Numerical Solution of Singularly Perturbed Boundary Value Problems Based on Optimal Control Strategy

Abstract  In this paper, we develop a numerical technique for singularly perturbed boundary value problems using B-spline functions
and least square method. The approximate solution derived in this article is convergent to the exact solution and can be applied
both to linear and nonlinear models. The numerical examples and computational results illustrate and guarantee a higher accuracy
for this technique.

• Content Type Journal Article
• DOI 10.1007/s10440-009-9553-y
• Authors
  
  
  • G. B. Loghmani, University of Yazd Department of Mathematics Yazd Iran
  • M. Ahmadinia, University of Qom Department of Mathematics Qom Iran
  
  

• Journal Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications
• Online ISSN 1572-9036
• Print ISSN 0167-8019

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Original source : http://www.springerlink.com/content/r53431354628m5...

A nonstandard mixed finite element family

Abstract  We show that standard mixed finite element methods, of second or higher degree, for second order elliptic equations can be
modified by imposing additional continuity conditions for the flux, which reduces the dimension of the space. This reduced
space still gives a stable method with an optimal order of convergence. We recall our postprocessing method and the a posteriori
error estimator based on this.

• Content Type Journal Article
• DOI 10.1007/s00211-009-0272-0
• Authors
  
  
  • Rolf Stenberg, Helsinki University of Technology–TKK Institute of Mathematics and Systems Analysis P. O. Box 1100 02015 TKK Helsinki Finland
  
  

• Journal Numerische Mathematik
• Online ISSN 0945-3245
• Print ISSN 0029-599X

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Original source : http://www.springerlink.com/content/b466866m423196...

Numerical simulation of the modified regularized long wave equation by He's variational iteration method

The modified regularized long wave (MRLW) equation, with some initial conditions, is solved numerically by variational iteration method. This method is useful for obtaining numerical solutions with high degree of accuracy. The variational iteration solution for the MRLW equation converges to its exact solution. Moreover, the conservation laws properties of the MRLW equation are also studied. Finally, interaction of two and three solitary waves is shown. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Published by

Original source : http://dx.doi.org/10.1002%2Fnum.20537...

Discrete Fourier analysis with lattices on planar domains. (arXiv:0910.5286v1 [math.NA])

A discrete Fourier analysis associated with translation lattices is developed
recently by the authors. It permits two lattices, one determining the integral
domain and the other determining the family of exponential functions. Possible
choices of lattices are discussed in the case of lattices that tile $RR^2$ and
several new results on cubature and interpolation by trigonometric, as well as
algebraic, polynomials are obtained.

Published by

Original source : http://arxiv.org/abs/0910.5286...

Olgierd C. Zienkiewicz, 1921-2009

No Abstract

Published by

Original source : http://dx.doi.org/10.1002%2Ffld.2203...

Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes

We obtain fully computable constant free a posteriori error bounds on the broken energy seminorm and the discontinuous Galerkin (DG) norm of the error for nonuniform polynomial order symmetric interior penalty Galerkin, nonsymmetric interior penalty Galerkin and incomplete interior penalty Galerkin finite-element approximations of a linear second-order elliptic problem on meshes containing hanging nodes and comprised of triangular elements. The estimators are completely free of unknown constants and provide guaranteed numerical bounds on the broken energy seminorm and the DG norm of the error. These estimators are also shown to provide a lower bound for the broken energy seminorm and the DG norm of the error up to a constant and higher-order data oscillation terms.

Published by

Original source : http://imajna.oxfordjournals.org/cgi/content/short...

Theorem of Expended Power and Finite Element Formulation: Hamiltonian Mechanics Framework

AIAA Journal Nov. 2009, Vol. 47: 2757-2769.

Published by

Original source : http://doi.aiaa.org/10.2514/1.40584...

Numerical Investigation of Constrained Direct Solutions Using Hamilton's Law

AIAA Journal Nov. 2009, Vol. 47: 2747-2756.

Published by

Original source : http://doi.aiaa.org/10.2514/1.45673...

Assessment of Computational Fluid Dynamics for Supersonic Shock Containing Jets

AIAA Journal Nov. 2009, Vol. 47: 2738-2746.

Published by

Original source : http://doi.aiaa.org/10.2514/1.44336...

