Name
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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1109/TASE.2009.2021342 | IEEE Transactions on Automation Science and Engineering |
Keywords | DocType | Volume |
matrix algebra,mesh generation,euler operators,hasse matrix,block-bidiagonal matrix,chain-based representations,local mesh refinements,multilinear transformations,physical modeling,solid modeling,topology-preserving mesh refinements,algorithms,computational geometry,finite-element methods,geometric modeling,sparse matrices,spatial data structures,topology,chain complex,computational science and engineering,data structure,sparse matrix,finite element method,first principle,geometric model,linear algebra,indexing terms,computer graphic,physical model | Journal | 6 |
Issue | ISSN | Citations |
3 | 1545-5955 | 10 |
PageRank | References | Authors |
0.81 | 9 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Antonio Di Carlo | 1 | 24 | 3.51 |
| Franco Milicchio | 2 | 27 | 6.61 |
| Alberto Paoluzzi | 3 | 92 | 14.74 |
| Vadim Shapiro | 4 | 10 | 0.81 |