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LeeNewmarkIterative

Syntax

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integrator LeeNewmarkIterative (1) (2) (3) ((4) (5) (6) [7...]...)
# (1) int, unique integrator tag
# (2) double, alpha in Newmark method
# (3) double, beta in Newmark method
# (4) string, type identifier
# (5) double, \zeta_p
# (6) double, \omega_p
# (7...) double/int, parameters associated with the mode

Remarks

  1. The definition of parameters is identical to that of LeeNewmarkFull.
  2. Instead of unrolling all modes into a single sparse damping matrix, this integrator uses an iterative procedure to solve system. The convergence rate is linear.
  3. Since the convergence rate is linear even with Newton method, one may use the (L)BFGS method to achieve a super-linear convergence rate.

It is recommended to use a dense matrix storage for the system with a (L)BFGS solver. For example,

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step dynamic 1 10
solver LBFGS 1 50
# the following are the default
set banded_mat true
set symm_mat false
set sparse_mat false

integrator LeeNewmarkIterative 1 .25 .5 ...

This configuration can maximize the performance.