Numerical Investigation of Decomposed Magnetofluid Dynamics Equations

AIAA Journal Nov. 2009, Vol. 47: 2666-2675.

Published by

Original source : http://doi.aiaa.org/10.2514/1.42626...

Interface Conditions of Finite Difference Compact Schemes for Computational Aeroacoustics

AIAA Journal Nov. 2009, Vol. 47: 2658-2665.

Published by

Original source : http://doi.aiaa.org/10.2514/1.42110...

A multiscale finite element formulation for axisymmetric elastoplasticity with volumetric locking

Similar to plane strain, axisymmetric stress problem is also highly kinematics constrained. Standard displacement-based finite element exhibits volumetric locking issue in simulating nearly/fully incompressible material or isochoric plasticity under axisymmetric loading conditions, which severely underestimates the deformation and overestimates the bearing capacity for structural/geotechnical engineering problems. The aim of this paper is to apply variational multiscale method to produce a stabilized mixed displacement-pressure formulation, which can effectively alleviate the volumetric locking issue for axisymmetric stress problem. Both nearly incompressible elasticity and isochoric J2 elastoplasticity are investigated. First-order 3-node triangular and 4-node quadrilateral elements are tested for locking issues. Severalrepresentative simulations are provided to demonstrate the performance of the linear elements, which include the convergence study and comparison with closed-form solutions. A comparative study with pressure Laplacian stabilized formulation is also presented. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnag.853...

Computational aspects in 2D SBEM analysis with domain inelastic actions

The Symmetric Boundary Element Method, applied to structures subjected to temperature and inelastic actions, shows singular domain integrals.In the present paper the strong singularity involved in the domain integrals of the stresses and tractions is removed, and by means of a limiting operation, this traction is evaluated on the boundary. First the weakly singular domain integral in the Somigliana Identity (S.I.) of the displacements is regularized and the singular integral is transformed into a boundary one using the Radial Integration Method; subsequently, using the differential operator applied to the displacement field, the S.I. of the tractions inside the body is obtained and through a limit operation its expression is evaluated on the boundary. The latter operation makes it possible to substitute the strongly singular domain integral in a strongly singular boundary one, defined as a Cauchy Principal Value, with which the related free term is associated. The expressions thus obtained for the displacements and the tractions, in which domain integrals are substituted by boundary integrals, were utilized in the Galerkin approach, for the evaluation in closed form of the load coefficients connected to domain inelastic actions.This strategy makes it possible to evaluate the load coefficients avoiding considerable difficulties due to the geometry of the solid analyzed; the obtained coefficients were implemented in the Karnak.sGbem calculus code. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnme.2765...

Registration for Natural Algorithms Workshop

Please fill this form to register to the Natural Algorithms workshop on November 2-3, 2009.

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5. Please email the organizers at natalg09 {at} gmail(.)com with any questions or comments. Submitting the form may take a couple of minutes. You will get a confirmation by email. Please allow a couple of minutes for the form submission to go through.

 

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Original source : http://intractability.princeton.edu/blog/2009/09/r...

The List-Chromatic Number of Infinite Graphs Defined on Euclidean Spaces

Abstract  If D is a countable set of positive reals, 2≤n<ω, let X

_n
(D) be the graph with the points of R

ⁿ
as vertices where two vertices are joined iff their distance is in D. We determine the list-chromatic number of X

_n
(D) as much as possible.

• Content Type Journal Article
• DOI 10.1007/s00454-009-9228-5
• Authors
  
  
  • Péter Komjáth, Eötvös University Department of Computer Science P.O. Box 120 Budapest 1518 Hungary
  
  

• Journal Discrete and Computational Geometry
• Online ISSN 1432-0444
• Print ISSN 0179-5376

Published by

Original source : http://www.springerlink.com/content/f44822267r2087...

