Chain-Based Representations for Solid and Physical Modeling

Antonio DiCarlo; Franco Milicchio; Alberto Paoluzzi; Vadim Shapiro

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arXiv · 0812.3249

Chain-Based Representations for Solid and Physical Modeling

Antonio DiCarlo·Franco Milicchio·Alberto Paoluzzi·Vadim Shapiro

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Abstract

In this paper we show that the (co)chain complex associated with a decomposition of the computational domain, commonly called a mesh in computational science and engineering, can be represented by a block-bidiagonal matrix that we call the Hasse matrix. Moreover, we show that topology-preserving mesh refinements, produced by the action of (the simplest) Euler operators, can be reduced to multilinear transformations of the Hasse matrix representing the complex. Our main result is a new representation of the (co)chain complex underlying field computations, a representation that provides new insights into the transformations induced by local mesh refinements. Our approach is based on first principles and is general in that it applies to most representational domains that can be characterized as cell complexes, without any restrictions on their type, dimension, codimension, orientability, manifoldness, connectedness.

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BibTeX RIS

Antonio DiCarlo, Franco Milicchio, Alberto Paoluzzi, Vadim Shapiro. 2008-12-17. Chain-Based Representations for Solid and Physical Modeling. https://arxiv.org/abs/0812.3249

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