Modified Newton Algorithm: Difference between revisions
No edit summary |
No edit summary |
||
| Line 9: | Line 9: | ||
{| | {| | ||
| style="width:150px" | '''-initial''' || optional flag to indicate using initial stiffness iterations | | style="width:150px" | '''-initial''' || optional flag to indicate using initial stiffness iterations. | ||
|} | |} | ||
| Line 39: | Line 39: | ||
The advantage of this method over the regular Newton method, is that the system Jacobian is formed only once at the start of the step and factored only once if a direct solver is used. The drawback of this method is that it requires more iterations than Newton's method. | The advantage of this method over the regular Newton method, is that the system Jacobian is formed only once at the start of the step and factored only once if a direct solver is used. The drawback of this method is that it requires more iterations than Newton's method. | ||
note: when -initial flag is provided <math>K_0</math> is Jacobian from undeformed configuration. | |||
---- | ---- | ||
Code Developed by: <span style="color:blue"> fmk </span> | Code Developed by: <span style="color:blue"> fmk </span> | ||
Revision as of 22:49, 3 March 2010
- Command_Manual
- Tcl Commands
- Modeling_Commands
- model
- uniaxialMaterial
- ndMaterial
- frictionModel
- section
- geometricTransf
- element
- node
- sp commands
- mp commands
- timeSeries
- pattern
- mass
- block commands
- region
- rayleigh
- Analysis Commands
- Output Commands
- Misc Commands
- DataBase Commands
This command is used to construct a ModifiedNewton algorithm object, which uses the modified newton algorithm to solve the nonlinear residual equation. The command is of the following form:
| algorithm ModifiedNewton <-initial> |
| -initial | optional flag to indicate using initial stiffness iterations. |
NOTES:
REFERENCES:
THEORY:
The theory for the ModifiedNewton method is similar to that for the Newton-Raphson method. The difference is that the tangent at the initial guess is used in the iterations, instead of the current tangent. The Modified Newmark method is thus an iterative method in which, starting at a good initial guess <math>U_0</math> we keep iterating until <math>\Delta U</math> is small enough using the following:
- <math> \Delta U = - K_0^{-1}R(U_n),\!</math>
- <math> U_{n+1} = U_n + \Delta U\,\!</math>
where:
- <math>K_0 = \frac{\partial R(U_0)}{\partial U}\,\!</math>
The advantage of this method over the regular Newton method, is that the system Jacobian is formed only once at the start of the step and factored only once if a direct solver is used. The drawback of this method is that it requires more iterations than Newton's method.
note: when -initial flag is provided <math>K_0</math> is Jacobian from undeformed configuration.
Code Developed by: fmk