A comment on the article"The Schwarz alternating method in solid mechanics"by Alejandro Mota, Irina Tezaur and Coleman Alleman [Comput. Methods Appl. Mech. Engrg. 319 (2017) 1951]
A comment on the article"The Schwarz alternating method in solid mechanics"by Alejandro Mota, Irina Tezaur and Coleman Alleman [Comput. Methods Appl. Mech. Engrg. 319 (2017) 1951]
Marcin Ma'zdziarz
TLDR
Four variants of the Schwarz alternating method are developed and introduced, proof of geometric convergence of the method is presented, and parallel implementation applied to some examples.
Abstract
Recently, in the paper"The Schwarz alternating method in solid mechanics"by Alejandro Mota, Irina Tezaur and Coleman Alleman [Comput. Methods Appl. Mech. Engrg. 319 (2017) 1951] the authors extended the well known Schwarz alternating method from linear to finite-deformation solid mechanics. They developed and introduced four variants of the Schwarz alternating method, presented proof of geometric convergence of the method and prepared parallel implementation applied to some examples. Unfortunately, the work contains serious errors, both from the point of view of finite-deformation solid mechanics as well as mathematical elasticity.