A Multilevel Nonlinear Method

SIAM JOURNAL ON SCIENTIFIC COMPUTING（2006）

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摘要

A multilevel nonlinear method (MNM) for the numerical solution of nonlinear partial differential equations is developed. The MNM algorithm is motivated and analyzed using a simplified model which retains the essential features of the new approach. It is thereby shown to combine the advantages of the two classical multigrid approaches to nonlinear problems. The analysis is supported by numerical tests for nonlinear differential equations in one and two dimensions.

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关键词

multigrid,nonlinear differential equation,multilevel nonlinear method,new approach,nonlinear partial differential equation,essential feature,numerical test,nonlinear partial differential equations,mnm algorithm,numerical methods for partial differential equations,classical multigrid approach,numerical solution,two dimensions,partial differential equation,numerical method

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