Overlapping Additive Schwarz (OAS) preconditioners are here constructed for isogeometric collocation discretizations of the system of linear elasticity in both two and three space dimensions. Isogeometric collocation methods are recent variants of isogeometric analysis based on the numerical approximation of the strong form of partial differential equations at appropriate collocation points. Numerical results in two and three dimensions show that two-level OAS preconditioners are scalable in the number of subdomains N, quasi-optimal with respect to the mesh size h and optimal with respect to the spline polynomial degree p. Moreover, two-level OAS preconditioners are more robust than one-level OAS and non-preconditioned GMRES solvers when the material tends to the incompressible limit, as well as in the presence of strong deformation of the NURBS geometry.

Overlapping Additive Schwarz preconditioners for isogeometric collocation discretizations of linear elasticity / D. Cho, L.F. Pavarino, S. Scacchi. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - 93(2021), pp. 66-77. [10.1016/j.camwa.2021.04.007]

Overlapping Additive Schwarz preconditioners for isogeometric collocation discretizations of linear elasticity

D. Cho
;
L.F. Pavarino;S. Scacchi
2021

Abstract

Overlapping Additive Schwarz (OAS) preconditioners are here constructed for isogeometric collocation discretizations of the system of linear elasticity in both two and three space dimensions. Isogeometric collocation methods are recent variants of isogeometric analysis based on the numerical approximation of the strong form of partial differential equations at appropriate collocation points. Numerical results in two and three dimensions show that two-level OAS preconditioners are scalable in the number of subdomains N, quasi-optimal with respect to the mesh size h and optimal with respect to the spline polynomial degree p. Moreover, two-level OAS preconditioners are more robust than one-level OAS and non-preconditioned GMRES solvers when the material tends to the incompressible limit, as well as in the presence of strong deformation of the NURBS geometry.
Collocation methods; Domain decomposition methods; Isogeometric analysis; Linear elasticity; Overlapping Schwarz; Scalable preconditioners
Settore MAT/08 - Analisi Numerica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/869791
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