A new method is developed for finite element domain decomposition. This method employs a hybrid graph-genetic algorithm for graph partitioning and correspondingly bisects finite element meshes. A weighted incidence graph is first constructed for the finite element mesh, denoted by G_0. A coarsening process is then performed using heavy-edge matching. A sequence of such operations is employed to form G_n, with specified size suitable for genetic application in n steps. Genetic algorithm is then applied to G_n, and its bisection is performed. For the formation of the initial population in genetic algorithm, a shortest route tree is used. Then an uncoarsening process is performed and the results are transferred to the graph G_n-1. The initial population for genetic algorithm on G_n-1, is constructed from the results of G_n. Repeating a sequence of uncoarsening and employing genetic algorithm, graph G_0 is bisected.

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