Penalty methods for time domain computational dynamics based on positive and negative inertia

Hetherington, Jack; Askes, Harm

doi:10.1016/j.compstruc.2009.05.011

Cited by 17 publications

(17 citation statements)

References 14 publications

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“…Hence, stiffness penalties tend to increase the wave speed and maximum eigenfrequency and therefore decrease the critical time step, while the inverse is true for mass penalties [6,7]. The goal here is to develop a method of calculating the critical penalty ratio for any finite element; that is, the ratio of stiffness and mass penalty parameters that preserves the maximum eigenfrequency (and therefore the critical time step) of that element.…”

Section: The Bipenalised Problemmentioning

confidence: 99%

“…For the eigenpair (ω n , u n ) to be a solution of the BP as well as the UP, we must make sure that the solution satisfies (7) as well as (6). Since, from (6),…”

Section: Proofmentioning

confidence: 99%

“…In dynamic analysis, penalty methods can also be applied to the mass matrix of a system [5,6]. This technique is known as the large mass, mass penalty or inertia penalty method.…”

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confidence: 99%

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A new bipenalty formulation for ensuring time step stability in time domain computational dynamics

Hetherington

Ferran

Askes

2011

Numerical Meth Engineering

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Section: The Bipenalised Problemmentioning

confidence: 99%

“…For the eigenpair (ω n , u n ) to be a solution of the BP as well as the UP, we must make sure that the solution satisfies (7) as well as (6). Since, from (6),…”

Section: Proofmentioning

confidence: 99%

See 1 more Smart Citation

A new bipenalty formulation for ensuring time step stability in time domain computational dynamics

Hetherington

Ferran

Askes

2011

Numerical Meth Engineering

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“…In their approach, the penalty method was used to enforce the essential boundary conditions. It is well-known that the larger the penalty parameter, the more accurate the numerical solution will be, but large penalty parameters can affect the conditioning of the system matrix adversely [10]. Arzani and Afshar [11] developed discrete least-squares meshless (DLSM) method for the solution of convection-dominated problems.…”

Section: Introductionmentioning

confidence: 99%

Local moving least square‐one‐dimensional integrated radial basis function networks technique for incompressible viscous flows

Ngo-Cong

Mai‐Duy

Karunasena

et al. 2012

Numerical Methods in Fluids

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This paper presents a local moving least square -one-dimensional integrated radial basis function networks (LMLS-1D-IRBFN) method for solving incompressible viscous flow problems using stream function-vorticity formulation. In this method, the partition of unity method is employed as a framework to incorporate the moving least square (MLS) and one-dimensional integrated radial basis function networks (1D-IRBFN) techniques. The major advantages of the proposed method include: (i) a banded sparse system matrix which helps reduce the computational cost; (ii) the Kronecker-δ property of the constructed shape function which helps impose the essential boundary condition in an exact manner; and (iii) high accuracy and fast convergence rate owing to the use of integration instead of conventional differentiation to construct the local RBF approximations. Several examples including two-dimensional Poisson problems, lid-driven cavity flow and flow past a circular cylinder are considered and the present results are compared with the exact solutions and numerical results from other methods in the literature to demonstrate the attractiveness of the proposed method.

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“…This result can be used to interpolate between results obtained with moderately large (but not very large) positive and negative penalty parameters. More recently, it was suggested to use inertia penalties instead of stiffness penalties (Ilanko 2005b;Williams & Ilanko 2005;Hetherington & Askes 2009). Whereas stiffness penalties can be interpreted as stiff springs, inertia penalties can be regarded as heavy masses; both types of penalties limit the motion of the relevant degree of freedom (d.f.).…”

Section: Introductionmentioning

confidence: 99%

Bipenalty method for time domain computational dynamics

2009

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Penalty functions can be used to add constraints to systems of equations. In computational mechanics, stiffness-type penalties are the common choice. However, in dynamic applications stiffness penalties have the disadvantage that they tend to decrease the critical time step in conditionally stable time integration schemes, leading to increased CPU times for simulations. In contrast, inertia penalties increase the critical time step. In this paper, we suggest the simultaneous use of stiffness penalties and inertia penalties, which is denoted as the bipenalty method. We demonstrate that the accuracy of the bipenalty method is at least as good as (and usually better than) using either stiffness penalties or inertia penalties. Furthermore, for a number of finite elements (bar elements, beam elements and square plane stress/plane strain elements) we have derived ratios of the two penalty parameters such that their combined effect on the critical time step is neutral. The bipenalty method is thus superior to using stiffness penalties, because the decrease in critical time step can be avoided. The bipenalty method is also superior to using inertia penalties, since the constraints are realized with higher accuracy.

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Penalty methods for time domain computational dynamics based on positive and negative inertia

Cited by 17 publications

References 14 publications

A new bipenalty formulation for ensuring time step stability in time domain computational dynamics

A new bipenalty formulation for ensuring time step stability in time domain computational dynamics

Local moving least square‐one‐dimensional integrated radial basis function networks technique for incompressible viscous flows

Bipenalty method for time domain computational dynamics

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