Solver Fundamentals

The solver computes the unknown displacement vector from the assembled linear system:

K u = f

For linear static analysis, the solution is obtained once per load case unless multiple steps or parameter variations are specified. Direct solvers factorize the stiffness matrix, while iterative solvers approximate the solution through repeated updates.

Solver success depends on matrix conditioning, boundary conditions, element quality, material stiffness contrast, and numerical tolerances. Solver warnings should be reviewed carefully because they often indicate modeling issues rather than purely numerical issues.