// @sect4{TopLevel::update_quadrature_point_history}
- // At the end of each time step, we should
- // have computed an incremental
- // displacement update so that the material
- // in its new configuration accomodates for
- // the difference between the external body
- // and boundary forces applied during this
- // time step minus the forces exerted
+ // At the end of each time step, we
+ // should have computed an
+ // incremental displacement update
+ // so that the material in its new
+ // configuration accomodates for
+ // the difference between the
+ // external body and boundary
+ // forces applied during this time
+ // step minus the forces exerted
// through pre-existing internal
// stresses. In order to have the
- // pre-existing stresses available at the
- // next time step, we therefore have to
- // update the pre-existing stresses with
- // the stresses due to the incremental
- // displacement computed during the present
- // time step. Ideally, the resulting sum of
- // internal stresses would exactly counter
- // all external forces. Indeed, a simple
- // experiment can make sure that this is
- // so: if we choose boundary conditions and
- // body forces to be time independent, then
- // the forcing terms (the sum of external
- // forces and internal stresses) should be
- // exactly zero. If you make this
- // experiment, you will realize from the
- // output of the norm of the right hand
- // side in each time step that this is
- // almost the case: it is not exactly zero,
+ // pre-existing stresses available
+ // at the next time step, we
+ // therefore have to update the
+ // pre-existing stresses with the
+ // stresses due to the incremental
+ // displacement computed during the
+ // present time step. Ideally, the
+ // resulting sum of internal
+ // stresses would exactly counter
+ // all external forces. Indeed, a
+ // simple experiment can make sure
+ // that this is so: if we choose
+ // boundary conditions and body
+ // forces to be time independent,
+ // then the forcing terms (the sum
+ // of external forces and internal
+ // stresses) should be exactly
+ // zero. If you make this
+ // experiment, you will realize
+ // from the output of the norm of
+ // the right hand side in each time
+ // step that this is almost the
+ // case: it is not exactly zero,
// since in the first time step the
- // incremental displacement and stress
- // updates were computed relative to the
- // undeformed mesh, which was then
- // deformed. In the second time step, we
- // again compute displacement and stress
- // updates, but this time in the deformed
- // mesh -- there, the resulting updates are
- // very small but not quite zero. This can
- // be iterated, and in each such iteration
- // the residual, i.e. the norm of the right
- // hand side vector, is reduced by
-
-//TODO: compute amount
+ // incremental displacement and
+ // stress updates were computed
+ // relative to the undeformed mesh,
+ // which was then deformed. In the
+ // second time step, we again
+ // compute displacement and stress
+ // updates, but this time in the
+ // deformed mesh -- there, the
+ // resulting updates are very small
+ // but not quite zero. This can be
+ // iterated, and in each such
+ // iteration the residual, i.e. the
+ // norm of the right hand side
+ // vector, is reduced; if one makes
+ // this little experiment, one
+ // realizes that the norm of this
+ // residual decays exponentially
+ // with the number of iterations,
+ // and after an initial very rapid
+ // decline is reduced by roughly a
+ // factor of about 3.5 in each
+ // iteration (for one testcase I
+ // looked at, other testcases, and
+ // other numbers of unknowns change
+ // the factor, but not the
+ // exponential decay).
// In a sense, this can then be considered
// as a quasi-timestepping scheme to