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Variational Approach (variational + approach)

Distribution by Scientific Domains

Engineering	47%
Physics and Astronomy	23%
Mathematics and Statistics	14%
3 Other Domains	16%

Selected Abstracts

Variational approach to the free-discontinuity problem of inverse crack identification

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008
R. TsotsovaArticle first published online: 17 DEC 200
Abstract This work presents a computational strategy for identification of planar defects (cracks) in homogenous isotropic linear elastic solids. The underlying strategy is a regularizing variational approach based on the diffuse interface model proposed by Ambrosio and Tortorelli. With the help of this model, the sharp interface problem of crack identification is split into two coupled elliptic boundary value problems solved using the finite element method. Numerical examples illustrate the application of the proposed approach for effective reconstruction of the position and the shape of a single crack using only the information collected on the surface of the analyzed body. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Applied Geometry:Discrete Differential Calculus for Graphics

COMPUTER GRAPHICS FORUM, Issue 3 2004
Mathieu Desbrun
Geometry has been extensively studied for centuries, almost exclusively from a differential point of view. However, with the advent of the digital age, the interest directed to smooth surfaces has now partially shifted due to the growing importance of discrete geometry. From 3D surfaces in graphics to higher dimensional manifolds in mechanics, computational sciences must deal with sampled geometric data on a daily basis-hence our interest in Applied Geometry. In this talk we cover different aspects of Applied Geometry. First, we discuss the problem of Shape Approximation, where an initial surface is accurately discretized (i.e., remeshed) using anisotropic elements through error minimization. Second, once we have a discrete geometry to work with, we briefly show how to develop a full- blown discrete calculus on such discrete manifolds, allowing us to manipulate functions, vector fields, or even tensors while preserving the fundamental structures and invariants of the differential case. We will emphasize the applicability of our discrete variational approach to geometry by showing results on surface parameterization, smoothing, and remeshing, as well as virtual actors and thin-shell simulation. Joint work with: Pierre Alliez (INRIA), David Cohen-Steiner (Duke U.), Eitan Grinspun (NYU), Anil Hirani (Caltech), Jerrold E. Marsden (Caltech), Mark Meyer (Pixar), Fred Pighin (USC), Peter Schröder (Caltech), Yiying Tong (USC). [source]

Microwave Breakdown Field in a Resonant Spherical Cavity

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 4 2006
R. Tomala
Abstract In the present work, the microwave breakdown threshold in a gas-filled spherical resonator, is determined for the case when the cavity is excited in its lowest order mode, which implies that the microwave field strength depends on both radius and azimuthal angle. A semi-analytical approximation of the breakdown threshold is found using a direct variational approach. The variational predictions are compared with the results of full numerical calculations and demonstrate very good agreement [source]

Strain-Gradient Elasticity for Bridging Continuum and Atomistic Estimates of Stiffness of Binary Lennard-Jones Crystals

ADVANCED ENGINEERING MATERIALS, Issue 6 2010
Andrei A. Gusev
Lagrangian variational approach is employed to derive the equations of equilibrium of strain-gradient elasticity. For a periodic lamellar-morphology strain-gradient medium, we present an exact formula for the overall, system stiffness. We compare the formula with direct atomistic estimates of stiffness of binary Lennard-Jones crystals. The comparison reveals that the strain-gradient formula remains fairly accurate for all the crystals studied, including those with order of unity atoms in the crystal unit cell. Thus, one can surmise that the strain-gradient correction alone can already be sufficient to extend the scope of validity of continuum-level elasticity to near atomistic length scales. [source]

Variational approach to the free-discontinuity problem of inverse crack identification

Lie-Poisson integrators: A Hamiltonian, variational approach

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010
Zhanhua Ma
Abstract In this paper we present a systematic and general method for developing variational integrators for Lie-Poisson Hamiltonian systems living in a finite-dimensional space ,,*, the dual of Lie algebra associated with a Lie group G. These integrators are essentially different discretized versions of the Lie-Poisson variational principle, or a modified Lie-Poisson variational principle proposed in this paper. We present three different integrators, including symplectic, variational Lie-Poisson integrators on G×,,* and on ,,×,,*, as well as an integrator on ,,* that is symplectic under certain conditions on the Hamiltonian. Examples of applications include simulations of free rigid body rotation and the dynamics of N point vortices on a sphere. Simulation results verify that some of these variational Lie-Poisson integrators are good candidates for geometric simulation of those two Lie-Poisson Hamiltonian systems. Copyright © 2009 John Wiley & Sons, Ltd. [source]

On the optimum support size in meshfree methods: A variational adaptivity approach with maximum-entropy approximants

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2010
Adrian Rosolen
Abstract We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum-entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non-linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Frictional granular mechanics: A variational approach

