A Robust Multigrid Solver for Isogeometric Analysis Based on Multiplicative Schwarz Smoothers

Pe de la Riva, Álvaro (Universidad de Zaragoza) ; Rodrigo, Carmen (Universidad de Zaragoza) ; Gaspar Lorenz, Francisco (Universidad de Zaragoza)

Resumen: The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of geometric multigrid methods to this type of discretization, and we propose a multigrid approach based on overlapping multiplicative Schwarz methods as smoothers. The size of the blocks considered within these relaxation procedures is adapted to the spline degree. A simple multigrid V-cycle with only one step of presmoothing results in a very efficient algorithm, whose convergence is independent on the spline degree and the spatial discretization parameter. Local Fourier analysis is shown to be very useful for the understanding of the problems encountered in the design of a robust multigrid method for IGA, and it is performed to support the good convergence properties of the proposed solver. In fact, an analysis for any spline degree and an arbitrary size of the blocks within the Schwarz smoother is presented for the one-dimensional case. The efficiency of the solver is also demonstrated through several numerical experiments, including a two-dimensional problem on a nontrivial computational domain.

Idioma: Inglés

DOI: 10.1137/18M1194407

Año: 2019

Publicado en: SIAM JOURNAL ON SCIENTIFIC COMPUTING 41, 5 (2019), S321–S345
ISSN: 1064-8275

Factor impacto JCR: 1.976 (2019)

Categ. JCR: MATHEMATICS, APPLIED rank: 47 / 260 = 0.181 (2019) - Q1 - T1

Factor impacto SCIMAGO: 1.928 - Computational Mathematics (Q1) - Applied Mathematics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R
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/MCYT-FEDER/MTM2016-75139-R

Tipo y forma: Artículo (Versión definitiva)

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