Abstract

We consider scalar-valued shape functionals on sets of shapes which are small perturbations of a reference shape. The shapes are described by parameterizations and their closeness is induced by a Hilbert space structure on the parameter domain. We justify a heuristic for finding the best low-dimensional parameter subspace with respect to uniformly approximating a given shape functional. We also propose an adaptive algorithm for achieving a prescribed accuracy when representing the shape functional with a small number of shape parameters.

中文翻译：

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形状的自适应近似

摘要

我们考虑形状集合上的标量值形状函数，这些形状函数是参考形状的小扰动。通过参数化描述形状，并通过参数域上的希尔伯特空间结构来诱导形状的紧密性。我们证明了一种启发式方法，可以找到关于统一逼近给定形状函数的最佳低维参数子空间。我们还提出了一种自适应算法，当用少量形状参数表示形状函数时，可以达到规定的精度。