Newest Results in Newest Vertex Bisection
53 mins 49 secs,
772.52 MB,
MPEG-4 Video
640x360,
29.97 fps,
44100 Hz,
1.91 Mbits/sec
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About this item
| Description: |
Licht, M
Wednesday 25th September 2019 - 14:05 to 14:50 |
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| Created: | 2019-11-04 09:03 |
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| Collection: | Geometry, compatibility and structure preservation in computational differential equations |
| Publisher: | Isaac Newton Institute |
| Copyright: | Licht, M |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | The algorithmic refinement of triangular meshes is an important component in numerical simulation codes. Newest vertex bisection is one of the most popular methods for geometrically stable local refinement. Its complexity analysis, however, is a fairly intricate recent result and many combinatorial aspects of this method are not yet fully understood. In this talk, we access newest vertex bisection from the perspective of theoretical computer science. We outline the amortized complexity analysis over generalized triangulations. An immediate application is the convergence and complexity analysis of adaptive finite element methods over embedded surfaces and singular surfaces. Moreover, we "combinatorialize" the complexity estimate and remove any geometry-dependent constants, which is only natural for this purely combinatorial algorithm and improves upon prior results. This is joint work with Michael Holst and Zhao Lyu. |
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