Bounds on eigenvalues of finite element systems

Lin, Jerry I.

doi:10.2514/6.1990-1079

Cited by 4 publications

(8 citation statements)

References 9 publications

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“…As shown in [25], the nonzero eigenvalues at an integration point can be found from the following matrix…”

Section: Stability and Time Step Controlmentioning

confidence: 99%

“…Further details of the derivation of (5.21) and (5.22) can be found in [23,25]. COYOTE uses (5.22) to estimate λ i max and the bound in (5.21) to estimate the maximum system eigenvalue; the system eigenvalue and Equation (5.20) allow computation of a usable time step.…”

Section: Stability and Time Step Controlmentioning

confidence: 99%

“…Such formulas have been derived for bar, quadrilateral and hexahedral elements with a linear temperature approximation [23,24], though these results are restricted to cases where one-point quadrature is used to evaluate the finite element integrals. For elements with multiple integration points, such as used in COYOTE, the theory and estimation procedure due to Lin [25] is employed. The largest element eigenvalue can be bounded by the sum of the largest eigenvalues at each integration point.…”

Section: Stability and Time Step Controlmentioning

confidence: 99%

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COYOTE : a finite element computer program for nonlinear heat conduction problems. Part I, theoretical background.

Glass¹,

Hogan²,

Gartling³

2010

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The theoretical and numerical background for the finite element computer program, COYOTE, is presented in detail. COYOTE is designed for the multi-dimensional analysis of nonlinear heat conduction problems. A general description of the boundary value problems treated by the program is presented. The finite element formulation and the associated numerical methods used in COYOTE are also outlined. Instructions for use of the code are documented in SAND2010-0714. iii iii PrefaceAt the time of release of the first version of COYOTE in mid-1978, it was not anticipated that the code would receive the usage and longevity that it currently enjoys. In response to user needs, the original program under went several minor upgrades plus a major revision during the late 1980's. In addition, a preliminary three-dimensional version of COYOTE was developed though it was not formally documented. Continued requests for additional capabilities combined with the significant changes in computer hardware and improved numerical algorithms, dictated the need for completely new versions of the older codes. In rewriting the COYOTE program, the two and three-dimensional codes were combined into a single software package, COYOTE II, that was released in 1994. The present series of reports describe the latest version (Version 5.0) of the program package, which has reverted to its original name, COYOTE, to avoid confusion in future releases.In an effort to make the program more flexible and more generally applicable, a number of new capabilities and features have been added to COYOTE to produce COYOTE, Version 5.0. The major extension of the code is the capability to optionally include one or two additional diffusion equations that may be coupled to the primary heat conduction equation. The variables in these added equations are available to the boundary conditions, source terms and material property functions in the conduction equation. Conversely, the temperature field is available to the auxiliary diffusion equations. As part of this expansion, a time harmonic option for heat transfer was also added. Two thermal diffusion equations are solved in this case for the real and imaginary parts of the temperature field. Some changes to the sequential solution algorithm for coupled conduction and radiation have been made to improve convergence of this type of method. A fully coupled conduction/radiation solution method has been generalized and reinstalled to allow operation in a parallel environment. The fully coupled algorithm was made possible by a complete changeover to the use of the Finite Element Interface (FEI) with the improved access to the solver libraries available in the Trilinos package. The code may now be compiled using either a single or double precision word length. Some minor changes in problem capability and control have also been added. Most notable among these changes are the allowance of a time evolving mass flow to a bulk node (due to chemical reaction) and user defined material parameters now being passed to user s...

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“…As shown in [25], the nonzero eigenvalues at an integration point can be found from the following matrix…”

Section: Stability and Time Step Controlmentioning

confidence: 99%

Section: Stability and Time Step Controlmentioning

confidence: 99%

Section: Stability and Time Step Controlmentioning

confidence: 99%

See 1 more Smart Citation

COYOTE : a finite element computer program for nonlinear heat conduction problems. Part I, theoretical background.

Glass¹,

Hogan²,

Gartling³

2010

View full text Add to dashboard Cite

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“…In case of 'stick', the term k sign(v rel ) in Equation (22) has to be replaced by s , which is denoted as static friction coefficient. Insertion of Equations (20)- (23) in condition (19) finally provides a linear equation for the determination of p N , which in turn allows the calculation of F S , F M I , d S and d M I . Normally, contact groups consist of several master segments and slave nodes.…”

Section: Contact Formulationmentioning

confidence: 99%

“…Alternatively, more enhanced critical time step estimates can be found in Reference [19]. With this critical time step estimate-often called CFL condition (Courant, Friedrichs and Lewy [20])-an adaptive time stepping can easily be realized: In regular intervals, the current time step size is set to a value little smaller than given by this stability limit.…”

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confidence: 99%

Robust adaptive remeshing strategy for large deformation, transient impact simulations

Erhart

Wall

Ramm

2005

Numerical Meth Engineering

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SUMMARYIn this paper, an adaptive approach, with remeshing as essential ingredient, towards robust and efficient simulation techniques for fast transient, highly non-linear processes including contact is discussed. The necessity for remeshing stems from two sources: the capability to deal with large deformations that might even require topological changes of the mesh and the desire for an error driven distribution of computational resources. The overall computational approach is sketched, the adaptive remeshing strategy is presented and the crucial aspect, the choice of suitable error indicator(s), is discussed in more detail. Several numerical examples demonstrate the performance of the approach.

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The effects of element shape on the critical time step in explicit time integrators for elasto-dynamics

Askes

Ferran

Hetherington

2014

Int. J. Numer. Meth. Engng

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SUMMARYIn this paper, the effects of element shape on the critical time step are investigated. The common ruleof-thumb, used in practice, is that the critical time step is set by the shortest distance within an element divided by the dilatational (compressive) wave speed, with a modest safety factor. For regularly shaped elements, many analytical solutions for the critical time step are available, but this paper focusses on distorted element shapes. The main purpose is to verify whether element distortion adversely affects the critical time step or not. Two types of element distortion will be considered, namely aspect ratio distortion and angular distortion, and two particular elements will be studied: four-noded bilinear quadrilaterals and three-noded linear triangles. The maximum eigenfrequencies of the distorted elements are determined and compared to those of the corresponding undistorted elements. The critical time steps obtained from single element calculations are also compared to those from calculations based on finite element patches with multiple elements.

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Bounds on eigenvalues of finite element systems

Cited by 4 publications

References 9 publications

COYOTE : a finite element computer program for nonlinear heat conduction problems. Part I, theoretical background.

COYOTE : a finite element computer program for nonlinear heat conduction problems. Part I, theoretical background.

Robust adaptive remeshing strategy for large deformation, transient impact simulations

The effects of element shape on the critical time step in explicit time integrators for elasto-dynamics

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