On the approximation and efficient evaluation of integral terms in PDE models of cell adhesion

Recently, a nonlocal term has been introduced in time-dependent partial differential equation (PDE) models of cell migration in tissue. This term is used to model adhesive effects between cells and also between cells and the extracellular matrix. We assume periodic boundary conditions for the model and that the PDE system is discretized following the method of lines and using a finite-volume scheme on a uniform grid in space. For high-resolution simulations of the PDE system an efficient evaluation of the approximation of the nonlocal term is crucial. For one and two spatial dimensions we develop suitable approximations of the nonlocal term and evaluate these using fast Fourier transform (FFT) techniques. Comprehensive numerical tests show the accuracy and efficiency of our approach. We also demonstrate the impact of the proposed scheme for the treatment of the nonlocal term on simulation times for a differential cell adhesion model. We discuss extensions and applicability of our work to systems with nonperiodic boundary conditions and for other nonlocal PDE models from mathematical biology.

Published by

Original source : http://imajna.oxfordjournals.org/cgi/content/short...

Numerical Modeling of Pressure-Driven Nitrogen Slip Flow in Long Rectangular Microchannels

Published by

Original source : http://www.informaworld.com/smpp/content~content=a...

HSL_MI20: An efficient AMG preconditioner for finite element problems in 3D

Algebraic multigrid (AMG) is one of the most effective iterative methods for the solution of large, sparse linear systems obtained from the discretization of second-order scalar elliptic self-adjoint partial differential equations. It can also be used as a preconditioner for Krylov subspace methods. In this communication, we report on the design and development of a robust, effective and portable Fortran 95 implementation of the classical Ruge-Stüben AMG, which is available as package HSL_MI20 within the HSL mathematical software library. The routine can be used as a 'black-box' preconditioner, but it also offers the user a range of options and parameters. Proper tuning of these parameters for a particular application can significantly enhance the performance of an AMG-preconditioned Krylov solver. This is illustrated using a number of examples arising in the unstructured finite element discretization of the diffusion, the convection-diffusion, and the Stokes equations, as well as transient thermal convection problems associated with the Boussinesq approximation of the Navier-Stokes equations in 3D. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnme.2758...

Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms

This paper investigates the extended finite element method (XFEM)-GA detection algorithm proposed by Rabinovich et al. (Int. J. Numer. Meth. Engng 2007; 71(9):1051-1080; Int. J. Numer. Meth. Engng 2009; 77(3):337-359) on elastostatic problems with different types of flaws. This algorithm is designed for non-destructive assessment of structural components. Trial flaws are modeled using the XFEM as the forward problem and genetic algorithms (GAs) are employed as the optimization method to converge to the true flaw location and size. The main advantage of the approach is that XFEM alleviates the need for re-meshing the domain at every new iteration of the inverse solution process and GAs have proven to be robust and efficient optimization techniques in particular for this type of problems.In this paper the XFEM-GA methodology is applied to elastostatic problems where flaws are considered as straight cracks, circular holes and non-regular-shaped holes. Measurements are obtained from strain sensors that are attached to the surface of the structure at specific locations and provide the target solution to the GA. The results show convergence robustness and accuracy provided that a sufficient number of sensors are employed and sufficiently large flaws are considered. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnme.2766...

http://www.chinahush.com/2009/10/21/amazing-pictures-pollution-in-china/

A new H(div)-conforming p-interpolation operator in two dimensions. (arXiv:0910.3891v1 [math.NA])

In this paper we construct a new H(div)-conforming projection-based
p-interpolation operator that assumes only $H^r(K) cap ilde
H^{-1/2}(div,K)$-regularity (r > 0) on the reference element K (either triangle
or square). We show that this operator is stable with respect to polynomial
degrees and satisfies the commuting diagram property. We also establish an
estimate for the interpolation error in the norm of the space $ ilde
H^{-1/2}(div,K)$, which is closely related to the energy spaces for boundary
integral formulations of time-harmonic problems of electromagnetics in three
dimensions.

Published by

Original source : http://arxiv.org/abs/0910.3891...

Numerical local analysis of relevant internal variables for constitutive modelling of granular materials

DEM simulations on spherical materials have been performed to study the behaviour of model granular materials not only under monotonous stress path such as triaxial compression or extension, but also under two-way cycling loading paths. Three reference states have been considered to characterize the behaviour of the granular material: the characteristic state, transitory state between volumetric contraction and dilation, the state of maximum resistance and the critical state. These states are regarded with respect to void ratio and anisotropy of fabric which are the two internal variables retained for the description of the internal state of the material. The characteristic state and the state at maximum resistance are clearly dependent on both levels of density and anisotropy at the beginning of a loading path. Bilinear models involving the two internal variables were designed for the characteristic state, the maximum dilatancy and the extent of the dilatancy domain for axisymetric loadings. They show that in each case the effect of density and anisotropy are different in compression and extension. The influence of anisotropy and density seems to be of the same order of magnitude. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnag.845...

