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