BatheTwoStep
Starting from version 2.7, customisation of spectral radius () and sub-step size () is supported.
The algorithm is known to be able to conserve energy and momentum.
References:
The implementation follows the original algorithm. The only difference is the step size defined in suanPan
is the mean step size of two sub-step sizes, that is in the references.
For further discussions on this type of algorithm, one can check the following references.
Syntax
integrator BatheTwoStep (1) [2] [3]
# (1) int, unique integrator tag
# [2] double, spectral radius, \rho_\infty, default: 0
# [2] double, sub-step size, gamma, default: 0.5
Using integrator BatheTwoStep (1)
with two optional parameters omitted gives the same results as in versions prior
to version 2.7.
The spectral radius ranges from 0 to 1, both ends inclusive.
The sub-step size ranges from 0 to 1, both ends exclusive.
Theory
The First Sub-step
For trapezoidal rule,
Then,
One could obtain
The effective stiffness is then
The Second Sub-step
The second step is computed by
The parameters satisfy , and
Hence,
The effective stiffness is then
Accuracy Analysis
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