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Title: Parallel graph-grammar-based algorithm for the longest-edge refinement of triangular meshes and the pollution simulations in Lesser Poland area
Authors: Podsiadło, Krzysztof
Oliver Serra, Albert 
Paszyńska, Anna
Montenegro, Rafael 
Henriksen, Ian
Paszyński, Maciej
Pingali, Keshav
UNESCO Clasification: 12 Matemáticas
1206 Análisis numérico
Keywords: Advection–diffusion equation
Longest edge refinement
Pollution simulations
Unstructured grids
Issue Date: 2021
Project: National Science Centre, Poland Grant no. 2017/26/M/ ST1/ 00281
NSF Grants 1337281, 1406355, and 1618425
DARPA contracts FA8750-16-2-0004 and FA8650-15-C-7563
Journal: Engineering with Computers 
Abstract: In this paper, we propose parallel graph-grammar-based algorithm for the longest-edge refinements and the pollution simulations in Lesser Poland area. We introduce graph-grammar productions for Rivara’s longest-edged algorithm for the local refinement of unstructured triangular meshes. We utilize the hyper-graph to represent the computational mesh and the graph-grammar productions to express the longest-edge mesh refinement algorithm. The parallelism in the original Rivara’s longest edge refinement algorithm is obtained by processing different longest edge refinement paths in different three ads. Our graph-grammar-based algorithm allows for additional parallelization within a single longest-edge refinement path. The graph-grammar-based algorithm automatically guarantees the validity and conformity of the generated mesh; it prevents the generation of duplicated nodes and edges, elongated elements with Jacobians converging to zero, and removes all the hanging nodes automatically from the mesh. We test the algorithm on generating a surface mesh based on a topographic data of Lesser Poland area. The graph-grammar productions also generate the layers of prismatic three-dimensional elements on top of the triangular mesh, and they break each prismatic element into three tetrahedral elements. Next, we propose graph-grammar productions generating element matrices and right-hand-side vectors for each tetrahedral element. We utilize the Streamline Upwind Petrov–Galerkin (SUPG) stabilization for the pollution propagation simulations in Lesser Poland area. We use the advection–diffusion-reaction model, the Crank–Nicolson time integration scheme, and the graph-grammar-based interface to the GMRES solver.
ISSN: 0177-0667
DOI: 10.1007/s00366-020-01253-y
Source: Engineering with Computers [ISSN 0177-0667], v. 37, p. 3857–3880
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