Global and local central non-upwind finite volume schemes for hyperbolic conservation laws in porous media

The focus of this paper is on the development of convective flow approximation schemes that offer the benefits of an upwind formalism without actually upwinding. Development of robust schemes that remove or reduce upwind dependence would represent a significant step forward leading to a fundamental simplification of current methods for flow in porous media and reservoir simulation. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Ffld.2178...

Hunting for rhythm's DNA: Computational geometry unlocks a musical phylogeny

(PhysOrg.com) -- Does Bo Diddley rule the world? Though he died last year, the iconic singer and guitarist of American blues and rock still rules the rhythms of the world, says computer scientist Godfried Toussaint. Toussaint uses complex algorithms to ferret where the rhythms of world music came from - in the same way an evolutionary biologist might hunt for the origins of, say, an arthropod body part.

Published by

Original source : http://www.physorg.com/news175248181.html...

Interpolation and Iteration for Nonlinear Filters. (arXiv:0910.3241v1 [math.NA])

We present a general form of the iteration and interpolation process used in
implicit particle filters. Implicit filters are based on a pseudo-Gaussian
representation of posterior densities, and are designed to focus the particle
paths so as to reduce the number of particles needed in nonlinear data
assimilation. Examples are given.

Published by

Original source : http://arxiv.org/abs/0910.3241...

Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods). (arXiv:0910.3621v1 [math.NA])

Recently, a new family of integrators (Hamiltonian Boundary ValueMethods) has
been introduced, which is able to precisely conserve the energy function of
polynomial Hamiltonian systems and to provide a practical conservation of the
energy in the non-polynomial case. We settle the definition and the theory of
such methods in a more general framework. Our aim is on the one hand to give
account of their good behavior when applied to general Hamiltonian systems and,
on the other hand, to find out what are the optimal formulae, in relation to
the distribution of the nodes. Such analysis is based upon the notion of
extended collocation conditions and the definition of discrete line integral,
and is carried out by looking at the limit of such family of methods as the
number of the so called silent stages tends to infinity.

Published by

Original source : http://arxiv.org/abs/0910.3621...

Inversion of the Laplace transform from the real axis using an adaptive iterative method. (arXiv:0910.3385v1 [math.NA])

In this paper a new method for inverting the Laplace transform from the real
axis is formulated. This method is based on a quadrature formula. We assume
that the unknown function $f(t)$ is continuous with (known) compact support. An
adaptive iterative method and an adaptive stopping rule, which yield the
convergence of the approximate solution to $f(t)$, are proposed in this paper.

Published by

Original source : http://arxiv.org/abs/0910.3385...

U2 concert to be streamed live on YouTube

Irish rock megastars U2 announced Monday that their upcoming concert at the Pasadena Rose Bowl in California will be streamed live on YouTube.

Published by

Original source : http://www.physorg.com/news175204255.html...

Justification of Asymptotic Two-dimensional Model for Steady Navier-Stokes Equations for Incompressible Flow

Abstract  We study the asymptotic behavior of solutions to steady Navier-Stokes equations for incompressible flow in thin three-dimensional
deformed cylinders. We prove that a sequence of the solutions converges strongly to a solution of a corresponding two-dimensional
asymptotic model if the thickness of the cylinders converges to zero.

• Content Type Journal Article
• DOI 10.1007/s10440-009-9551-0
• Authors
  
  
  • Rostislav Vodák, Palacky University Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science tř. 17. listopadu 1192/12 771 46 Olomouc Czech Republic
  
  

• Journal Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications
• Online ISSN 1572-9036
• Print ISSN 0167-8019

Published by

Original source : http://www.springerlink.com/content/rp0332107mhh24...

