Index

Evolution parameters

Ver: 1
 

DESCRIPTION

Most non-linear problems require successive incrementations (or decrementation) of the parameters controlling the non-linearity.
Each iterative step starts from the solution obtained at the previous step, or from a solution extrapolated on the basis of previous solutions.

The evolution scheme establishes a relationship between the above parameters and a scalar variable S with a view to an automatic incremental procedure which involves:

- dependence upon the S variable (parameters, boundary conditions).
- a continuation scheme (0-order, 1-order, 2-order) in S.
- an incrementation or decrementation strategy.


A solution set is generated for each converged value of S.

Evolution parameters are data for the evolution scheme, but not for the S-dependence of each parameter of the simulation.

  OPTIONS
 
-1
 Upper level menu
1
 Modify the initial value of S
Sinit is the value of S corresponding to the initial condition.
The first solution will be evaluated at Sinit. 
Default : Sinit = 0
2
 Modify the upper limit of S
Sfin is the value of S corresponding to the final condition.
Default : Sfin = 1
3
 Modify the initial value of delta-S
dSinit is the value of delta-S at the first step.
After the first step, dS is dynamically adapted. 
Default : dSinit = 0.01
4
 Modify the min value of delta-S
The evolution algorithm stops when the current value of dS becomes smaller than dSmin.
Default : dSmin = 0.0001
5
 Modify the max value of delta-S
The largest step of deltat-S which can be used
#
 Modify the tolerance
Not relevant for evolution problems
7
 Modify the max number of successful steps
Default : 20 steps
8
 Use of 0-order prediction
No extrapolation.
9
 Use of the implicit Euler method
First order S-marching scheme based on :
Explicit Euler (pred.) - Implicit Euler (corr.).
This is the default scheme.
10
 Use of the Galerkin method
First order S-marching scheme based on :
Explicit Euler (pred.) -
(1/3 Expl. Euler + 2/3 Impl. Euler) (corr.).
11
 Use of the Crank-Nicholson method
Second order S-marching scheme based on :
Adams Bashforth (pred.) - Trapezoid (corr.).
NOTES Convergence of the fixed-S iteration governs the incremention or decrementation of S.
If convergence occurs, dS is multiplied by 1.5, upto dSmax.
If divergence occurs, dS is divided by 2.   SEE ALSO