Least-squares spectral element preconditioners for fourth order elliptic problems

• Verfasst von: Husain, Akhlaq [VerfasserIn]
• Verfasst von: Khan, Arbaz [VerfasserIn]
• Titel: Least-squares spectral element preconditioners for fourth order elliptic problems
• Verf.angabe: Akhlaq Husain, Arbaz Khan
• E-Jahr: 2017
• Jahr: 1 August 2017
• Umfang: 22 S.
• Teil: volume:74
• Teil: year:2017
• Teil: number:3
• Teil: pages:482-503
• Teil: extent:22
• Fussnoten: Available online: 25 May 2017 ; Gesehen am 09.10.2018
• Titel Quelle: Enthalten in: Computers and mathematics with applications
• Ort Quelle: Amsterdam [u.a.] : Elsevier Science, 1975
• Jahr Quelle: 2017
• Band/Heft Quelle: 74(2017), 3, Seite 482-503
• ISSN Quelle: 1873-7668
• DOI: doi:10.1016/j.camwa.2017.04.032
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Condition number
• Sach-SW: Fourth order problems
• Sach-SW: Preconditioners
• Sach-SW: Separation of variables
• Sach-SW: Spectral element method
• Sach-SW: Spectral equivalence
• K10plus-PPN: 1581692005

Abstract

In this paper, we propose preconditioners for the system of linear equations that arise from a discretization of fourth order elliptic problems in two and three dimensions (d=2,3) using spectral element methods. These preconditioners are constructed using separation of variables and can be diagonalized and hence easy to invert. For second order elliptic problems this technique has proven to be successful and performs better than other preconditioners in the framework of least-squares methods. We show that these preconditioners are spectrally equivalent to the quadratic forms by which we approximate them. Numerical results for the condition number reflects the effectiveness of the preconditioners.