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Fast Adaptive Hybrid Mesh Generation Based on Quad-tree Decomposition Mohamed Ebeida Mechanical and Aeronautical Eng. Dept –UCDavis.

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Presentation on theme: "Fast Adaptive Hybrid Mesh Generation Based on Quad-tree Decomposition Mohamed Ebeida Mechanical and Aeronautical Eng. Dept –UCDavis."— Presentation transcript:

1 Fast Adaptive Hybrid Mesh Generation Based on Quad-tree Decomposition Mohamed Ebeida Mechanical and Aeronautical Eng. Dept –UCDavis Bay Area Scientific Computing Day 2008 March 29, 2008

2 Motivation Structured Grids Relatively simple geometries Algebraic – Elliptic – Hyperbolic methods Line relaxation solvers Structured Multigrid solvers Adaptation using quad-tree or oct-tree decomp (FEM) Grid quality Unstructured Grids Complex geometries Delaunay point insertion algorithms / advancing front re-triangulation mesh points can move Agglomeration Multigrid solvers Adaptation using quad-tree or oct-tree (FEM) Grid quality

3 Overlapping grid system on space shuttle (Slotnick, Kandula and Buning 1994) Sophisticated Multiblock and Overlapping Structured Grid Techniques are required for Complex Geometries Motivation

4 Multigrid solvers –Multigrid techniques enable optimal O(N) solution complexity –Based on sequence of coarse and fine meshes –Originally developed for structured grids

5 Agglomeration Multigrid solvers for unstructured meshes Motivation

6 Quad-tree decomposition Fast Adaptive Grid Quality Line solvers Hanging nodes Multigrid Complex geometries

7 Our Goals A fast technique Quality Complex geometries Adaptive (geometries – solution variables) Multigrid Line relaxation solvers No hanging nodes Simple optimization steps (3D) Parallelizable

8 Spatial Decomposition

9 Strategy Algorithm Algorithm 1 Adaptive grid based on the geometries Algorithm 2 Adaptive grid based on the Simulation

10 Algorithm 1 - Geometries Start with a coarse Cartesian grid with aspect ratio = 1.0 Dim: 30x30 Sp = points

11 Algorithm 1 - Geometries Perform successive refinements till you reach a level that resolves the curvature of the geometries of the domain

12 Algorithm 1 - Geometries Level of refinements depend on the curvature of each shape

13 Algorithm 1 - Geometries Define a buffer zone and delete any element with a node in that zone

14 Algorithm 1 - Geometries Project nodes on the edge of the buffer zone orthogonally to the geometry

15 Algorithm 1 - Geometries Move nodes on the edge of the buffer zone orthogonally to the geometry to adjust B.L. elements

16 Algorithm 1 - Geometries

17 Another way ! Increase the width of the buffer zone and create boundary elements explicitly better bounds!

18

19 Algorithm 1 - Geometries Final mesh pts elem. Quad dom % Min edge length 7.6 x 10 Max A.R. = 64 -6

20 Complex geometries

21 Testing Algorithm 1 output

22 Algorithm 2 – Simulation based Use the output of Algorithm 1 as a base mesh for the spatial decomposition Run the simulation for n time steps (unsteady) or n iterations (steady) Perform Spatial decomposition on the base mesh based on a level set function. Map the variables from the grid used in the last simulation

23 How about transition elements? In order to ensure quality, transition element has to advance one step per spatial decomposition level x x

24 Results

25

26 Multigrid Levels Spatial decomposition allows us to generate prolongation and restriction operators easily How about the elements of each grid level? We already have them

27 Multigrid Levels

28 Multigrid Results For elliptic equations, the application of Multigrid is straight forward once we have the grid levels. For convection diffusion equations, line solvers are crucial for good results

29 Checking our Goals A fast technique Quality Complex geometries Adaptive with a starting coarse grid Multigrid Line relaxation solvers No hanging nodes Simple optimization steps (3D) Parallelizable

30 Thank you!


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