Università degli Studi dell'Insubria Insubria Space
 

InsubriaSPACE - Thesis PhD Repository >
Insubria Thesis Repository >
01 - Tesi di dottorato >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10277/763

Authors: Turati, Valentina
Internal Tutor: DONATELLI, MARCO
Tutor: ROMANI, LUCIA
CHARINA, MARIA
Title: Multigrid methods and stationary subdivisions
Abstract: Multigridmethods are fast iterative solvers for sparse large ill-conditioned linear systems of equations derived, for instance, via discretization of PDEs in fluid dynamics, electrostatics and continuummechanics problems. Subdivision schemes are simple iterative algorithms for generation of smooth curves and surfaces with applications in 3D computer graphics and animation industry. This thesis presents the first definition and analysis of subdivision based multigrid methods. The main goal is to improve the convergence rate and the computational cost of multigrid taking advantage of the reproduction and regularity properties of underlying subdivision. The analysis focuses on the grid transfer operators appearing at the coarse grid correction step in the multigrid procedure. The convergence of multigrid is expressed in terms of algebraic properties of the trigonometric polynomial associated to the grid transfer operator. We interpreter the coarse-to-fine grid transfer operator as one step of subdivision. We reformulate the algebraic properties ensuring multigrid convergence in terms of regularity and generation properties of subdivision. The theoretical analysis is supported by numerical experiments for both algebraic and geometric multigrid. The numerical tests with the bivariate anisotropic Laplacian ask for subdivision schemes with anisotropic dilation. We construct a family of interpolatory subdivision schemes with such dilation which are optimal in terms of the size of the support versus their polynomial generation properties. The numerical tests confirmthe validity of our theoretical analysis.
Keywords: Multigrid, grid transfer operator, subdivision schem, anisotropic dilation
Subject MIUR : MAT/08 ANALISI NUMERICA
Issue Date: 2017
Language: eng
Doctoral course: Informatica e matematica del calcolo
Academic cycle: 30
Publisher: Università degli Studi dell'Insubria
Citation: Turati, V.Multigrid methods and stationary subdivisions (Doctoral Thesis, Università degli Studi dell'Insubria, 2017).

Files in This Item:

File Description SizeFormatVisibility
PhD_Thesis_TuratiValentina_completa.pdftesto completo tesi2,31 MBAdobe PDFView/Open

This item is licensed under a Creative Commons License
Creative Commons


Items in InsubriaSPACE are protected by copyright, with all rights reserved, unless otherwise indicated.


Share this record
Del.icio.us

Citeulike

Connotea

Facebook

Stumble it!

reddit


 

  ICT Support, development & maintenance are provided by the AePIC team @ CILEA. Powered on DSpace Software.  Feedback