A Nonlinear Domain Decomposition Technique for Scalar Elliptic PDEs

0436705 - ÚTIA 2015 RIV CH eng C - Conference Paper (international conference)
Turner, J. - Kočvara, Michal - Loghin, D.
A Nonlinear Domain Decomposition Technique for Scalar Elliptic PDEs.
Domain Decomposition Methods in Science and Engineering XXI. Cham: Springer, 2014, s. 869-877. Lecture Notes in Computational Science and Engineering, 98. ISBN 978-3-319-05788-0.
[Domain Decomposition Methods 2012 /21./. Le Chesnay Cedex (FR), 25.06.2012-29.06.2012]
R&D Projects: GA AV ČR IAA100750802
Institutional support: RVO:67985556
Keywords : domain decompositiond * nonlinear partial differential equations * Newton–Krylov method
Subject RIV: BA - General Mathematics
http://library.utia.cas.cz/separaty/2014/MTR/kocvara-0436705.pdf

Nonlinear problems are ubiquitous in a variety of areas, including fluid dynamics, biomechanics, viscoelasticity and finance, to name a few. A number of computational methods exist already for solving such problems, with the general approach being Newton-Krylov type methods coupled with an appropriate preconditioner. However, it is known that the strongest nonlinearity in a domain can directly impact the convergence of Newton-type algorithms. Therefore, local nonlinearities may have a direct impact on the global convergence of Newton’s method, as illustrated in both [3] and [5]. Consequently, Newton-Krylov approaches can be expected to struggle when faced with domains containing local nonlinearities.
Permanent Link: http://hdl.handle.net/11104/0243058