Kubični Clough-Tocherjevi zlepki

magistrsko delo

Katarina Stupica (Author), Marjetka Krajnc (Mentor)

Abstract

V nalogi opišemo prostor kubičnih Clough-Tocherjevih zlepkov nad triangulacijo domene, pri čemer vsak trikotnik iz triangulacije z izbiro delilne točke razdelimo na tri manjše. Nad vsakim trikotnikom želimo dobiti kubični polinom, nad celotno triangulacijo pa ${\cal C}^1$ zlepek. Zanimal nas bo poseben podprostor tega prostora, prostor zreduciranih Clough-Tocherjevih zlepkov, za katerega lahko konstruiramo normalizirano bazo. Bazni zlepki imajo lokalni nosilec, so nenegativni in tvorijo particijo enote. Iskanje baze lahko prevedemo na geometrijski problem iskanja množice trikotnikov, ki morajo vsebovati določen nabor točk. To nas pripelje do strukture kontrolnih trikotnikov in stabilnega računanja zreduciranih Clough-Tocherjevih zlepkov.

Keywords

matematika;Clough-Tocherjevi zlepki;B zlepki;makro-elementi;določitvene množice;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[K. Stupica]
UDC:	519.6
COBISS:	18474329
Views:	681
Downloads:	229
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Cubic Clough-Tocher splines
Secondary abstract:	In this thesis we present the Clough-Tocher space of cubic splines on a triangulation, where we make a refinement of the triangulation by splitting each triangle on three smaller ones. The spline is composed of cubic polynomials over each triangle and it is ${\cal C}^1$ over the whole triangulation. We focus on a special subspace - the reduced Clough-Tocher spline space and construct a normalized basis for it. The basis splines have a local support, they are nonnegative and they form a partition of unity. Geometrically, the basis construction problem is converted to a problem of finding a set of triangles that contain specific points. This leads us to control triangles and a stable way of computing with Clough-Tocher splines.
Secondary keywords:	mathematics;Clough-Tocher splines;B-splines;macro-elements;determining sets;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 2. stopnja
Pages:	VII, 63 str.
ID:	10980334