A Multigrid Preconditioner for Jacobian-free Newton–Krylov Methods

The numerical solution of partial differential equations (PDEs) is often carried out using discretization techniques, such as the finite element method (FEM), and typically requires the solution of a nonlinear system of equations. These nonlinear systems are often solved using some variant of the Newton method, which utilizes a sequence of iterates generated by solving a linear system of equations. However, for problems such as inverse problems, optimal control problems, or higher-order coupled PDEs, it can be computationally expensive, or even impossible to assemble a Jacobian matrix.

Authors and Affiliations

1. Euler Institute, Università della Svizzera italiana, Lugano, Switzerland

   Hardik Kothari, Alena Kopaničáková & Rolf Krause

Corresponding author

Correspondence to Hardik Kothari .

Editors and Affiliations

1. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, USA

   Susanne C. Brenner

2. Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, China

   Eric Chung

3. Department Mathematik/Informatik, Abteilung Mathematik, Universität zu Köln, Köln, Germany

   Axel Klawonn

4. Département de mathématiques et de statistique, Université Laval, Québec, QC, Canada

   Felix Kwok

5. Department of Mathematics, Pennsylvania State University, University Park, PA, USA

   Jinchao Xu

6. Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, China

   Jun Zou

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