Parallel graph-grammar-based algorithm for the longest-edge refinement of triangular meshes and the pollution simulations in Lesser Poland area

Abstract In this paper, we propose parallel graph-grammar-based algorithm for the longest-edge refinements and pollution simulations in Lesser Poland area. We introduce graph-grammar productions Rivara’s longest-edged local refinement of unstructured triangular meshes. utilize hyper-graph to represent computational mesh express algorithm. The parallelism original longest edge is obtained by processing different paths three ads. Our allows additional parallelization within a single path. automatically guarantees validity conformity generated mesh; it prevents generation duplicated nodes edges, elongated elements with Jacobians converging zero, removes all hanging from mesh. test on generating surface based topographic data also generate layers prismatic three-dimensional top mesh, they break each element into tetrahedral elements. Next, matrices right-hand-side vectors element. Streamline Upwind Petrov–Galerkin (SUPG) stabilization propagation use advection–diffusion-reaction model, Crank–Nicolson time integration scheme, interface GMRES solver.