Abstract
The first part of the paper deals with the interpolation and triangulation of closed manifolds. Let Γ be a closed surface in ℝ3, which is implicitly given by a function H(x) = 0. We present a new algorithm which creates a “nearly” uniform triangulation of this manifold. Our ideas are based on the procedures by E.L. Allgower [1] and on local geometry properties [2], The algorithm allows a parallel discretization and was tested for several examples.
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References
Allgower, E.L., Gnutzmann, S. (1987): An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces. SIAMJ. Numer. Anal. 24, 425–469
Kalik, K., Wendland, W.L. (1992): The approximation of closed manifolds by triangulated manifolds and the triangulation of closed manifolds. Computing 47, 255–275
Kalik, K., Quatember, R., Wendland, W.L. (1993): Load-Balancer unter Helios. Preprint 93-2, Universität Stuttgart
Kieser, R., Schwab, C., Wendland, W.L. (1992): Numerical evaluation of singular and finite-part surface integrals on curved surfaces using symbolic manipulation. Computing 49, 279–301
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© 1997 Springer-Verlag Berlin Heidelberg
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Kalik, K., Quatember, R., Wendland, W.L. (1997). Interpolation, Triangulation and Numerical Integration on Closed Manifolds. In: Wendland, W.L. (eds) Boundary Element Topics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60791-2_19
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DOI: https://doi.org/10.1007/978-3-642-60791-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64554-9
Online ISBN: 978-3-642-60791-2
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