A two-level method for isogeometric discretizations based on multiplicative Schwarz iterations

Pé de la Riva, Álvaro (Universidad de Zaragoza) ; Rodrigo, Carmen (Universidad de Zaragoza) ; Gaspar, Francisco J. (Universidad de Zaragoza)

Resumen: Isogeometric Analysis (IGA) is a computational technique for the numerical approximation of partial differential equations (PDEs). This technique is based on the use of spline-type basis functions, that are able to hold a global smoothness and allow to exactly capture a wide set of common geometries. The current rise of this approach has encouraged the search of fast solvers for isogeometric discretizations and nowadays this topic is receiving a lot of attention. In this framework, a desired property of the solvers is the robustness with respect to both the polynomial degree p and the mesh size h. For this task, in this paper we propose a two-level method such that a discretization of order p is considered in the first level whereas the second level consists of a linear or quadratic discretization. On the first level, we suggest to apply one single iteration of a multiplicative Schwarz method. The choice of the block-size of such an iteration depends on the spline degree p, and is supported by a local Fourier analysis (LFA). At the second level one is free to apply any given strategy to solve the problem exactly. However, it is also possible to get an approximation of the solution at this level by using an h-multigrid method. The resulting solver is efficient and robust with respect to the spline degree p. Finally, some numerical experiments are given in order to demonstrate the good performance of the proposed solver.

Idioma: Inglés

DOI: 10.1016/j.camwa.2021.08.020

Año: 2021

Publicado en: COMPUTERS & MATHEMATICS WITH APPLICATIONS 100 (2021), 41-50
ISSN: 0898-1221

Factor impacto JCR: 3.218 (2021)

Categ. JCR: MATHEMATICS, APPLIED rank: 25 / 267 = 0.094 (2021) - Q1 - T1

Factor impacto CITESCORE: 6.4 - Mathematics (Q1) - Computer Science (Q1)

Factor impacto SCIMAGO: 0.984 - Modeling and Simulation (Q1) - Computational Theory and Mathematics (Q1)

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)