Transfinite Patches for Isogeometric Analysis

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

Mathematics, 2025, vol. 13, issue 3, 1-38

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.

Keywords: interpolation; approximation; isogeometric analysis; B-splines; NURBS; T-splines (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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