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010
R. Holtzman
Abstract The mechanical properties of a cohesionless granular material are evaluated from grain-scale simulations. Intergranular interactions, including friction and sliding, are modeled by a set of contact rules based on the theories of Hertz, Mindlin, and Deresiewicz. A computer-generated, three-dimensional, irregular pack of spherical grains is loaded by incremental displacement of its boundaries. Deformation is described by a sequence of static equilibrium configurations of the pack. A variational approach is employed to find the equilibrium configurations by minimizing the total work against the intergranular loads. Effective elastic moduli are evaluated from the intergranular forces and the deformation of the pack. Good agreement between the computed and measured moduli, achieved with no adjustment of material parameters, establishes the physical soundness of the proposed model. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Approximate imposition of boundary conditions in immersed boundary methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2009
Ramon Codina
Abstract We analyze several possibilities to prescribe boundary conditions in the context of immersed boundary methods. As basic approximation technique we consider the finite element method with a mesh that does not match the boundary of the computational domain, and therefore Dirichlet boundary conditions need to be prescribed in an approximate way. As starting variational approach we consider Nitsche's methods, and we then move to two options that yield non-symmetric problems but that turned out to be robust and efficient. The essential idea is to use the degrees of freedom of certain nodes of the finite element mesh to minimize the difference between the exact and the approximated boundary condition. Copyright © 2009 John Wiley & Sons, Ltd. [source]

An approximate projection method for incompressible flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2002
David E. Stevens
This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139,1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40,65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency. A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A variational approach to boundary elements,two dimensional Helmholtz problems

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2003
Y. Kagawa
Abstract The boundary element method is a discretized version of the boundary integral equation method. The variational formulation is presented for the boundary element approach to Helmholtz problems. The numerical calculation of the eigenvalues in association with hollow waveguides demonstrates that the variational approach provides the upper and lower bounds of the eigenvalues. The drawback of the discretized system equation must be solved by a trial and error approach, which is shown to be removed by the introduction of the dual reciprocity method. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Analysis of the timing jitter of dispersion-managed solitons controlled by filters

LASER PHYSICS LETTERS, Issue 10 2004
M. H. Sousa
Abstract Using a variational approach, an exact analytical expression is derived for the variance of the timing jitter of a dispersion-managed soliton in the presence of lumped narrowband filters. The asymptotic timing jitter shows a linear dependence with distance, which is in contrast with the cubic dependence in the unfiltered case. We show that the suppression of the timing can be achieved by choosing conveniently the position and the strength of the optical filter. (© 2004 by ASTRO, Ltd. Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA) [source]

Positive solutions and multiple solutions for periodic problems driven by scalar p -Laplacian

MATHEMATISCHE NACHRICHTEN, Issue 12 2006
Shouchuan Hu
Abstract In this paper we study a nonlinear second order periodic problem driven by a scalar p -Laplacian and with a nonsmooth, locally Lipschitz potential function. Using a variational approach based on the nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of nontrivial positive solutions and then establish the existence of a second distinct solution (multiplicity theorem) by strengthening further the hypotheses. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Far-infrared optical spectrum of donor impurities in quantum dots in a magnetic field

PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 1 2003
M. Pacheco
Abstract We report calculations for far-infrared absorption in GaAs/Ga1,xAlxAs quantum dots doped with shallow-donor impurities in the presence of a magnetic field. The wave functions and the eigenvalues are obtained in the effective-mass approximation by using a variational approach in which the ground and excited magneto-impurity states are simultaneously obtained. The allowed intra-donor transitions have been investigated by using far-infrared radiation circularly polarized in the plane perpendicular to the magnetic field. We present results for the absorption coefficient as a function of the photon energy for several field strengths and arbitrary impurity positions. We have found that, as a consequence of the quantum dot confinement the infrared magneto-absorption strongly depends on the position of the impurity in the dot. [source]

Exciton-donor complexes in a semiconductor quantum dot in a magnetic field

PHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 4 2006
A. P. Djotyan
Abstract The binding energy of the ground state of a charged exciton-donor complex in a spherical semiconductor quantum dot in the presence of a homogeneous magnetic field has been calculated. The theoretical analysis is carried out using a variational approach in the framework of the adiabatic approximation. The behavior of the binding energy of the complex in a QD on magnetic field is investigated for different values of the QD radius. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Nonlocal electron,phonon coupling: influence on the nature of polarons

PHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 1 2004
V. M. Stojanovi
Abstract We present a variational approach to an extended Holstein model, comprising both local and nonlocal electron,phonon coupling. The approach is based on the minimization of a Bogoliubov bound to the free energy of the coupled electron-phonon system, and is implemented for a one-dimensional nearest-neighbor model, with Einstein phonons. The ambivalent character of nonlocal coupling, which both promotes and hinders transport, is clearly observed. A salient feature of our results is that the local and nonlocal couplings can compensate each other, leading to a supression of polaronic effects. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2009
C. A. McGrory
Summary The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach. [source]

A variational approach to the explicit formula,

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2003
Enrico Bombieri
First page of article [source]

The VMFCI method: A flexible tool for solving the molecular vibration problem

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 5 2006
P. Cassam-Chenaï
Abstract The present article introduces a general variational scheme to find approximate solutions of the spectral problem for the molecular vibration Hamiltonian. It is called the "vibrational mean field configuration interaction" (VMFCI) method, and consists in performing vibrational configuration interactions (VCI) for selected modes in the mean field of the others. The same partition of modes can be iterated until self-consistency, generalizing the vibrational self-consistent field (VSCF) method. As in contracted-mode methods, a hierarchy of partitions can be built to ultimately contract all the modes together. So, the VMFCI method extends the traditional variational approaches and can be included in existing vibrational codes based on the latter approaches. The flexibility and efficiency of this new method are demonstrated on several molecules of atmospheric interest. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 627,640, 2006 [source]