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