BFGS Algorithm

The BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm is a quasi-Newton method that builds an approximation to the inverse Hessian matrix. It is particularly useful for problems where the tangent stiffness matrix is difficult to compute.

Description

The BFGS algorithm: - Builds an approximation to the inverse Hessian 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 Hessian approximation

Parameters

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

Usage Example

# Create a Femora instance


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

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

Notes

The BFGS algorithm is a quasi-Newton method
It does not require the computation of the tangent stiffness matrix
It can be more efficient for problems where the tangent stiffness matrix is difficult to compute
The count parameter controls the memory usage and accuracy of the Hessian approximation
A larger count value generally leads to better convergence but uses more memory