The Instability in the Dimensions of Spline Spaces over $T$-Meshes with Nested $T$-Cycles

The Instability in the Dimensions of Spline Spaces over $T$-Meshes with Nested $T$-Cycles

Year:    2019

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 1 : pp. 187–211

Abstract

This paper studies on the dimensions of spline spaces over some given $T$-meshes. Using the smoothing cofactor-conformality method, we study the instability in the dimensions of the spline spaces over $T$-meshes with 2-nested and 3-nested $T$-cycles. We define a singularity factor of each simple $T$-cycle, the instability and the structure's degeneration are associated with the singularity factors. In order to get a stable dimension formula over $T$-mesh with a $N$-nested $T$-cycle, a constraint on the $T$-mesh is introduced. Finally, a possible degeneration for a case of parallel $T$-cycles is illustrated.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2017-0110

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 1 : pp. 187–211

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords: