1,720,971 research outputs found
Analysis and performance of a predictor-multicorrector Time Discontinuous Galerkin method in non-linear elastodynamics
No full textA predictor-multicorrector implementation of a Time Discontinuous Galerkin method for non-linear dynamic analysis is described. This implementation is intended to limit the high computational expense typically required by implicit Time Discontinuous Galerkin methods, without degrading their accuracy and stability properties. The algorithm is analysed with reference to conservative Duffing oscillators for which closed-form solutions are available. Therefore, insight into the accuracy and stability properties of the predictor-multicorrector algorithm for different approximations of non-linear internal forces is gained, showing that the properties of the underlying scheme can be substantially retained. Finally, the results of representative numerical simulations relevant to Duffing oscillators and to a stiff spring pendulum discretized with finite elements illustrate the performance of the numerical scheme and confirm the analytical estimates. Copyrigh
Collocation methods with controllable dissipation for linear dynamics
No full textThis paper introduces a unified set of collocation methods for linear dynamics in which a parameter is used to control the position of the collocation points. In this manner, both A-stable algorithms of order 2p and L-stable algorithms of order 2p - 1 are derived from collocation polynomials of degree p. In addition, algorithms with intermediate accuracy and stability properties are made available. The effects of varying the algorithmic parameter are investigated with particular reference to the numerical dissipation of spurious high-frequency modes. Numerical tests are reported which support the theoretical analysis and demonstrate the performance of the proposed algorithms. (C) 2001 Elsevier Science B.V. All rights reserved
An efficient time discontinuous Galerkin procedure for non-linear structural dynamics
No full textThis paper presents an effective time discontinuous Galerkin procedure for non-linear dynamics. The procedure is based on a cheap iterative algorithm, which is rather different from previous efforts. In fact, the algorithm is designed so that the corrected solutions inherit the desired stability and dissipative properties and the iterations serve only to improve accuracy. Some numerical tests illustrate the good performance of the present procedure, which appears to be competitive with the available implementations of time discontinuous Galerkin methods
On the behavior of dissipative time integration methods near the resonance condition
No full textTHE BEHAVIOR OF DISSIPATIVE TIME INTEGRATIONMETHODS NEAR THE RESONANCE CONDITION IS ANALYZE
A methodology for the generation of low-cost higher-order methods for linear dynamics
No full textThis work presents a methodology which generates efficient higher-order methods for linear dynamics by improving the accuracy properties of Norsett methods towards those of Pade methods. The methodology is based on a simple and low-cost iterative procedure which is used to implement a set of higher-order methods with controllable dissipation. A sequence of improved solutions is obtained which correspond to algorithms offering an effective compromise between the efficiency of Norsett methods and the accuracy of Pade methods. Moreover, a direct control over high-frequency dissipation is possible by means of an algorithmic parameter. Numerical tests are reported which confirm that this set of algorithms is really attractive for linear dynamic analysis. Copyrigh
The Norsett time integration methodology for finite element transient analysis
No full textThis paper presents a set of methods for time integration of problems arising from finite element semidiscretizations. The purpose is to obtain computationally efficient methods which possess higher-order accuracy and controllable dissipation in the spurious high modes. The methods are developed and analysed by a general collocation methodology which leads to the class of Norsett approximants. An algorithmic parameter is used to achieve an effective control over numerical dissipation. Moreover, a simple and efficient implementation scheme is presented. At each time step, algorithms based on p-order collocation polynomials require the solution of p sets of linear algebraic equations with the same coefficient matrix. In this way, a single factorization is needed and no transformations are required to recover the approximate solution at the end or within the time interval. To demonstrate the performance of the proposed algorithms, a wide experimental evaluation is carried out on typical test problems in finite element transient analysis. (C) 2002 Elsevier Science B.V. All rights reserved
An efficient integration procedure for linear dynamics based on a time discontinuous Galerkin formulation
No full textThis work presents an effective procedure devised to implement the time discontinuous Galerkin method for linear dynamics. In particular, the method with piecewise linear time interpolation is considered. The procedure is based on a simple and low-cost iterative scheme, which is designed not as a mere solution algorithm, but rather as a method to generate improved approximations to the exact solution. The corrected solutions inherit the desired stability and dissipative properties from the target solution, while accuracy is improved by iterations. Indeed, no more than two iterations are shown to be needed. The resultant algorithm leads to remarkable computational savings and can be easily implemented into existing finite element codes. Numerical tests confirm that the present procedure possesses many attractive features for applications to dynamic analysis
Spurious resonances in numerical time integration methods for linear dynamics
No full textThis paper deals with the accuracy of time integration methods for linear dynamics when applied near the resonance condition. An approach for the analysis is considered which allows spurious resonance conditions to be detected. The analysis of Newmark methods shows the existence of such conditions which can adversely affect the quality of numerical computations, As an alternative, a higher order algorithm, which can be viewed as a generalization of the trapezoidal rule, is investigated. The analysis reveals that the spurious disturbance near the resonance condition is greatly reduced. The reported numerical tests confirm the theoretical predictions and demonstrate that high-quality simulations can be obtained by means of higher order algorithms
Explicit predictor-multicorrector Time Discontinuous Galerkin methods for linear dynamics
No full textThis paper focuses on the formulation and implementation of explicit predictor– multicorrector Time Discontinuous Galerkin methods for linear structural dynamics. The formulation of the schemes is based on piecewise linear functions in time that approximate displacements and momenta. Both the predictors and correctors are designed to inherit third order accuracy from the exact parent implicit Time Discontinuous Galerkin method. Moreover, they are endowed with large stability limits and controllable numerical dissipation by means of an algorithmic parameter. Thereby, the resulting algorithms appear to be competitive with standard explicit algorithms for structural dynamics. Representative numerical simulations are presented illustrating the performance of the proposed numerical schemes and confirming the analytical results
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