An efficient solver for space–time isogeometric Galerkin methods for parabolic problems. (1st December 2020)

• Record Type: Journal Article
• Authors: Loli, Gabriele; Montardini, Monica; Sangalli, Giancarlo; Tani, Mattia
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 11(2020)
• Page Start: 2586
• Page End: 2603
• Publication Date: 2020-12-01
• Subjects: Isogeometric analysis -- Splines -- Heat equation -- Space–time Galerkin formulation -- Fast diagonalization; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.09.014
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this work we focus on the preconditioning of a Galerkin space–time isogeometric discretization of the heat equation. Exploiting the tensor product structure of the basis functions in the parametric domain, we propose a preconditioner that is the sum of Kronecker products of matrices and that can be efficiently applied thanks to an extension of the classical Fast Diagonalization method. The preconditioner is robust w.r.t. the polynomial degree of the spline space and the time required for the application is almost proportional to the number of degrees-of-freedom, for a serial execution. By incorporating some information on the geometry parametrization and on the equation coefficients, we keep high efficiency with non-trivial domains and variable thermal conductivity and heat capacity coefficients.