Calculated Reliability
Calculated results measured against the tolerance of a solver determine the reliability of a mathematical simulation. Maintaining numerical convergence stability requires selecting appropriate time steps and mesh densities for the calculation. A stable model arrives at a solution that remains consistent as the iteration progresses.
This condition fails if the solution oscillates or grows without bound due to mathematical errors in the mesh or the time integration.
Solver Performance
Maintaining this balance involves monitoring the residual errors at every step of the calculation. If the residuals do not decrease, the solver may be stuck in a local minimum or a divergent path.
A Stable
A stable simulation is one where small changes in the input parameters result in small and predictable changes in the output. High non-linearity in material models often challenges this stability by causing rapid changes in the stiffness matrix.
Monitoring Convergence
Monitoring the energy balance of the system provides a way to verify that no artificial energy is being created by the solver. If the internal energy deviates from the work done, the stability of the solution is compromised. Reliable convergence ensures that the final result is a true representation of the physical physics.
