This repository contains several applications presenting the usage of the GTMesh library. GTMesh library is a basic library for handling unstructured meshes and computation on them.

The computation is demonstrated on the heat conduction problem:

$$\begin{array}{cll} \frac{\partial T\left(\boldsymbol{x},t\right)}{\partial t} & =\Delta T(\boldsymbol{x},t) & \text{ for }\boldsymbol{x}\in\varOmega^{\circ}\\\ T\left(\boldsymbol{x},t\right) & =T_{\text{wall}} & \text{ for }\boldsymbol{x}\in\partial\varOmega \end{array}$$

There are three solutions demonstrated. All use finite volume method and Merson version of the Runge-Kutta explicit solver.

• simple single threaded approach,
• multithreaded approach utilizing graph coloring to prevent race conditions,
• multithreaded approach utilizing storing of auxiliary quantities to prevent race conditions.

Dependencies

• C++ compiler with OpenMP support
• CMake
• Paraview or another tool to display output data
• python3 for generation of basic meshes

How to run examples

1. fetch submodules git submodule update --init
2. generate the mesh

    cd Meshes
    python3 simple_mesh_generator.py
    cd ..

   This will produce Meshes/mesh3D.vtk. To produce a finer mesh, increase the number of cells in the main function.
3. build the application

   mkdir build_dir
   cmake -S . -B build_dir
   cmake --build build_dir --config Release

4. execute the example

   mkdir -p out
   ./build_dir/GTMesh-example "Meshes/mesh3D.vtk" "out"
   mkdir -p out-graph
   ./build_dir/GTMesh-example-omp_parallel_graph "Meshes/mesh3D.vtk" "out-graph"
   mkdir -p out-struct
   ./build_dir/GTMesh-example-omp_parallel_struct "Meshes/mesh3D.vtk" "out-struct"

   the result is stored in the out, out-graph and out-struct directories.

Unstructured mesh

There is mesh3D-unstructured.fpma file in the Meshes directory. It contains an example of an unstructured mesh. The mesh was kindly provided by J. Hahn, Slovak University of Technology, Bratislava.

Try running

mkdir -p out
./build_dir/GTMesh-example "Meshes/mesh3D-unstructured.fpma" "out"
mkdir -p out-graph
./build_dir/GTMesh-example-omp_parallel_graph "Meshes/mesh3D-unstructured.fpma" "out-graph"
mkdir -p out-struct
./build_dir/GTMesh-example-omp_parallel_struct "Meshes/mesh3D-unstructured.fpma" "out-struct"

The results are still exported in VTK format, however, the cells are tessellated to tetrahedrons. Use the surface with edges to see the tessellation.

Note that the computation on the unstructured mesh is more time-consuming. The causes might be as follows:

• The number of cells and faces increases.
• The regular mesh geometry might be more suitable for the current problem.

Running in 2D

To instruct the algorithm to compute in 2D, uncomment the lines that commented with 2D version and comment out the ones with 3D version. Recompile the project and try running.

mkdir -p out-2D
./build_dir/GTMesh-example "Meshes/mesh2D.vtk" "out-2D"
mkdir -p out-2D-graph
./build_dir/GTMesh-example-omp_parallel_graph "Meshes/mesh2D.vtk" "out-2D-graph"
mkdir -p out-2D-struct
./build_dir/GTMesh-example-omp_parallel_struct "Meshes/mesh2D.vtk" "out-2D-struct"