Parameter-robust preconditioners for Biot’s model

Rodrigo, Carmen (Universidad de Zaragoza) ; Gaspar, Francisco J. (Universidad de Zaragoza) ; Adler, James ; Hu, Xiaozhe ; Ohm, Peter ; Zikatanov, Ludmil

Resumen: This work presents an overview of the most relevant results obtained by the authors regarding the numerical solution of the Biot’s consolidation problem by preconditioning techniques. The emphasis here is on the design of parameter-robust preconditioners for the efficient solution of the algebraic system of equations resulting after proper discretization of such poroelastic problems. The classical two- and three-field formulations of the problem are considered, and block preconditioners are presented for some of the discretization schemes that have been proposed by the authors for these formulations. These discretizations have been proved to be well-posed with respect to the physical and discretization parameters, what provides a framework to develop preconditioners that are robust with respect to such parameters as well. In particular, we construct both norm-equivalent (block diagonal) and field-of-value-equivalent (block triangular) preconditioners, which are proved to be parameter-robust. The theoretical results on this parameter-robustness are demonstrated by considering typical benchmark problems in the literature for Biot’s model.

Idioma: Inglés

DOI: 10.1007/s40324-023-00336-2

Año: 2024

Publicado en: SEMA Journal 81, 1 (2024), 51-80
ISSN: 2254-3902

Factor impacto CITESCORE: 3.3 - Applied Mathematics (Q2) - Control and Optimization (Q2) - Modeling and Simulation (Q2) - Numerical Analysis (Q2)

Factor impacto SCIMAGO: 0.516 - Applied Mathematics (Q2) - Numerical Analysis (Q2) - Modeling and Simulation (Q2) - Control and Optimization (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/MCIU-AEI-FEDER/PGC2018-099536-A-I00
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2019-105574GB-I00

Tipo y forma: Article (Published version)

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