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Transfinite Patches for Isogeometric Analysis

Author

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  • Christopher Provatidis

    (School of Mechanical Engineering, National Technical University of Athens, 9, Iroon Polytechniou Str., 15780 Zografou, Greece)

Abstract

This paper extends the well-known transfinite interpolation formula, which was developed in the late 1960s by the applied mathematician William Gordon at the premises of General Motors as an extension of the pre-existing Coons interpolation formula. Here, a conjecture is formulated, which claims that the meaning of the involved blending functions can be enhanced, such that it includes any linear independent and complete set of functions, including piecewise-linear, trigonometric functions, Bernstein polynomials, B-splines, and NURBS, among others. In this sense, NURBS-based isogeometric analysis and aspects of T-splines may be considered as special cases. Applications are provided to illustrate the accuracy in the interpolation through the L 2 error norm of closed-formed functions prescribed at the nodal points of the transfinite patch, which represent the solution of partial differential equations under boundary conditions of the Dirichlet type.

Suggested Citation

  • Christopher Provatidis, 2025. "Transfinite Patches for Isogeometric Analysis," Mathematics, MDPI, vol. 13(3), pages 1-38, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:335-:d:1572659
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