Pseudospectral time-domain method for pressure-release rough surface scattering using a surface transformation and image method

Abstract  When numerically analyzing acoustic scattering at a pressure-release rough surface, the conventional pseudospectral time domain
(PSTD) method using Fourier transform requires rigorous stability conditions in order to solve the spatial derivative in the
wave equation on the irregular boundaries between the two media due to the Gibbs phenomenon and short wavelength in air. To
eliminate such disadvantages, a new algorithm is proposed based on the Fourier PSTD method utilizing a surface boundary transformation
and an image method. Irregular surface boundaries are flattened by transformation and then an image method is applied to the
half-space domain. The efficiency and accuracy of the proposed PSTD method are better than the conventional Fourier PSTD method.
Numerical results are presented for a sloped and a sinusoidal pressure-release surface.

• Content Type Journal Article
• Category Original Paper
• DOI 10.1007/s11075-009-9343-7
• Authors
  
  
  • Yonghoon Ha, Seoul National University Department of Naval Architecture and Ocean Engineering Seoul 151–744 South Korea
  • Keunwha Lee, Seoul National University Department of Naval Architecture and Ocean Engineering Seoul 151–744 South Korea
  • Woojae Seong, Seoul National University Department of Naval Architecture and Ocean Engineering Seoul 151–744 South Korea
  
  

• Journal Numerical Algorithms
• Online ISSN 1572-9265
• Print ISSN 1017-1398

Published by

Original source : http://www.springerlink.com/content/818q5574181723...

Hybrid Numerical Solution of the Chemical Master Equation

We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the construction of a stochastic hybrid model in which certain discrete random variables of the original Markov chain are approximated by continuous deterministic variables. We compute the solution of the stochastic hybrid model using a numerical algorithm that discretizes time and in each step performs a mutual update of the transient probability distribution of the discrete stochastic variables and the values of the continuous deterministic variables. We implemented the algorithm and demonstrate its usefulness and efficiency on several case studies from systems biology.

Published by

Original source : http://infoscience.epfl.ch/record/141971...

Variational iteration method for solving three-dimensional Navier-Stokes equations of flow between two stretchable disks

The similarity transform for the steady three-dimensional Navier-Stokes equations of flow between two stretchable disks gives a system of nonlinear ordinary differential equations. In this article, the variational iteration method was used for solving these equations. The results have been compared with the numerical results. This article depicts that the VIM is an efficient and powerful method for solving nonlinear differential equations. This method is applicable to strongly and weakly nonlinear problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Published by

Original source : http://dx.doi.org/10.1002%2Fnum.20522...

An improved compact finite difference scheme for solving an N-carrier system with Neumann boundary conditions

Recently, we have developed a higher-order and unconditionally stable compact finite difference scheme for solving a model of energy exchanges in an N-carrier system with Neumann boundary conditions, which extends the concept of the well-known parabolic two-step model for microheat transfer. However, the combined compact finite difference scheme for the boundary is second-order accurate. Unfortunately, our statement in (Dai and Tzou, Numer Methods Partial Differential Equation, Zhao et al., Numer Methods Partial Differential Equations 23 (2007), 949-959.), that it is a fourth-order scheme is inaccurate, because the scheme was multiplied by [Delta]x2 in the derivation. In this article, we develop a new combined compact finite difference scheme for the boundary, which is third-order accurate. Using the exact same proof for stability analysis as in (Dai and Tzou, Numer Methods Partial Differential Equations), the new scheme is unconditionally stable with respect to the initial conditions and source terms. The improved compact scheme is then tested by a numerical example. Results show that the convergence rate with respect to the spatial variable from the new scheme is higher and the solution is much more accurate, when compared with those obtained using our previous compact scheme in (Dai and Tzou, Numer Methods Partial Differential Equations). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Published by

Original source : http://dx.doi.org/10.1002%2Fnum.20531...

An optimization-based domain decomposition method for numerical simulation of the incompressible Navier-Stokes flows

This article is concerned about an optimization-based domain decomposition method for numerical simulation of the incompressible Navier-Stokes flows. Using the method, an classical domain decomposition problem is transformed into a constrained minimization problem for which the objective functional is chosen to measure the jump in the dependent variables across the common interfaces between subdomains. The Lagrange multiplier rule is used to transform the constrained optimization problem into an unconstrained one and that rule is applied to derive an optimality system from which optimal solutions may be obtained. The optimality system is also derived using "sensitivity" derivatives instead of the Lagrange multiplier rule. We consider a gradient-type approach to the solution of domain decomposition problem. The results of some numerical experiments are presented to demonstrate the feasibility and applicability of the algorithm developed in this article. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Published by

Original source : http://dx.doi.org/10.1002%2Fnum.20519...

