Quadratic Spline Wavelets with Short Support Satisfying Homogeneous Boundary Conditions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F18%3A00005664" target="_blank" >RIV/46747885:24510/18:00005664 - isvavai.cz</a>

Výsledek na webu

<a href="http://etna.mcs.kent.edu/volumes/2011-2020/vol48/abstract.php?vol=48&pages=15-39" target="_blank" >http://etna.mcs.kent.edu/volumes/2011-2020/vol48/abstract.php?vol=48&pages=15-39</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1553/etna_vol48s15" target="_blank" >10.1553/etna_vol48s15</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Quadratic Spline Wavelets with Short Support Satisfying Homogeneous Boundary Conditions

Popis výsledku v původním jazyce

In this paper, we construct a new quadratic spline-wavelet basis on the interval and on the unit square satisfying homogeneous Dirichlet boundary conditions of the first order. The wavelets have one vanishing moment and the shortest support among quadratic spline wavelets with at least one vanishing moment adapted to the same type of boundary conditions. The stiffness matrices arising from the discretization of the second-order elliptic problems using the constructed wavelet basis have uniformly bounded condition numbers, and the condition numbers are small. We present some quantitative properties of the constructed basis. We provide numerical examples to show that the Galerkin method and the adaptive wavelet method using our wavelet basis require fewer iterations than methods with other quadratic spline wavelet bases. Moreover, due to the small support of the wavelets, when using these methods with the new wavelet basis, the system matrix is sparser, and thus one iteration requires a smaller number of floating point operations than for other quadratic spline wavelet bases.

Název v anglickém jazyce

Quadratic Spline Wavelets with Short Support Satisfying Homogeneous Boundary Conditions

Popis výsledku anglicky

In this paper, we construct a new quadratic spline-wavelet basis on the interval and on the unit square satisfying homogeneous Dirichlet boundary conditions of the first order. The wavelets have one vanishing moment and the shortest support among quadratic spline wavelets with at least one vanishing moment adapted to the same type of boundary conditions. The stiffness matrices arising from the discretization of the second-order elliptic problems using the constructed wavelet basis have uniformly bounded condition numbers, and the condition numbers are small. We present some quantitative properties of the constructed basis. We provide numerical examples to show that the Galerkin method and the adaptive wavelet method using our wavelet basis require fewer iterations than methods with other quadratic spline wavelet bases. Moreover, due to the small support of the wavelets, when using these methods with the new wavelet basis, the system matrix is sparser, and thus one iteration requires a smaller number of floating point operations than for other quadratic spline wavelet bases.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS

ISSN

1068-9613

e-ISSN

—

Svazek periodika

48

Číslo periodika v rámci svazku

neuvedeno

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

25

Strana od-do

15-39

Kód UT WoS článku

000459295400002

EID výsledku v databázi Scopus

2-s2.0-85045282491