TY - JOUR
T1 - A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation
AU - Caboussat, Alexandre
AU - Glowinski, Roland
AU - Gourzoulidis, Dimitrios
N1 - Open access funding provided by University of Applied Sciences and Arts Western Switzerland (HES-SO) This work was supported by the Swiss National Science Foundation (Grant Number 165785). Roland Glowinski has received research support from the Hong Kong based Kennedy Wong Foundation.
This work was partially funded by the Swiss National Science Foundation (Grant Number 165785), and by the Hong Kong based Kennedy Wong Foundation.
Publisher Copyright:
© 2022, The Author(s).
PY - 2022/8/24
Y1 - 2022/8/24
N2 - We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares problem into a sequence of local nonlinear problems and variational linear problems. We develop dedicated solvers for the algebraic problems based on Newton’s method and we solve the differential problems using mixed low-order finite elements. Various numerical experiments demonstrate the accuracy, efficiency and the robustness of the proposed method, compared for instance to augmented Lagrangian approaches.
AB - We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares problem into a sequence of local nonlinear problems and variational linear problems. We develop dedicated solvers for the algebraic problems based on Newton’s method and we solve the differential problems using mixed low-order finite elements. Various numerical experiments demonstrate the accuracy, efficiency and the robustness of the proposed method, compared for instance to augmented Lagrangian approaches.
KW - Biharmonic regularization
KW - Finite element method
KW - Jacobian determinant
KW - Least-squares method
KW - Newton methods
KW - Nonlinear constrained minimization
UR - http://www.scopus.com/inward/record.url?scp=85137062243&partnerID=8YFLogxK
UR - https://link.springer.com/article/10.1007/s10915-022-01968-8#article-info
U2 - 10.1007/s10915-022-01968-8
DO - 10.1007/s10915-022-01968-8
M3 - Journal article
AN - SCOPUS:85137062243
SN - 0885-7474
VL - 93
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 1
M1 - 15
ER -
