A general technique to embed non-uniform discontinuities into standard solid finite elements

A general technique to embed non-uniform displacement discontinuities into standard solid finite elements is presented. The technique is based on the decomposition of the kinematic fields into a component related to the deformation of the solid portion of the element and one related to the rigid-body motion due to a displacement discontinuity. This decomposition simplifies the incorporation of discontinuity interfaces and provides a suitable framework to account for non-uniform discontinuity modes. The present publication addresses two families of finite element formulations: displacement-based and stress hybrid finite element. © 2005 Elsevier Ltd. All rights reserved.

A two-dimensional finite element model of front surface current flow in cells under non-uniform, concentrated illumination

A two-dimensional finite element model of current flow in the front surface of a PV cell is presented. In order to validate this model we perform an experimental test. Later, particular attention is paid to the effects of non-uniform illumination in the finger direction which is typical in a linear concentrator system. Fill factor, open circuit voltage and efficiency are shown to decrease with increasing degree of non-uniform illumination. It is shown that these detrimental effects can be mitigated significantly by reoptimization of the number of front surface metallization fingers to suit the degree of non-uniformity. The behavior of current flow in the front surface of a cell operating at open circuit voltage under non-uniform illumination is discussed in detail.

Neurite, a finite difference large scale parallel program for the simulation of the electrical signal propagation in neurites under mechanical loading

With the growing body of research on traumatic brain injury and spinal cord injury, computational neuroscience has recently focused its modeling efforts on neuronal functional deficits following mechanical loading. However, in most of these efforts, cell damage is generally only characterized by purely mechanistic criteria, function of quantities such as stress, strain or their corresponding rates. The modeling of functional deficits in neurites as a consequence of macroscopic mechanical insults has been rarely explored. In particular, a quantitative mechanically based model of electrophysiological impairment in neuronal cells has only very recently been proposed (Jerusalem et al., 2013). In this paper, we present the implementation details of Neurite: the finite difference parallel program used in this reference. Following the application of a macroscopic strain at a given strain rate produced by a mechanical insult, Neurite is able to simulate the resulting neuronal electrical signal propagation, and thus the corresponding functional deficits. The simulation of the coupled mechanical and electrophysiological behaviors requires computational expensive calculations that increase in complexity as the network of the simulated cells grows. The solvers implemented in Neurite-explicit and implicit-were therefore parallelized using graphics processing units in order to reduce the burden of the simulation costs of large scale scenarios. Cable Theory and Hodgkin-Huxley models were implemented to account for the electrophysiological passive and active regions of a neurite, respectively, whereas a coupled mechanical model accounting for the neurite mechanical behavior within its surrounding medium was adopted as a link between lectrophysiology and mechanics (Jerusalem et al., 2013). This paper provides the details of the parallel implementation of Neurite, along with three different application examples: a long myelinated axon, a segmented dendritic tree, and a damaged axon. The capabilities of the program to deal with large scale scenarios, segmented neuronal structures, and functional deficits under mechanical loading are specifically highlighted.

A compact difference scheme for numerical solutions of second order dual-phase-lagging models of microscale heat transfer

Dual-phase-lagging (DPL) models constitute a family of non-Fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient. These lags may need to be considered when modeling microscale heat transfer, and thus DPL models have found application in the last years in a wide range of theoretical and technical heat transfer problems. Consequently, analytical solutions and methods for computing numerical approximations have been proposed for particular DPL models in different settings. In this work, a compact difference scheme for second order DPL models is developed, providing higher order precision than a previously proposed method. The scheme is shown to be unconditionally stable and convergent, and its accuracy is illustrated with numerical examples.

Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

2000 Mathematics Subject Classification: 65M06, 65M12.

Numerical investigation of the three-dimensional secondary instabilities in the time-developing compressible mixing layer

Mixing layers are present in very different types of physical situations such as atmospheric flows, aerodynamics and combustion. It is, therefore, a well researched subject, but there are aspects that require further studies. Here the instability of two-and three-dimensional perturbations in the compressible mixing layer was investigated by numerical simulations. In the numerical code, the derivatives were discretized using high-order compact finite-difference schemes. A stretching in the normal direction was implemented with both the objective of reducing the sound waves generated by the shear region and improving the resolution near the center. The compact schemes were modified to work with non-uniform grids. Numerical tests started with an analysis of the growth rate in the linear regime to verify the code implementation. Tests were also performed in the non-linear regime and it was possible to reproduce the vortex roll-up and pairing, both in two-and three-dimensional situations. Amplification rate analysis was also performed for the secondary instability of this flow. It was found that, for essentially incompressible flow, maximum growth rates occurred for a spanwise wavelength of approximately 2/3 of the streamwise spacing of the vortices. The result demonstrated the applicability of the theory developed by Pierrehumbet and Widnall. Compressibility effects were then considered and the maximum growth rates obtained for relatively high Mach numbers (typically under 0.8) were also presented.

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.

Fly Ash Soil Stabilization for Non-Uniform Subgrade Soils, Volume II: Influence of Subgrade Non-Uniformity on PCC Pavement Performance, TR-461, 2005

To provide insight into subgrade non-uniformity and its effects on pavement performance, this study investigated the influence of non-uniform subgrade support on pavement responses (stress and deflection) that affect pavement performance. Several reconstructed PCC pavement projects in Iowa were studied to document and evaluate the influence of subgrade/subbase non-uniformity on pavement performance. In situ field tests were performed at 12 sites to determine the subgrade/subbase engineering properties and develop a database of engineering parameter values for statistical and numerical analysis. Results of stiffness, moisture and density, strength, and soil classification were used to determine the spatial variability of a given property. Natural subgrade soils, fly ash-stabilized subgrade, reclaimed hydrated fly ash subbase, and granular subbase were studied. The influence of the spatial variability of subgrade/subbase on pavement performance was then evaluated by modeling the elastic properties of the pavement and subgrade using the ISLAB2000 finite element analysis program. A major conclusion from this study is that non-uniform subgrade/subbase stiffness increases localized deflections and causes principal stress concentrations in the pavement, which can lead to fatigue cracking and other types of pavement distresses. Field data show that hydrated fly ash, self-cementing fly ash-stabilized subgrade, and granular subbases exhibit lower variability than natural subgrade soils. Pavement life should be increased through the use of more uniform subgrade support. Subgrade/subbase construction in the future should consider uniformity as a key to long-term pavement performance.

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.