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The study aims to improve the computational cost and convergence rate of nonlinear solvers using reduced order modeling.

November 23, 2022Scientific ReportsOpen Access

Enhancing high-fidelity nonlinear solver with reduced order model

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Randomized trial demonstrates improved convergence in nonlinear solvers, suggesting wide applicability in physics-based problems.

The study aims to improve the computational cost and convergence rate of nonlinear solvers using reduced order modeling.
Developed a novel ROM-assisted approach to enhance nonlinear solvers for FOMs.
Tested on four physical problems with different nonlinearities: Richards' equation, a hyperelastic material contact problem, two-phase flow, and fracture propagation.
Evaluated the impact of ROM's predictions as initial guesses on the solver's performance.
The approach improved the convergence speed of FOM nonlinear solvers by 18-73%.
Using closer ROM predictions to real solutions enhanced convergence for solvers that might diverge otherwise.
The methodology is adaptable to various FOM discretizations, maintaining accuracy while reducing computational costs.

Kadeethum et al. (2022) studied this question.

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