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Acceleration of nonlinear solvers for natural convection problems
- Source :
- Journal of Numerical Mathematics. 29:323-341
- Publication Year :
- 2021
- Publisher :
- Walter de Gruyter GmbH, 2021.
-
Abstract
- This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing the fixed point operator associated with the nonlinear iteration to prove that certain stability and regularity properties hold, we apply the authors’ recently constructed theory for Anderson acceleration, which yields a convergence result for the Anderson accelerated Picard iteration for the Boussinesq system. The result shows that the leading term in the residual is improved by the gain in the optimization problem, but at the cost of additional higher order terms that can be significant when the residual is large. We perform numerical tests that illustrate the theory, and show that a 2-stage choice of Anderson depth can be advantageous. We also consider Anderson acceleration applied to the Newton iteration for the Boussinesq equations, and observe that the acceleration allows the Newton iteration to converge for significantly higher Rayleigh numbers that it could without acceleration, even with a standard line search.
- Subjects :
- Numerical Analysis
Numerical Analysis (math.NA)
010103 numerical & computational mathematics
Fixed point
Residual
01 natural sciences
010101 applied mathematics
Computational Mathematics
Nonlinear system
symbols.namesake
Acceleration
Flow (mathematics)
Fixed-point iteration
Convergence (routing)
FOS: Mathematics
symbols
Applied mathematics
Mathematics - Numerical Analysis
0101 mathematics
Newton's method
Mathematics
Subjects
Details
- ISSN :
- 15693953 and 15702820
- Volume :
- 29
- Database :
- OpenAIRE
- Journal :
- Journal of Numerical Mathematics
- Accession number :
- edsair.doi.dedup.....d87f1f85f417fac8f96a958db59a39a2