0436705 20240103205237.720150121235959.9 84910649502 000347877900084 10.1007/978-3-319-05789-7_84 9 s. P cav_un_epca*0439880978-3-319-05788-0869-877ChamSpringer2014 domain decompositiond nonlinear partial differential equations Newton–Krylov method cav_un_auth*0289253 Turner J. GB cav_un_auth*0101131 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Kočvara Michal UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0313203 Loghin D. GB http://library.utia.cas.cz/separaty/2014/MTR/kocvara-0436705.pdf cav_un_auth*0241214 IAA100750802 GA AV ČR 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. cav_un_auth*0313204 Domain Decomposition Methods 2012 /21./ 25.06.2012-29.06.2012 Le Chesnay Cedex FR BA 2015 3 PR RVO:67985556 http://hdl.handle.net/11104/0243058 S 2014 84910649502 SCOPUS 000347877900084 WOS cav_un_epca*0439880 Domain Decomposition Methods in Science and Engineering XXI 978-3-319-05788-0 869 877 Cham Springer 2014 Lecture Notes in Computational Science and Engineering 98