A quasi-meshfree method for constructing boundary-aware reproducing bases on geometrically complex domains using manifold geodesics
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING(2024)
摘要
In many applications, physical domains are geometrically complex making it challenging to perform coarse-scale approximation. A defeaturing process is often used to simplify the domain in preparation for approximation and analysis at the coarse scale. Herein, a methodology is presented for constructing a coarse-scale reproducing basis on geometrically complex domains given an initial fine-scale mesh of the fully featured domain. The initial fine-scale mesh can be of poor quality and extremely refined. The construction of the basis functions begins with a coarse-scale covering of the domain and generation of weighting functions with local support. Manifold geodesics are used to define distances within the local support for general applicability to non-convex domains. Conventional moving least squares is used to construct the coarse-scale reproducing basis. Applications in quasi-interpolation and linear elasticity are presented.
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关键词
Moving least squares,Weighting function,Reproducing basis,Geodesic,Elasticity,Quasi-interpolation
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