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NUMERICAL TREATMENT OF MULTIPLE BIFURCATION POINTS
"... Key Words: continuation algorithm, multiple bifurcation, branch switching, FEM Abstract. Branch switching procedures which are capable to handle critical points with coincident or nearly coincident buckling loads in a geometrically nonlinear continuation process are presented. The proposed branch s ..."
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switching algorithm is based on a LiapunovSchmidtKoitertype asymptotic reduction. Numerical examples of some plate and shell structures are shown. 1 Reijo Kouhia and Martti Mikkola 1 INTRODUCTION Procedures to handle simple critical points on an equilibrium path of elastic structures are now well
Numerical Treatment and Evaluation of Inverse Problems
"... Abstract: All regularization methods for computing stable solutions to inverse problems, involve a tradeoff between the “size ” of the regularized solution and the quality of the fit that it provides to the given data. Though the appropriate choice of the regularization parameters is important, re ..."
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Abstract: All regularization methods for computing stable solutions to inverse problems, involve a tradeoff between the “size ” of the regularized solution and the quality of the fit that it provides to the given data. Though the appropriate choice of the regularization parameters is important, resolution and uncertainty analysis are as significant. Thus, we should also proceed to the resolution analysis in order to determine what scale features in the model can actually be resolved. In this work, we choose the proper values of damping and smoothing factors using two of the most well known regularization tools, the Picard condition and the Lcurve [8], which generally provide a good estimation of the regularization parameters in combination with the standard maximum likelihood approach [3]. Additionally, the spread function as proposed by Menke [18] and a checkerboard test are applied in order to have an estimate of the resolution. The efficiency of the preferred methods is tested through a series of tests in real data from the area of Urals in Russia.
Numerical Treatment of Microstructure Evolution Modeling
"... Introduction; plasticity by twinning Plasticity in metals can be caused, beside a classical slip mechanism like in the PrandtlReuss model, also by twinning within a martensitic phase transformation; such plasticity is addressed in particular cases as quasiplasticity or pseudoelasticity [6]. The ..."
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Introduction; plasticity by twinning Plasticity in metals can be caused, beside a classical slip mechanism like in the PrandtlReuss model, also by twinning within a martensitic phase transformation; such plasticity is addressed in particular cases as quasiplasticity or pseudoelasticity [6]. The martensitic transformation in monoclinic or tetragonal crystals (cf. Figure 1a) is usually activated in much lower energies than the slip plasticity and may sometimes cause dominant effects. Typical phenomena governing the martensitic transformation are: (a) activation, i.e. the phase transformation requires sufficiently high energy; (b) dissipation, i.e. considerable amount of energy is dissipated within the phase transformation; (c) geometric relations, i.e. rankone connections between adjacent twins are energetically preferred. almost pure phases. a) A "monoclinic" atomic grid c) Simplelaminated d) Deformed twined crystal,
Adaptive numerical treatment of elliptic systems on manifolds
 Advances in Computational Mathematics, 15(1):139
, 2001
"... ABSTRACT. Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first reviewed, and then adaptive multilevel finite element ..."
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Cited by 55 (25 self)
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element software package for 2 and 3manifolds developed over several years at Caltech and UC San Diego. It employs a posteriori error estimation, adaptive simplex subdivision, unstructured algebraic multilevel methods, global inexact Newton methods, and numerical continuation methods for the numerical
A Framework for the Numerical Treatment of Aerosol Dynamics
, 2005
"... a Corresponding author. This paper presents a general framework for the discretization of particle dynamics equations by projection methods, which include Galerkin and collocation techniques. The framework enables a uni¯ed and simultaneous numerical treatment of di®erent dynamic processes like coa ..."
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a Corresponding author. This paper presents a general framework for the discretization of particle dynamics equations by projection methods, which include Galerkin and collocation techniques. The framework enables a uni¯ed and simultaneous numerical treatment of di®erent dynamic processes like
Numerical Treatment of Differential Equations of Fractional Order
, 1996
"... The collocation approximation with polynomial splines is applied to differential equations of fractional order and the systems of equations characterizing the numerical solution are determined. In particular, the weight matrices resulting from the fractional derivative of the spline are deduced and ..."
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Cited by 14 (0 self)
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The collocation approximation with polynomial splines is applied to differential equations of fractional order and the systems of equations characterizing the numerical solution are determined. In particular, the weight matrices resulting from the fractional derivative of the spline are deduced
On the Numerical Treatment and Dependence of the Third DredgeUp Phenomenon
"... We present results of an investigation into the behaviour of the base of the convective envelope of models of AGB stars during third dredgeup. We find that the extent, and even presence, of third dredgeup depends critically on the treatment of convection within a stellar structure calculation. Sub ..."
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Cited by 1 (0 self)
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We present results of an investigation into the behaviour of the base of the convective envelope of models of AGB stars during third dredgeup. We find that the extent, and even presence, of third dredgeup depends critically on the treatment of convection within a stellar structure calculation
© Hindawi Publishing Corp. ON THE NUMERICAL TREATMENT OF THE CONTACT PROBLEM
, 1999
"... Abstract. The problem of the contact of two elastic bodies of arbitrary shape with a kernel in the form of a logarithmic function—which is investigated fromHertz problem—is reduced to an integral equation. A numerical method is adapted to determine the pressure between the two surfaces under certain ..."
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Abstract. The problem of the contact of two elastic bodies of arbitrary shape with a kernel in the form of a logarithmic function—which is investigated fromHertz problem—is reduced to an integral equation. A numerical method is adapted to determine the pressure between the two surfaces under
The LCurve and its Use in the Numerical Treatment of Inverse Problems
 in Computational Inverse Problems in Electrocardiology, ed. P. Johnston, Advances in Computational Bioengineering
, 2000
"... The Lcurve is a loglog plot of the norm of a regularized solution versus the norm of the corresponding residual norm. It is a convenient graphical tool for displaying the tradeoff between the size of a regularized solution and its fit to the given data, as the regularization parameter varies. The ..."
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Cited by 63 (1 self)
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The Lcurve is a loglog plot of the norm of a regularized solution versus the norm of the corresponding residual norm. It is a convenient graphical tool for displaying the tradeoff between the size of a regularized solution and its fit to the given data, as the regularization parameter varies. The Lcurve thus gives insight into the regularizing properties of the underlying regularization method, and it is an aid in choosing an appropriate regularization parameter for the given data. In this chapter we summarize the main properties of the Lcurve, and demonstrate by examples its usefulness and its limitations both as an analysis tool and as a method for choosing the regularization parameter. 1 Introduction Practically all regularization methods for computing stable solutions to inverse problems involve a tradeoff between the "size" of the regularized solution and the quality of the fit that it provides to the given data. What distinguishes the various regularization methods is how...
NOTE Numerical Treatment of Polar Coordinate Singularities
, 1999
"... The treatment of the geometrical singularity in cylindrical and spherical coordinates has for many years been a difficulty in the development of accurate finite difference (FD) and pseudospectral (PS) schemes. A variety of numerical procedures for dealing with the singularity have been suggested. F ..."
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The treatment of the geometrical singularity in cylindrical and spherical coordinates has for many years been a difficulty in the development of accurate finite difference (FD) and pseudospectral (PS) schemes. A variety of numerical procedures for dealing with the singularity have been suggested
Results 11  20
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870,428