02073nas a2200121   4500008004100000245007100041210006900112260002600181520164500207100002301852700001801875856005801893       1999                        eng d00aNumerical Performance of a Graph-Theoretic HVAC Simulation Program0 aNumerical Performance of a GraphTheoretic HVAC Simulation Progra  aKyoto, Japanc09/19993 aThe Simulation Problem Analysis and Research Kernel (SPARK) uses graph-theoretic techniques to match equations to variables and build computational graphs, yielding solution sequences indicated by needed data flow. Additionally, the problem graph is decomposed into strongly connected components, thus reducing the size of simultaneous equation sets, and small cut sets are determined, thereby reducing the number of iteration variables needed to solve each equation set. The improvement in computational efficiency produced by this graph theoretic preprocessing depends on the nature of the problem. The paper explores the improvement one might expect in practice in three ways. First, two problems chosen to span the range of performance are studied and some of the factors determining the performance are identified and discussed. The problem selected to exhibit a large improvement consists of a set of sparsely coupled non-linear equations. The problem selected to represent the other end of the performance spectrum is a set of equations obtained by discretizing Laplace's equation in two dimensions, e.g. a heat conduction problem. Execution time versus problem size is compared to that obtained with sparse matrix implementations of the same problems. Then, to see if the results of these somewhat contrived limiting cases extend to actual problems in building simulation, a detailed control system model of a six- zone VAV HVAC system is simulated with and without the use of cut set reduction. Execution times are compared between the reduced and non-reduced SPARK models, and with those from an HVACSIM+ model of the same system.1 aSowell, Edward, F.1 aHaves, Philip  uhttp://www.ibpsa.org/proceedings/BS1999/BS99_A-05.pdf