Newmarksolver context

The <newmarksolver> context is used for everything related to the incremental solution of a dynamic systems of equations, based on Newmark time integration formulas.

Attributes:

• alpha - The Hilber-Hughes-Taylor alpha-parameter, α_H
• alpha1 - The mass-proportional damping factor, α₁
• alpha2 - The stiffness-proportional damping factor, α₂. If negative, it applies on material the stiffness only for nonlinear problems.
• beta - The Newmark parameter β. Default: β=0.25(1-α_H)².
• gamma - The Newmark parameter γ. Default: γ=0.5-α_H.
• rho_inf - The spectral radius at infinity, ρ_∞

If ρ_∞ is defined and not α_H, then α_H = (ρ_∞-1)/(ρ_∞+1).

The <newmarksolver> context can have the following sub-contexts:

<timestepping>

Use this to control everything related to the time stepping itself. See the Timestepping context page.

<maxits>

Use this to control the maximum number of Newton-Raphson iterations in a time step.

Attributes: None

Value: The maximum number of iterations

Example:

<maxits>10</maxits>

<rtol>

Use this to control the convergence tolerance.

Attributes: None

Value: The convergence tolerance, ε_tol (default 1.0e-6)

The nonlinear iterations are converged when δE = δuR < ε_tol E_ref where δu denotes the iterative solution vector, R is the associated force residual, and E_ref is the reference energy norm, typically δE evaluated in iteration 0 of the time step in question.

Example:

<rtol>1.0e-6</rtol>

<dtol>

Use this to control the divergence tolerance.

Attributes: None

Value: The divergence tolerance, ε_div (default 10.0)

The nonlinear iterations have diverged if δE > ε_divE_ref or if δE is increasing in three consecutive iterations. Iteration cut-back is then performed (if possible), or the simulation is terminated.

Example:

<dtol>1.0e3</dtol>

<referenceNorm>

Use this to specify how the reference norm used in the convergence check should be updated.

Attributed: None

Value: MAX (default) or ALL. If ALL, always use the energy norm of iteration 0 as reference in the subsequent iterations of that time step. If MAX, use the highest energy norm of the zero'th iteration detected so far, as reference norm in the next time step.

<predictor>

Use this to control the type of predictor to use.

Attributes: None

Value: Either "constant displacement", "constant velocity", or "zero acceleration".

Example:

<predictor>constant displacement</predictor>