Linear Algorithm

The Linear algorithm is a simple solution algorithm that performs just one iteration to solve the system of equations. It is suitable for linear problems or as a single-iteration approach in nonlinear problems.

Description

The Linear algorithm: - Solves the system of equations in one iteration - Can use either the initial or current stiffness matrix - Can optionally factor the stiffness matrix only once - Does not iterate to convergence, making it suitable only for linear or linearized problems

Parameters

Parameter	Type	Description
`initial`	bool	If True, uses the initial stiffness matrix (default: False)
`factor_once`	bool	If True, only sets up and factors the matrix once (default: False)

Usage Example

# Create a Femora instance


# Create a Linear algorithm with default settings
fm.analysis.algorithm.create_algorithm("Linear")

# Create a Linear algorithm using initial stiffness
fm.analysis.algorithm.create_algorithm("Linear", initial=True)

# Create a Linear algorithm that factors the matrix only once
fm.analysis.algorithm.create_algorithm("Linear", factor_once=True)

# Create a Linear algorithm with both options
fm.analysis.algorithm.create_algorithm("Linear", initial=True, factor_once=True)

Notes

The Linear algorithm is the simplest and fastest algorithm
It is only suitable for linear problems or for specific nonlinear analysis approaches
It does not iterate to convergence
The initial option uses the initial stiffness matrix for all time steps
The factor_once option can improve performance by factoring the matrix only once