NDLI: Chain-Based Representations for Solid and Physical Modeling

Content Provider	IEEE Xplore Digital Library
Author	DiCarlo, A. Milicchio, F. Paoluzzi, A. Shapiro, V.
Copyright Year	2004
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, and connectedness.
Sponsorship	IEEE Robotics and Automation Society
Starting Page	454
Ending Page	467
Page Count	14
File Size	903634
File Format	PDF
ISSN	15455955
Volume Number	6
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Solid modeling Data structures Physics computing Topology Matrix decomposition Computational modeling Finite element methods Refining Computer graphics Data engineering topology Algorithms computational geometry finite-element methods geometric modeling mesh generation sparse matrices spatial data structures
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering

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