Table 2 Summary of each example’s nonlinear solver scheme and initialization.
From: Enhancing high-fidelity nonlinear solver with reduced order model
Example 1 | Example 2 | Example 3 | Example 4 | |
|---|---|---|---|---|
Nonlinear solver | Newton iteration | PETSc SNES | Picard iteration | Newton iteration |
Linear solver | Direct solver | MUMPS | GMRES with multigrid | Direct solver |
Time characteristic | Steady-state | Steady-state | Transient | Transient |
Default initialization | \(\varvec{0}\) | \(\varvec{0}\) | \({\varvec{X}_h}\left( t^{n-1}, \varvec{\mu }^{(i)} \right)\) | \({\varvec{X}_h}\left( t^{n-1}, \varvec{\mu }^{(i)} \right)\) |
ROM-assisted | \(\widehat{\varvec{X}}_h\left( \varvec{\mu }^{(i)} \right)\) | \(\widehat{\varvec{X}}_h\left( \varvec{\mu }^{(i)} \right)\) | \(\widehat{\varvec{X}}_h\left( t^n, \varvec{\mu }^{(i)}\right)\) | \(\widehat{\varvec{X}}_h\left( t^n, \varvec{\mu }^{(i)}\right)\) |
