A fast boundary integral method for high-order multiscale mesh generation
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In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and multiscale features, and our algorithm has computational complexity which is linear in the number of input triangles. We use a smoothing kernel to define a function Φ whose level set defines the surface of interest. Charts are subsequently generated as maps from the original user-specified triangles to R^3. The degree of smoothness is controlled locally by the kernel to be commensurate with the fineness of the input triangulation. The expression for Φ can be transformed into a boundary integral, whose evaluation can be accelerated using a fast multipole method. We demonstrate the effectiveness and cost of the algorithm with polyhedral and quadratic skeleton surfaces obtained from CAD and meshing software.
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