Line Search
*Line Search, method [, default]
lambda_{min}, lambda_{max}, psi, n^{max}
In strongly nonlinear problems the Newton-Raphson solution technique,
which is used in numgeo
by default, may sometimes diverge during
equilibrium iterations. To handle such difficulties, a line search
algorithm is implemented in numgeo
to enhance the convergence of the
iterative method. The line search algorithm detects divergence and
applies a scale factor \(\lambda\) to the computed solution correction
(during the iterative refinement of one increment). The aim is to find a
better configuration which would help to overcome divergence. By
default, the line search algorithm is not enabled. The line search
procedure can be activated by using the command above. For more detailed
information on the implemented line search algorithm, the reader is
referred to the numgeo
Theory Manual.
-
method
Set this keyword equal to root finding method to be used in the line search algorithm. This parameter is mandatory. As root finding methods a "Regula Falsi" and a "Secant" method are available. To choose which one to use, set
method
toRegula-Falsi
,Secant
orLinear
respectively. In the subsequent line, the following parameter have to be specified:-
\(\lambda_{min}\): is the lower bound for the Line Search scaling factor
-
\(\lambda_{max}\): is the upper bound for the Line Search scaling factor
-
\(\psi\): is the stop criterion. Line Search stops if the interval in the root finding process is less than \(\psi\) times the initial energy (see the Theory Manual)
-
\(n^{max}\): is the maximum number of line searches in each global iteration
In case of the
Linear
line search approach, only \(\lambda_{min}\) and \(\lambda_{max}\) are required. -
-
default
Use this keyword to specify that the default values for the line search algorithm should be used. These are \(\lambda_{min}=0.25\), \(\lambda_{max}=1.25\), \(\psi = 0.8\) (\(\psi = 0.0\) in case of the
Linear
approach) and \(n^{max}=5\) (\(n^{max}=1\) in case of theLinear
approach). Note that ifdefault
is used, no subsequent line is required.
Line search is not only useful in situations where equilibrium is not achieved due to divergence, but it can also increase the convergence rate for the problems with slow convergence.