- journal article metadata
European Mathematical Society Publishing House
2018-02-05 23:30:02
Journal of Spectral Theory
J. Spectr. Theory
JST
1664-039X
1664-0403
Quantum theory
10.4171/JST
http://www.ems-ph.org/doi/10.4171/JST
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
8
2018
1
Spectral distribution of PDE discretization matrices from isogeometric analysis: the case of $L^1$ coefficients and non-regular geometry
Carlo
Garoni
Università di Roma "Tor Vergata", Italy and Università degli Studi dell’Insubria, Como, Italy
GLT sequences, spectral distribution, symbol, $L^1$ PDE coefficients, non-regular geometry, PDE discretization matrices, IgA, trace-norm
We consider the matrices arising from the Galerkin B-spline Isogeometric Analysis (IgA) approximation of a $d$-dimensional second-order Partial Di fferential Equation (PDE). We compute the singular value and eigenvalue distribution of these matrices under minimal assumptions on the PDE coeffi cients and the geometry map involved in the IgA discretization. In particular, $L^1$ coe fficients 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.
Partial differential equations
Linear and multilinear algebra; matrix theory
Numerical analysis
297
313
10.4171/JST/197
http://www.ems-ph.org/doi/10.4171/JST/197
2
2
2018