The decomposition of an arbitrary polyhedral domain into tetrahedra is currently more tractable than its decomposition into hexahedra. However, for some engineering applications, a mesh composed of hexahedra, or even a mixture of hexahedra, pentahedra and tetrahedra, is preferable. One such application is the p-type ÿnite element method, where the total number of elements should be as small as possible. We show in this paper that, given a tetrahedral decomposition, some of the tetrahedra can be e ciently combined into hexahedra and pentahedra. The basis of the method is a classiÿcation, using a generalized graph representation, of all possible tetrahedral decompositions of pentahedra and hexahedra. We then present a tetrahedral merge algorithm that utilizes this result to search for the subgraphs of hexahedra and pentahedra in a tetrahedral mesh. The problem of ÿnding an optimal solution is NP-complete. We present heuristics to increase the number of hexahedra and pentahedra, within a reasonable amount of computation time. The algorithm has been implemented in the PolyFEM mesher, and examples showing the typical merge success of the algorithm are included.

The decomposition of an arbitrary polyhedral domain into tetrahedra is currently more tractable than its decomposition into hexahedra. However, for some engineering applications, a mesh composed of hexahedra, or even a mixture of hexahedra, pentahedra and tetrahedra, is preferable. One such application is the p‐type finite element method, where the total number of elements should be as small as possible. We show in this paper that given a tetrahedral decomposition, some of the tetrahedra can be efficiently combined into hexahedra and pentahedra. The basis of the method is a classification, using a generalized graph representation, of all possible tetrahedral decompositions of pentahedra and hexahedra. We then present a tetrahedral merge algorithm that utilizes this result to search for the subgraphs of hexahedra and pentahedra in a tetrahedral mesh. The problem of finding an optimal solution is NP‐complete. We present heuristics to increase the number of hexahedra and pentahedra, within a reasonable amount of computation time. The algorithm has been implemented in the PolyFEM mesher, and examples showing the typical merge success of the algorithm are included. Copyright © 2000 John Wiley & Sons, Ltd.

The development of small-molecule drugs to counter the threat of bioterrorism will differ from classical drug discovery because it will be impossible to evaluate efficacy in clinical trials for many agents. This difference focuses biodefense on the identification of multiple drug candidates for each threat organism so that multiple treatments can be mounted simultaneously when needed to maximize the probability of success. Accordingly, drug discovery will become the rate-and cost-limiting phase of the overall drug development process. We address the potential of computational chemistry to optimize efficiency and efficacy in the discovery phase. The major elements required for a successful computational approach are the calculation of binding free energy, accounting for changes in solvation on ligand binding, and compensating for protein flexibility. Drug Dev Res 70 : 279-287, 2009. r