TY - GEN
T1 - A Multigrid Preconditioner for Jacobian-free Newton–Krylov Methods
AU - Kothari, Hardik
AU - Kopaničáková, Alena
AU - Krause, Rolf
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85151148988&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-95025-5_38
DO - 10.1007/978-3-030-95025-5_38
M3 - Conference contribution
AN - SCOPUS:85151148988
SN - 9783030950248
T3 - Lecture Notes in Computational Science and Engineering
SP - 365
EP - 372
BT - Domain Decomposition Methods in Science and Engineering XXVI
A2 - Brenner, Susanne C.
A2 - Klawonn, Axel
A2 - Xu, Jinchao
A2 - Chung, Eric
A2 - Zou, Jun
A2 - Kwok, Felix
PB - Springer Science and Business Media Deutschland GmbH
T2 - 26th International Conference on Domain Decomposition Methods, 2020
Y2 - 7 December 2020 through 12 December 2020
ER -