t8_time_fractal.cxx

t8_time_fractal

Overview

t8_time_fractal is a benchmarking and visualization tool included in the t8code adaptive mesh refinement (AMR) library. It generates fractal-like meshes using various element types (e.g., triangles, quadrilaterals, hexahedra) and supports both 2D and 3D configurations.

The tool is valuable for:

• Evaluating AMR performance.
• Visualizing refinement patterns.
• Testing recursive and iterative refinement strategies.

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Usage

The basic syntax for running t8_time_fractal is:

./t8_time_fractal [OPTIONS]

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Options

Option(s)	Argument(s)	Description	Values/Defaults
-h, --help		Display help message
-u, --uniform_level	INT	Initial uniform refinement level (must be even and > 0 for quads/hexahedra)
-f, --final_level	INT	Final refinement level (must be greater than -u)
-e, --elements	INT	Element type:	2: Quadrilateral 3: Triangle 4: Hexahedron (default) 5: Tetrahedron 6: Prism 7: Pyramid
-r, --runs	INT	Number of fractal construction iterations	Default: 1
-i, --iterative	INT	Refinement method:	0: Recursive (default) 1: Iterative
-d, --delete	INT	Element deletion after refinement:	0: Never delete 1: Delete elements (default)
-t, --trees	INT	Number of trees in the forest (must be 1 if -o 1 is set)	Default: 512
-o, --output	INT	Output mesh:	0: No visual output (default) 1: Visual output (VTK)
-c, --coarse	INT	Number of coarsening steps applied to holes

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Constraints

• For quadrilateral and hexahedral elements (-e 2 or -e 4), both -u and -f must be even numbers greater than 0.
• If visual output is enabled (-o 1), the number of trees (-t) must be set to 1.

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Examples

1. Basic Quadrilateral Mesh with Visual Output

./t8_time_fractal -u 2 -f 4 -e 2 -r 1 -o 1 -t 1

Generates a quadrilateral mesh with:

• -u 2: Starts with a 2-level uniformly refined square mesh.
• -f 4: Refines to level 4 (higher resolution).
• -e 2: Uses quadrilateral elements (squares).
• -r 1: Applies the fractal hole-cutting process once.
• -o 1 & -t 1: Enables VTK visual output for a single tree (a single, centered structure).

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2. Triangle Mesh with Iterative Refinement and Deletion

./t8_time_fractal -u 2 -f 4 -e 3 -i 1 -r 2 -d 1 -o 1 -t 1

• -u 2: Start with uniform refinement level 2.
• -f 4: Refine up to level 4.
• -e 3: Use triangle elements.
• -i 1: Use iterative (not recursive) refinement.
• -r 2: Apply two fractal refinement passes.
• -d 1: Delete elements during fractal pattern creation.
• -o 1 -t 1: Output to VTK file (requires only 1 tree).

Creates a triangular mesh using one iterative refinement pass, where elements are deleted according to a fractal pattern. The resulting mesh is written to a .vtu file for visualization (requires one tree).

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Output

If visual output is enabled (-o 1), the program generates a VTK file (e.g., output.vtu) that can be opened with visualization tools like ParaView to inspect the mesh structure and refinement patterns.

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Troubleshooting

• Invalid Option or Missing Argument:
  Ensure all options are provided with the required arguments. For example, -r must be followed by an integer.

• Refinement Level Errors:
  For quadrilateral and hexahedral elements, both -u and -f must be even numbers greater than 0, with -f greater than -u.

• Visual Output Constraints:
  When enabling visual output (-o 1), set the number of trees (-t) to 1.