Construction of signed distance functions with an elliptic equation
Analysis of PDEs
2024-02-01 v1
Abstract
Motivated by recent progress of structural optimization problems, the paper presents a new method for constructing the distance function to the boundary of given sets of interest, which simplifies the optimization procedure. We extend the celebrated Varadhan's elliptic equation theory in 1967 by adding the source term to the equation, in which we encode the information about the set. We will also establish the rate of convergence in this new framework, which is sharp at least in the one-dimensional case.
Keywords
Cite
@article{arxiv.2401.17665,
title = {Construction of signed distance functions with an elliptic equation},
author = {Takahiro Hasebe and Jun Masamune and Tomoyuki Oka and Kota Sakai and Takayuki Yamada},
journal= {arXiv preprint arXiv:2401.17665},
year = {2024}
}