Residual-based a posteriori error estimator for the mixed finite element approximation of the biharmonic equation

A reliable and efficient residual-based a posteriori error estimator is derived for the Ciarlet-Raviart mixed finite element method for the biharmonic equation on polygonal domains. The performance of the estimator is illustrated by numerical experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Published by

Original source : http://dx.doi.org/10.1002%2Fnum.20524...

Convergence of the interpolated coefficient finite element method for the two-dimensional elliptic sine-Gordon equations

An interpolated coefficient finite element method is presented and analyzed for the two-dimensional elliptic sine-Gordon equations with Dirichlet boundary conditions. It is proved that the discretization scheme admits at least one solution, and that a subsequence of the approximation solutions converges to an exact solution in L2-norm as the mesh size tends to zero. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Published by

Original source : http://dx.doi.org/10.1002%2Fnum.20526...

Finite element approximation of coupled seismic and electromagnetic waves in fluid-saturated poroviscoelastic media

This work presents a collection of global and iterative finite element procedures for the numerical approximation of coupled seismic and electromagnetic waves in 2D bounded fluid-saturated porous media, with absorbing boundary conditions at the artificial boundaries. The equations being analyzed are the coupled Biot's equations of motion and Maxwell equations in the diffusive range. Both seismoelectric and electroseismic coupling are simultaneously included and analyzed in the model. The case of compressional and vertically polarized shear waves coupled with the transverse magnetic polarization (PSVTM-mode) is analyzed in detail, including the derivation of a priori error estimates on the global finite element procedure and results on the convergence of a domain decomposition iterative algorithm. Later, the corresponding results for the case of horizontally polarized shear waves coupled with the transverse electric polarization (SHTE-mode) are stated. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Published by

Original source : http://dx.doi.org/10.1002%2Fnum.20527...

Numerical and analytical method for the design of piezoelectric modal sensors/actuators for shell-type structures

In this paper we treat the problem of designing distributed piezoelectric modal sensors/actuators for cylindrically curved panels. The design problem is tackled as an optimization problem where the design variable is a function (the polarization profile of the electrode) that takes on three values only: -1 (negative polarization), 0 (zero polarization or no piezoelectric material), 1 (positive polarization), and the objective function is connected with the frequency response of the transducer. For the model described here, we analytically prove that the electrode patterns that make it possible to ideally isolate particular vibration modes must entirely cover the piezoelectric lamina with either positive or negative polarization. Further, we propose an accurate numerical method for systematically designing these polarization patterns and a novel algorithm for parameterizing and visualizing them in 3d. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnme.2757...

Comments on 'An efficient iterative method for solving the matrix equation AXB+CYD=E'

In this note, a technical error is pointed out in the proof of a lemma in the above paper. A correct proof of this lemma is given. In addition, a further result on the algorithm in the above paper is also given. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnla.675...

Discrete element modeling of direct shear tests for a granular material

A succinct 3D discrete element model, with clumps to resemble the real shapes of granular materials, is developed. The quaternion method is introduced to transform the motion and force of a clump between local and global coordinates. The Hertz-Mindlin elastic contact force model, incorporated with the nonlinear normal viscous force and the Mohr-Coulomb friction law, is used to describe the interactions between particles. The proposed discrete element model is used to simulate direct shear tests of the irregular limestone rubbles. The simulation results of vertical displacements and shear stresses with a mixture of clumps are compared well with that of laboratory tests. The bulk friction coefficients are calculated and discussed under different contact friction coefficients and normal stresses. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnag.848...

Finite resolution dynamics. (arXiv:0910.2319v1 [math.DS])

We develop a new mathematical model for describing a dynamical system at
limited resolution (or finite scale),and we give precise meaning to the notion
of a dynamical system having some property at finite resolution. Open covers
are used to approximate the topology of the phase space in a finite way,and the
dynamical system is represented by means of a combinatorial multivalued map.We
translate notions of transitivity and mixing known for general dynamical
systems into the finite setting in a consistent way. Moreover, we formulate
equivalent conditions for these properties in terms of graphs,and provide
effective algorithms for their verification. As an application we show that the
Henon attractor is topologically mixing at all resolutions coarser than 10^-5.

