Modified Newton Algorithm
The Modified Newton algorithm is a variation of the Newton-Raphson method that uses the same tangent stiffness matrix for multiple iterations. This can be more efficient for problems where the tangent stiffness matrix is expensive to compute.
Description
The Modified Newton algorithm: - Uses the same tangent stiffness matrix for multiple iterations - Updates the geometry and internal forces based on the displacement increment - Repeats until convergence is achieved - Can optionally use initial stiffness or factor the matrix only once
Parameters
Parameter |
Type |
Description |
|---|---|---|
|
bool |
If True, uses the initial stiffness matrix for all iterations (default: False) |
|
bool |
If True, factors the matrix only once and reuses it (default: False) |
Usage Example
# Create a Femora instance
# Create a Modified Newton algorithm with default settings
fm.analysis.algorithm.create_algorithm("ModifiedNewton")
# Create a Modified Newton algorithm using initial stiffness
fm.analysis.algorithm.create_algorithm("ModifiedNewton", initial=True)
# Create a Modified Newton algorithm that factors the matrix only once
fm.analysis.algorithm.create_algorithm("ModifiedNewton", factor_once=True)
Notes
The Modified Newton algorithm is generally less efficient than the standard Newton algorithm
It can be more efficient for problems where the tangent stiffness matrix is expensive to compute
It may require more iterations to converge than the standard Newton algorithm
The
initialandfactor_onceoptions can be used together