000163135 001__ 163135
000163135 005__ 20251009145936.0
000163135 0247_ $$2doi$$a10.1016/j.apnum.2025.07.012
000163135 0248_ $$2sideral$$a145618
000163135 037__ $$aART-2025-145618
000163135 041__ $$aeng
000163135 100__ $$aArrarás, Andrés
000163135 245__ $$aSpace-time parallel solvers for reaction-diffusion problems forming Turing patterns
000163135 260__ $$c2025
000163135 5060_ $$aAccess copy available to the general public$$fUnrestricted
000163135 5203_ $$aIn recent years, parallelization has become a strong tool to avoid the limits of classical sequential computing. In the present paper, we introduce four space-time parallel methods that combine the parareal algorithm with suitable splitting techniques for the numerical solution of reaction-diffusion problems. In particular, we consider a suitable partition of the elliptic operator that enables the parallelization in space by using splitting time integrators. Those schemes are then chosen as the propagators of the parareal algorithm, a well-known parallel-in-time method. Both first- and second-order time integrators are considered for this task. The resulting space-time parallel methods are applied to integrate reaction-diffusion problems that model Turing pattern formation. This phenomenon appears in chemical reactions due to diffusion-driven instabilities, and rules the pattern formation for animal coat markings. Such reaction-diffusion problems require fine space and time meshes for their numerical integration, so we illustrate the usefulness of the proposed methods by solving several models of practical interest.
000163135 536__ $$9info:eu-repo/grantAgreement/ES/MCIU/PID2019-105574GB-I00$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-140108NB-I00
000163135 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
000163135 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000163135 700__ $$0(orcid)0000-0002-9777-5245$$aGaspar, Francisco J.$$uUniversidad de Zaragoza
000163135 700__ $$aJimenez-Ciga, Iñigo
000163135 700__ $$aPortero, Laura
000163135 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000163135 773__ $$g218 (2025), 91-108$$pAppl. numer. math.$$tAPPLIED NUMERICAL MATHEMATICS$$x0168-9274
000163135 8564_ $$s2133007$$uhttps://zaguan.unizar.es/record/163135/files/texto_completo.pdf$$yVersión publicada
000163135 8564_ $$s1898421$$uhttps://zaguan.unizar.es/record/163135/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000163135 909CO $$ooai:zaguan.unizar.es:163135$$particulos$$pdriver
000163135 951__ $$a2025-10-08-12:59:53
000163135 980__ $$aARTICLE