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Title
Computations on Parameterized Surfaces with Chebfun2
Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
Date Created
2016-05
Contributors
- Page-Bottorff, Courtney Michelle (Author)
- Platte, Rodrigo (Thesis director)
- Kostelich, Eric (Committee member)
- School of Mathematical and Statistical Sciences (Contributor)
- Barrett, The Honors College (Contributor)
Topical Subject
Resource Type
Extent
32 pages
Language
Copyright Statement
In Copyright
Primary Member of
Series
Academic Year 2015-2016
Handle
https://hdl.handle.net/2286/R.I.37645
Level of coding
minimal
Cataloging Standards
System Created
- 2017-10-30 02:50:58
System Modified
- 2021-08-11 04:09:57
- 2 years 8 months ago
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