| Autor: |
DALLAS, MATT, POLLOCK, SARA, REBHOLZ, LEO G. |
| Předmět: |
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| Zdroj: |
Advances in Computational Science & Engineering (ACSE); Sep2024, Vol. 2 Issue 3, p246-270, 25p |
| Abstrakt: |
The purpose of this paper is to develop a practical strategy to accelerate Newton's method in the vicinity of singular points. We present an adaptive safeguarding scheme with a tunable parameter, which we call adaptive γ-safeguarding, that one can use in tandem with Anderson acceleration to improve the performance of Newton's method when solving problems at or near singular points. The key features of adaptive γ-safeguarding are that it converges locally for singular problems, and it can detect nonsingular problems automatically, in which case the Newton-Anderson iterates are scaled towards a standard Newton step. The result is a flexible algorithm that performs well for singular and nonsingular problems, and can recover convergence from both standard Newton and Newton-Anderson with the right parameter choice. This leads to faster local convergence compared to both Newton's method, and Newton-Anderson without safeguarding, with effectively no additional computational cost. We demonstrate three strategies one can use when implementing Newton-Anderson and γ-safeguarded Newton-Anderson to solve parameterdependent problems near singular points. For our benchmark problems, we take two parameter-dependent incompressible flow systems: flow in a channel and Rayleigh-Bénard convection. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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