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A monolithic homotopy continuation algorithm with application to computational fluid dynamics
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DOI：10.1016/j.jcp.2016.05.031.png)
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摘要
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A new class of homotopy continuation methods is developed suitable for globalizing quasi-Newton methods for large sparse nonlinear systems of equations. The new continuation methods, described as monolithic homotopy continuation, differ from the classical predictor-corrector algorithm in that the predictor and corrector phases are replaced with a single phase which includes both a predictor and corrector component. Conditional convergence and stability are proved analytically. Using a Laplacian-like operator to construct the homotopy, the new algorithm is shown to be more efficient than the predictor-corrector homotopy continuation algorithm as well as an implementation of the widely-used pseudo-transient continuation algorithm for some inviscid and turbulent, subsonic and transonic external aerodynamic flows over the ONERA M6 wing and the NACA 0012 airfoil using a parallel implicit Newton-Krylov finite-difference flow solver. (C) 2016 Elsevier Inc. All rights reserved.
Keyword:
Homotopy
Continuation
Globalization
Newton-Krylov
Computational fluid dynamics
期刊
IF:
3.8
论文数:
1.6W
被引数:
7.4W
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