Numeric Libraries

Solution Algorithms

Iteration from the last time step to the current is done by the following methods

• Linear – Uses the solution at the first iteration and continues
• Newton – Uses the tangent at the current iteration to iterate to convergence
• Modified Newton – Uses the tangent at the first iteration to iterate to convergence

Convergence Tests

Accepting the current state of the domain as being on the converged solution path is accomplished by the following tests

• Norm Unbalance – Specifies a tolerance on the norm of the unbalanced load at the current iteration
• Norm Displacement Increment – Specifies a tolerance on the norm of the displacement increments at the current iteration
• Energy Increment – Specifies a tolerance on the inner product of the unbalanced load and displacement increments at the current iteration

Constraint Handlers

The constraints defined on the domain can be handled by the following methods

• Plain – Removes constrained degrees of freedom from the system of equations
• Lagrange – Uses the method of Lagrange multipliers to enforce constraints
• Penalty – Uses penalty numbers to enforce constraints
• Transformation – Performs a condensation of constrained degrees of freedom