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An adaptive algorithm for efficient computation of level curves of surfaces

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Abstract

A new efficient algorithm for the computation of z = constant level curves of surfaces z = f(x,y) is proposed and tested on several examples. The set of z-level curves in a given rectangle of the (x,y)-plane is obtained by evaluating f on a first coarse square grid which is then adaptively refined by triangulation to eventually match a desired tolerance. Adaptivity leads to a considerable reduction in terms of evaluations of f with respect to uniform grid computation as in Matlab®’s contour. Furthermore, especially when the evaluation of f is computationally expensive, this reduction notably decreases the computational time. A comparison of performances is shown for two real-life applications such as the determination of stability charts and of ε −pseudospectra for linear time delay systems. The corresponding Matlab code is also discussed.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Udine, via delle Scienze 208, 33100, Udine, Italy

    Dimitri Breda & Rossana Vermiglio

  2. Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, p.le Europa 1, 34127, Trieste, Italy

    Stefano Maset

Authors
  1. Dimitri Breda
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  2. Stefano Maset
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  3. Rossana Vermiglio
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Correspondence to Dimitri Breda.

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Breda, D., Maset, S. & Vermiglio, R. An adaptive algorithm for efficient computation of level curves of surfaces. Numer Algor 52, 605–628 (2009). https://doi.org/10.1007/s11075-009-9303-2

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  • DOI: https://doi.org/10.1007/s11075-009-9303-2

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