Space-time parallel solvers for reaction-diffusion problems forming Turing patterns

Arrarás, Andrés ; Gaspar, Francisco J. (Universidad de Zaragoza) ; Jimenez-Ciga, Iñigo ; Portero, Laura

Resumen: In 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.

Idioma: Inglés

DOI: 10.1016/j.apnum.2025.07.012

Año: 2025

Publicado en: APPLIED NUMERICAL MATHEMATICS 218 (2025), 91-108
ISSN: 0168-9274

Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2019-105574GB-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2022-140108NB-I00

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)