Recent in vitro evidence has demonstrated significant alterations in cell survival occurring out-of-field which cannot be accounted for on the basis of scattered dose. The radiobiological effect of area, dose and dose-rate on out-of-field cell survival responses following exposure to intensity-modulated radiation fields is presented in this study. Cell survival was determined by clonogenic assay in human prostate cancer (DU-145) and primary fibroblast (AG0-1522) cells following exposure to different modulated field configurations delivered using a X-Rad 225 kVp x-ray source. Uniform survival responses were compared to in- and out-of-field responses in which 25-99% of the cell population was shielded. Dose delivered to the out-of-field region was varied from 1.6-37.2% of that delivered to the in-field region using different levels of brass shielding. Dose rate effects were determined for 0.2-4 Gy min⁻¹ for uniform and modulated exposures with no effect seen in- or out-of-field. Survival responses showed little dependence on dose rate and area in- and out-of-field with a trend towards increased survival with decreased in-field area. Out-of-field survival responses were shown to scale in proportion to dose delivered to the in-field region and also local dose delivered out-of-field. Mathematical modelling of these findings has shown survival response to be highly dependent on dose delivered in- and out-of-field but not on area or dose rate. These data provide further insight into the radiobiological parameters impacting on cell survival following exposure to modulated irradiation fields highlighting the need for refinement of existing radiobiological models to incorporate non-targeted effects and modulated dose distributions.

Physical and numerical constraints in source modeling for finite difference simulation of room acoustics

In finite difference time domain simulation of room acoustics, source functions are subject to various constraints. These depend on the way sources are injected into the grid and on the chosen parameters of the numerical scheme being used. This paper addresses the issue of selecting and designing sources for finite difference simulation, by first reviewing associated aims and constraints, and evaluating existing source models against these criteria. The process of exciting a model is generalized by introducing a system of three cascaded filters, respectively, characterizing the driving pulse, the source mechanics, and the injection of the resulting source function into the grid. It is shown that hard, soft, and transparent sources can be seen as special cases within this unified approach. Starting from the mechanics of a small pulsating sphere, a parametric source model is formulated by specifying suitable filters. This physically constrained source model is numerically consistent, does not scatter incoming waves, and is free from zero- and low-frequency artifacts. Simulation results are employed for comparison with existing source formulations in terms of meeting the spectral and temporal requirements on the outward propagating wave.

Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

Non-uniform data distribution for communication-efficient parallel clustering

Global communicationrequirements andloadimbalanceof someparalleldataminingalgorithms arethe major obstacles to exploitthe computational power of large-scale systems. This work investigates how non-uniform data distributions can be exploited to remove the global communication requirement and to reduce the communication costin parallel data mining algorithms and, in particular, in the k-means algorithm for cluster analysis. In the straightforward parallel formulation of the k-means algorithm, data and computation loads are uniformly distributed over the processing nodes. This approach has excellent load balancing characteristics that may suggest it could scale up to large and extreme-scale parallel computing systems. However, at each iteration step the algorithm requires a global reduction operationwhichhinders thescalabilityoftheapproach.Thisworkstudiesadifferentparallelformulation of the algorithm where the requirement of global communication is removed, while maintaining the same deterministic nature ofthe centralised algorithm. The proposed approach exploits a non-uniform data distribution which can be either found in real-world distributed applications or can be induced by means ofmulti-dimensional binary searchtrees. The approachcanalso be extended to accommodate an approximation error which allows a further reduction ofthe communication costs. The effectiveness of the exact and approximate methods has been tested in a parallel computing system with 64 processors and in simulations with 1024 processing element

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.

Evolution of spherical non-uniform perturbations in the universe

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Embedded crack elements with non-uniform discontinuity modes

The consequences of the use of embedded crack finite elements with uniform discontinuity modes (opening and sliding) to simulate crack propagation in concrete are investigated. It is shown the circumstances in which the consideration of uniform discontinuity modes is not suitable to accurately model the kinematics induced by the crack and must be avoided. It is also proposed a technique to embed cracks with non-uniform discontinuity modes into standard displacement-based finite elements to overcome the shortcomings of the uniform discontinuity modes approach.

