Spectral distribution of PDE discretization matrices from isogeometric analysis: the case of \(L^1\) coefficients and non-regular geometry
type: Item
instance of: scholarly article
title: Spectral distribution of PDE discretization matrices from isogeometric analysis: the case of \(L^1\) coefficients and non-regular geometry
zbMATH Open document ID: 1390.35211
DOI: 10.4171/JST/197
author: Carlo Garoni
published in: Journal of Spectral Theory
publication date: 2018-03-23T00:00:00Z
review text: Summary: We consider the matrices arising from the Galerkin B-spline Isogeometric Analysis (IgA) approximation of a \(d\)-dimensional second-order Partial Differential Equation (PDE). We compute the singular value and eigenvalue distribution of these matrices under minimal assumptions on the PDE coefficients and the geometry map involved in the IgA discretization. In particular, \(L^1\) coefficients and non-regular geometries are allowed. The mathematical technique used in our derivation is entirely based on the theory of Generalized Locally Toeplitz (GLT) sequences, which is a quite general technique that can also be applied to several other PDE discretization methods.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 15B05
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 6852564
zbMATH Keywords: GLT sequences
zbMATH Keywords: spectral distribution
zbMATH Keywords: symbol
zbMATH Keywords: \(L^1\) PDE coefficients
zbMATH Keywords: non-regular geometry
zbMATH Keywords: PDE discretization matrices
zbMATH Keywords: IgA
zbMATH Keywords: trace-norm
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6852564