High-order implicit time integration scheme with controllable numerical dissipation based on mixed-order Padé expansions

06/08/2022
by   Chongmin Song, et al.
0

A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequency is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled by a user-specified value of the spectral radius ρ_∞ in the high frequency limit. Using this user-specified parameter as a weight factor, a Padé expansion of the matrix exponential solution of the equation of motion is constructed by mixing the diagonal and sub-diagonal expansions. An efficient time stepping scheme is designed where systems of equations similar in complexity to the standard Newmark method are solved recursively. It is shown that the proposed high-order scheme achieves high-frequency dissipation while minimizing low-frequency dissipation and period errors. The effectiveness of dissipation control and efficiency of the scheme are demonstrated with numerical examples. A simple recommendation on the choice of the controlling parameter and time step size is provided. The source code written in MATLAB and FORTRAN is available for download at: https://github.com/ChongminSong/HighOrderTimeIntegration.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/23/2021

High-order implicit time integration scheme based on Padé expansions

A single-step high-order implicit time integration scheme for the soluti...
research
06/14/2019

Higher-order generalized-α methods for hyperbolic problems

The generalized-α time-marching method provides second-order accuracy in...
research
04/12/2023

Numerical differentiation by the polynomial-exponential basis

Our objective is to calculate the derivatives of data corrupted by noise...
research
08/01/2023

Multi-frequency averaging and uniform accuracy towards numerical approximations for a Bloch model

We are interested in numerically solving a transitional model derived fr...
research
02/23/2021

Explicit high-order generalized-α methods for isogeometric analysis of structural dynamics

We propose a new family of high-order explicit generalized-α methods for...
research
05/22/2017

ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations

Recently, ParaExp was proposed for the time integration of linear hyperb...
research
08/09/2021

Damping perturbation based time integration asymptotic method for structural dynamics

The light damping hypothesis is usually assumed in structural dynamics s...

Please sign up or login with your details

Forgot password? Click here to reset