Published by

Original source : http://arxiv.org/abs/0910.2319...

Adaptive finite element computation of dielectric and mechanical intensity factors in piezoelectrics with impermeable cracks

The paper deals with the application of an adaptive, hierarchic-iterative finite element technique to solve two-dimensional electromechanical boundary value problems with impermeable cracks in piezoelectric plates. In order to compute the dielectric and mechanical intensity factors, the interaction integral technique is used. The iterative finite element solver takes advantage of a sequence of solutions on hierarchic discretizations. Based on an a posteriori error estimation, the finite element mesh is locally refined or coarsened in each step. Two crack configurations are investigated in an infinite piezoelectric plate: A finite straight crack and a finite kinked crack. Fast convergence of the numerical intensity factors to the corresponding analytical solution is exemplarily proved during successive adaptive steps for the first configuration. Similar tendency can be observed for the second configuration. Furthermore, the computed intensity factors for the kinks are found to coincide well with the corresponding analytical values. In order to simulate the kinks spreading from a straight crack, the finite element mesh is modified automatically with a specially developed algorithm. This forms the basis for a fully adaptive simulation of crack propagation. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnme.2742...

An approximate solution to an initial boundary value problem to the one-dimensional Kuramoto-Sivashinsky equation

The aim of this paper is to present an approximate solution to the initial boundary-valued problem for the one-dimensional Kuramoto-Sivashinsky equation. The Fourier Method is combined with the Adomian's Decomposition Method in order to provide an approximate solution. One example of application is presented. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fcnm.1339...

Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals. (arXiv:0910.1841v1 [math.NA])

High-order derivatives of analytic functions are expressible as Cauchy
integrals over circular contours, which can very effectively be approximated by
trapezoidal sums. Whereas analytically each radius r up to the radius of
convergence is equal, numerical stability strongly depends on r. We give a
comprehensive study of this effect; in particular we show that there is a
unique radius that minimizes the loss of accuracy caused by round-off errors.
For large classes of functions, though not all, this radius actually gives
about full accuracy; a remarkable fact that we explain by the theory of Hardy
spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and
by the saddle-point method of asymptotic analysis. Many examples and
non-trivial applications are discussed in detail.

Published by

Original source : http://arxiv.org/abs/0910.1841...

Finite Elements for a Beam System With Nonlinear Contact Under Periodic Excitation. (arXiv:0910.2092v1 [math.NA])

Solar arrays are structures which are connected to satellites; during launch,
they are in a folded position and submitted to high vibrations. In order to
save mass, the flexibility of the panels is not negligible and they may strike
each other; this may damage the structure. To prevent this, rubber snubbers are
mounted at well chosen points of the structure; a prestress is applied to the
snubber; but it is quite difficult to check the amount of prestress and the
snubber may act only on one side; they will be modeled as one sided springs
(see figure 2). In this article, some analysis for responses (displacements) in
both time and frequency domains for a clamped-clamped Euler-Bernoulli beam
model with a spring are presented. This spring can be unilateral or bilateral
fixed at a point. The mounting (beam +spring) is fixed on a rigid support which
has a sinusoidal motion of constant frequency. The system is also studied in
the frequency domain by sweeping frequencies between two fixed values, in order
to save the maximum of displacements corresponding to each frequency. Numerical
results are compared with exact solutions in particular cases which already
exist in the literature. On the other hand, a numerical and theoretical
investigation of nonlinear normal mode (NNM) can be a new method to describe
nonlinear behaviors, this work is in progress.

Published by

Original source : http://arxiv.org/abs/0910.2092...

Iterative Methods for the Force-based Quasicontinuum Approximation. (arXiv:0910.2013v1 [math.NA])

Force-based atomistic-continuum hybrid methods are the only known pointwise
consistent methods for coupling a general atomistic model to a finite element
continuum model. For this reason, and due to their algorithmic simplicity,
force-based coupling methods have become a popular approach for
atomistic-continuum hybrid methods as well as other types of multiphysics model
coupling. However, the recently discovered unusual stability properties of the
linearized force-based quasicontinuum approximation, especially its
indefiniteness, present a challenge to the development of efficient and
reliable iterative methods. Using a combination of rigorous analysis and
computational experiments, we present a systematic study of the stability and
rate of convergence of a variety of linear stationary iterative methods and
generalized minimal residual methods (GMRES) for the solution of the linearized
force-based quasicontinuum equations.

