A fast boundary integral method for high-order multiscale mesh generation

This is the authors' abstract. We don't add key points for this paper.

In this work we present an algorithm to construct an infinitely smooth surface from an input consisting of a (rectilinear) of a surface of arbitrary shape. The original surface can have-trivial genus and multiscale features, and our algorithm has computational which is linear in the number of input triangles. We use a smoothing to define a function \Φ whose level set defines the surface of. Charts are subsequently generated as maps from the original-specified triangles to \ R³. The degree of smoothness is locally by the kernel to be commensurate with the fineness of the triangulation. The expression for~\Φ can be transformed into a integral, whose evaluation can be accelerated using a fast multipole. We demonstrate the effectiveness and cost of the algorithm with and quadratic skeleton surfaces obtained from CAD and meshing.