On an Uzawa smoother in multigrid for poroelasticity equations

Luo, P. ; Rodrigo, C. (Universidad de Zaragoza) ; Gaspar, F.J. (Universidad de Zaragoza) ; Oosterlee, C.W.

Resumen: A poroelastic saturated medium can be modeled by means of Biot''s theory of consolidation. It describes the time-dependent interaction between the deformation of porous material and the fluid flow inside of it. Here, for the efficient solution of the poroelastic equations, a multigrid method is employed with an Uzawa-type iteration as the smoother. The Uzawa smoother is an equation-wise procedure. It shall be interpreted as a combination of the symmetric Gauss-Seidel smoothing for displacements, together with a Richardson iteration for the Schur complement in the pressure field. The Richardson iteration involves a relaxation parameter which affects the convergence speed, and has to be carefully determined. The analysis of the smoother is based on the framework of local Fourier analysis (LFA) and it allows us to provide an analytic bound of the smoothing factor of the Uzawa smoother as well as an optimal value of the relaxation parameter. Numerical experiments show that our upper bound provides a satisfactory estimate of the exact smoothing factor, and the selected relaxation parameter is optimal. In order to improve the convergence performance, the acceleration of multigrid by iterant recombination is taken into account. Numerical results confirm the efficiency and robustness of the acceleration scheme.

Idioma: Inglés

DOI: 10.1002/nla.2074

Año: 2017

Publicado en: NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 24, 1 (2017), e2074 [14 pp]
ISSN: 1070-5325

Factor impacto JCR: 1.281 (2017)

Categ. JCR: MATHEMATICS rank: 39 / 309 = 0.126 (2017) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 81 / 252 = 0.321 (2017) - Q2 - T1

Factor impacto SCIMAGO: 1.104 - Applied Mathematics (Q1) - Algebra and Number Theory (Q1)

Financiación: info:eu-repo/grantAgreement/EC/H2020/705402/EU/Efficient numerical methods for deformable porous media. Application to carbon dioxide storage./poro sos
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2013-40842-P

Tipo y forma: Article (Published version)

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