Tchamwa

First order explicit time integration method using the Tchamwa scheme.

References:

1. 10.1002/nme.6574

Syntax

integrator Tchamwa (1) [2]
# (1) int, unique integrator tag
# [2] double, spectral radius, \rho_\infty, default: 0.5

Theory

The integration relationship is given by the following.

$$u_{n+1}=u_n+\mathrm{\Delta }t{v}_n+\varphi \mathrm{\Delta }{t}^2{a}_n,$$

$$v_{n+1}=v_n+\mathrm{\Delta }t{a}_n,$$

where

$$\varphi ={\displaystyle \frac{2}{1+{\rho }_{\mathrm{\infty }}}}.$$

The Tchamwa scheme has a first order accuracy and controllable numerical dissipation.

Remarks

If the model is linear elastic, it is possible to indicate using

set linear_system true

to speed up the computation.