Broyden Algorithm

The Broyden algorithm is a quasi-Newton method that builds an approximation to the inverse Jacobian matrix. It is a simpler alternative to the BFGS algorithm, using less memory but potentially with slower convergence.

Description

The Broyden algorithm: - Builds an approximation to the inverse Jacobian matrix - Updates the geometry and internal forces based on the displacement increment - Repeats until convergence is achieved - Uses a specified number of vectors to store the Jacobian approximation

Parameters

Parameter	Type	Description
`count`	int	Number of vectors to store the Jacobian approximation

Usage Example

# Create a Femora instance


# Create a Broyden algorithm with default settings
fm.analysis.algorithm.create_algorithm("Broyden", count=3)

# Create a Broyden algorithm with more vectors
fm.analysis.algorithm.create_algorithm("Broyden", count=5)

Notes

The Broyden algorithm is a quasi-Newton method
It does not require the computation of the tangent stiffness matrix
It uses less memory than the BFGS algorithm but may converge more slowly
The count parameter controls the memory usage and accuracy of the Jacobian approximation
A larger count value generally leads to better convergence but uses more memory