Abstract—In this paper we present a new graph grammar based direct solver algorithm delivering linear O(N) computational cost and linear O(N) memory usage for adaptive finite element method simulations. Classical direct solvers on regular grids deliver O(N1.5) complexity for 2D problems and O(N2) in 3D ones. The linear computational cost of our solver is obtained by generating graph representation of the adaptive mesh and by utilizing dynamic construction prescribing the solver algorithm as graph grammar productions.
Index Terms—Direct solvers, graph grammar, adaptive finite element method.
Anna Paszyńska is with the Jagiellonian University, Krakow, Poland (e-mail: email@example.com).
Piotr Gurgul, Marcin Sieniek, Maciej Paszyński are with the AGH University of Science and Technology, Krakow, Poland (e-mail: firstname.lastname@example.org, msieniek @agh.edu.pl, email@example.com).
Cite:Anna Paszyńska, Piotr Gurgul, Marcin Sieniek, and Maciej Paszyński, "Linear Computational Cost Graph Grammar Based Direct Solver for 3D Adaptive Finite Element Method Simulations," International Journal of Materials, Mechanics and Manufacturing vol. 1, no. 3, pp. 225-230, 2013.