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An Accelerated Method for Nonlinear Elliptic PDE

Schaeffer, Hayden and Hou, Thomas Y. (2016) An Accelerated Method for Nonlinear Elliptic PDE. Journal of Scientific Computing, 69 (2). pp. 556-580. ISSN 0885-7474. http://resolver.caltech.edu/CaltechAUTHORS:20161103-105632603

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Abstract

We propose two numerical methods for accelerating the convergence of the standard fixed point method associated with a nonlinear and/or degenerate elliptic partial differential equation. The first method is linearly stable, while the second is provably convergent in the viscosity solution sense. In practice, the methods converge at a nearly linear complexity in terms of the number of iterations required for convergence. The methods are easy to implement and do not require the construction or approximation of the Jacobian. Numerical examples are shown for Bellman’s equation, Isaacs’ equation, Pucci’s equations, the Monge–Ampère equation, a variant of the infinity Laplacian, and a system of nonlinear equations.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s10915-016-0215-8DOIArticle
http://link.springer.com/article/10.1007%2Fs10915-016-0215-8PublisherArticle
http://rdcu.be/tsZ9PublisherFree ReadCube access
Additional Information:© 2016 Springer Science+Business Media New York.
Subject Keywords:Nonlinear elliptic PDE; Degenerate elliptic PDE; Accelerated convergence; Elliptic systems; Finite difference methods; Viscosity solutions; Fixed point methods
Classification Code:Mathematics Subject Classification: 65B05; 65N06; 65M22; 49L25; 35J60; 35B51; 35J70
Record Number:CaltechAUTHORS:20161103-105632603
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161103-105632603
Official Citation:Schaeffer, H. & Hou, T.Y. J Sci Comput (2016) 69: 556. doi:10.1007/s10915-016-0215-8
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71705
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 Nov 2016 18:08
Last Modified:14 Jun 2017 18:00

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