| 杨开林.基于图论的渠网非恒定流稀疏矩阵技术[J].水利学报,2011,42(12): |
| 基于图论的渠网非恒定流稀疏矩阵技术 |
| Sparse matrix techniques for graph-theory-based mathematical model of unsteady flows in open channel networks |
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| DOI： |
| 中文关键词: 渠网 非恒定流 图论 稀疏矩阵技术 |
| 英文关键词: Sparse matrix techniques for graph-theory-based mathematical model of unsteady flows in open channel networks |
| 基金项目: |
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| 中文摘要: |
| 基于图论的渠网非恒定流数学模型，提出采用节支关联表、支节关联表和节点关联表描述渠网拓扑结构，研究了节支关联矩阵A 和节点水深关联矩阵C 的稀疏矩阵技术，包括：数据结构，压缩存储方法，以及计算机生成方法等。提出并证明了两个关于矩阵 C 性质的定理。研究表明，采用稀疏矩阵技术不仅可以大大减少渠网拓扑结构信息输入量，计算机内存空间占用量，而且显著提高非恒定流的计算求解速度。 |
| 英文摘要: |
| The graph-theory-based mathematical model of unsteady flow in open channel networks is presented. Three incidence tables are used to represent the relationships of vertices-edges，edges-vertices ，and vertices-vertices in an open channel network，respectively. The sparse matrix techniques are investigated for the incidence matrix A and adjacency matrix C for water depths at vertices，including their dada structures ，compact storage and generation. Finaly，two theorems at adjacency matrix C are proved. |
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