A multigrid scheme for 3D Monge–Ampère equations*

Document Type

Article

Publication Date

9-2-2017

Abstract

The elliptic Monge–Ampère equation is a fully nonlinear partial differential equation which has been the focus of increasing attention from the scientific computing community. Fast three-dimensional solvers are needed, for example in medical image registration but are not yet available. We build fast solvers for smooth solutions in three dimensions using a nonlinear full-approximation storage multigrid method. Starting from a second-order accurate centred finite difference approximation, we present a nonlinear Gauss–Seidel iterative method which has a mechanism for selecting the convex solution of the equation. The iterative method is used as an effective smoother, combined with the full-approximation storage multigrid method. Numerical experiments are provided to validate the accuracy of the finite difference scheme and illustrate the computational efficiency of the proposed multigrid solver.

Identifier

84996558197 (Scopus)

Publication Title

International Journal of Computer Mathematics

External Full Text Location

https://doi.org/10.1080/00207160.2016.1247443

e-ISSN

10290265

ISSN

00207160

First Page

1850

Last Page

1866

Issue

9

Volume

94

Grant

1419028

Fund Ref

National Science Foundation

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