Published by

Original source : http://arxiv.org/abs/0910.2013...

Barycentric-Remez algorithms for best polynomial approximation in the chebfun system

Abstract  The Remez algorithm, 75 years old, is a famous method for computing minimax polynomial approximations. Most implementations
of this algorithm date to an era when tractable degrees were in the dozens, whereas today, degrees of hundreds or thousands
are not a problem. We present a 21st-century update of the Remez ideas in the context of the chebfun software system, which
carries out numerical computing with functions rather than numbers. A crucial feature of the new method is its use of chebfun
global rootfinding to locate extrema at each iterative step, based on a recursive algorithm combining ideas of Specht, Good,
Boyd, and Battles. Another important feature is the use of the barycentric interpolation formula to represent the trial polynomials,
which points the way to generalizations for rational approximations. We comment on available software for minimax approximation
and its scientific context, arguing that its greatest importance these days is probably for fundamental studies rather than
applications.

• Content Type Journal Article
• DOI 10.1007/s10543-009-0240-1
• Authors
  
  
  • Ricardo Pachón, University of Oxford Computing Laboratory Parks Rd. Oxford OX1 3QD UK
  • Lloyd N. Trefethen, University of Oxford Computing Laboratory Parks Rd. Oxford OX1 3QD UK
  
  

• Journal BIT Numerical Mathematics
• Online ISSN 1572-9125
• Print ISSN 0006-3835

Published by

Original source : http://www.springerlink.com/content/5n17515j262845...

Generating series for irreducible polynomials over finite fields. (arXiv:0910.1680v1 [math.AG])

We count the number of irreducible polynomials in several variables of a
given degree over a finite field. The results are expressed in terms of a
generating series, an exact formula and an asymptotic approximation. We also
consider the case of the multi-degree and the case of indecomposable
polynomials.

Published by

Original source : http://arxiv.org/abs/0910.1680...

On new iterative method for solving systems of nonlinear equations

Abstract  Solving systems of nonlinear equations is a relatively complicated problem for which a number of different approaches have
been proposed. In this paper, we employ the Homotopy Analysis Method (HAM) to derive a family of iterative methods for solving
systems of nonlinear algebraic equations. Our approach yields second and third order iterative methods which are more efficient
than their classical counterparts such as Newton’s, Chebychev’s and Halley’s methods.

• Content Type Journal Article
• Category Original Paper
• DOI 10.1007/s11075-009-9342-8
• Authors
  
  
  • Fadi Awawdeh, Hashemite University Zarqa Jordan
  
  

• Journal Numerical Algorithms
• Online ISSN 1572-9265
• Print ISSN 1017-1398

Published by

Original source : http://www.springerlink.com/content/6804745r423t26...

Non-linear dynamic analyses by meshless local Petrov-Galerkin formulations

In this work, meshless methods based on the local Petrov-Galerkin approach are proposed for the solution of dynamic problems considering elastic and elastoplastic materials. Formulations adopting the Heaviside step function and the Gaussian weight function as the test functions in the local weak form are considered. The moving least-square method is used for the approximation of physical quantities in the local integral equations. After spatial discretization is carried out, a non-linear system of ordinary differential equations of second order is obtained. This system is solved by Newmark/Newton-Raphson techniques. At the end of the paper numerical results are presented, illustrating the potentialities of the proposed methodologies. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnme.2756...

Accurate and efficient simulation of transport in multidimensional flow

A new numerical method to obtain high-order approximations of the solution of the linear advection equation in multidimensional problems is presented. The proposed conservative formulation is explicit and based on a single updating step. Piecewise polynomial spatial discretization using Legendre polynomials provides the required spatial accuracy. The updating scheme is built from the functional approximation of the exact solution of the advection equation and a direct evaluation of the resulting integrals. The numerical details for the schemes in one and two spatial dimensions are provided and validated using a set of numerical experiments. Test cases have been oriented to the convergence and the computational efficiency analysis of the schemes. Copyright © 2009 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Ffld.2189...