Assimilation of data from conventional and non conventional networks through a LETKF scheme in the COSMO model

The present work studies a km-scale data assimilation scheme based on a LETKF developed for the COSMO model. The aim is to evaluate the impact of the assimilation of two different types of data: temperature, humidity, pressure and wind data from conventional networks (SYNOP, TEMP, AIREP reports) and 3d reflectivity from radar volume. A 3-hourly continuous assimilation cycle has been implemented over an Italian domain, based on a 20 member ensemble, with boundary conditions provided from ECMWF ENS. Three different experiments have been run for evaluating the performance of the assimilation on one week in October 2014 during which Genova flood and Parma flood took place: a control run of the data assimilation cycle with assimilation of data from conventional networks only, a second run in which the SPPT scheme is activated into the COSMO model, a third run in which also reflectivity volumes from meteorological radar are assimilated. Objective evaluation of the experiments has been carried out both on case studies and on the entire week: check of the analysis increments, computing the Desroziers statistics for SYNOP, TEMP, AIREP and RADAR, over the Italian domain, verification of the analyses against data not assimilated (temperature at the lowest model level objectively verified against SYNOP data), and objective verification of the deterministic forecasts initialised with the KENDA analyses for each of the three experiments.

Gravitational actions upon a tether in a non-uniform gravity field with arbitrary number of zonal harmonics

We develop general closed-form expressions for the mutual gravitational potential, resultant and torque acting upon a rigid tethered system moving in a non-uniform gravity field produced by an attracting body with revolution symmetry, such that an arbitrary number of zonal harmonics is considered. The final expressions are series expansion in two small parameters related to the reference radius of the primary and the length of the tether, respectively, each of which are scaled by the mutual distance between their centers of mass. A few numerical experiments are performed to study the convergence behavior of the final expressions, and conclude that for high precision applications it might be necessary to take into account additional perturbation terms, which come from the mutual Two-Body interaction.

Difference schemes for time-dependent heat conduction models with delay

Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

An object-oriented designed finite-difference time-domain simulator for electromagnetic analysis and design in MRI - application to high field analyses

This paper presents a finite-difference time-domain (FDTD) simulator for electromagnetic analysis and design applications in MRI. It is intended to be a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The pro-ram has been constructed in an object-oriented framework. The design procedure is detailed and the numerical solver has been verified against analytical solutions for simple cases and also applied to various field calculation problems. In particular, the simulator is demonstrated for inverse RF coil design, optimized source profile generation, and parallel imaging in high-frequency situations. The examples show new developments enabled by the simulator and demonstrate that the proposed FDTD framework can be used to analyze large-scale computational electromagnetic problems in modern MRI engineering. (C) 2004 Elsevier Inc. All rights reserved.

Numerical evaluation of the fields induced by body motion in or near high-field MRI scanners

In modern magnetic resonance imaging, both patients and health care workers are exposed to strong. non-uniform static magnetic fields inside and outside of the scanner. In which body movement may be able to induce electric currents in tissues which could be potentially harmful. This paper presents theoretical investigations into the spatial distribution of induced E-fields in a tissue-equivalent human model when moving at various positions around the magnet. The numerical calculations are based on an efficient. quasi-static, finite-difference scheme. Three-dimensional field profiles from an actively shielded 4 T magnet system are used and the body model projected through the field profile with normalized velocity. The simulation shows that it is possible to induce E-fields/currents near the level of physiological significance under some circumstances and provides insight into the spatial characteristics of the induced fields. The methodology presented herein can be extrapolated to very high field strengths for the evaluation of the effects of motion at a variety of field strengths and velocities. (C) 2004 Elsevier Ltd. All rights reserved.