Mesh generation

PETGEM operates on unstructured tetrahedral meshes. The usual workflow generates them with Gmsh (.msh), but the preprocess stage also accepts VTK meshes (.vtk/.vtu); the format is auto-detected from the file passed to -mesh_filename. This page covers how mesh regions map to material ids, and how a mesh is generated.

Physical groups and material ids

Each volumetric region is tagged with a Gmsh physical volume. The tag maps to a 0-based material id as material_id = gmsh:physical - 1, and that id is the row index into sigmas.txt (see Data formats).

For example, examples/canonical_model declares four regions with tags 1-4, so sigmas.txt row 0 is the volume tagged 1, row 1 the volume tagged 2, and so on. Number physical volumes consecutively from 1, and provide one sigmas.txt row per material.

For a VTK mesh there are no Gmsh physical tags; the per-cell region is read from an integer cell-data array, auto-detected among cell_scalars, materials_id, material_id, MaterialID, material, and CellEntityIds. Its codes need not be contiguous or 0-based: the preprocess maps the distinct codes to 0-based ids in ascending order, so sigmas.txt row i corresponds to the i-th smallest code (codes {10, 20, 30, 40} map to rows {0, 1, 2, 3}). The preprocess prints the resulting code -> row table with per-region cell counts, and errors if the number of codes does not match the sigmas.txt row count.

Element sizing

The shipped .geo files parameterize the characteristic length with named constants applied to different parts of the geometry - for example, in examples/canonical_model/mesh.geo, a coarse far-field size, a fine size along the source/receiver line, and a size inside the target layer. Adjust them in the .geo file to control the mesh.

Generating a mesh

gmsh -3 examples/canonical_model/mesh.geo -o examples/canonical_model/mesh.msh

The resulting .msh is passed to utils/preprocess.py via -mesh_filename, which embeds the mesh and the per-cell conductivity (looked up from sigmas.txt by material id) into the input bundle. A pre-generated .msh can be used directly.

One mesh, any order

The polynomial order is a property of the basis, not of the mesh: the same tetrahedral mesh serves every order in 1..6. Each example therefore ships a single mesh.geo. The order is chosen at preprocessing time with -order, and can be overridden at run time with the kernel’s -order flag - which bypasses the bundle’s stored value, so one bundle can be reused for all orders.

VTK input

A tetrahedral VTK mesh (legacy .vtk or XML .vtu) is passed to the same -mesh_filename argument; no separate script or flag is needed:

python3 utils/preprocess.py \
    -mode fm -order 1 \
    -case_dir ${CASE_DIR} \
    -mesh_filename model.vtk \
    -source_filename sources.txt \
    -receiver_filename receivers.txt \
    -sigma_file sigmas.txt

Requirements:

  • The file must contain a tetrahedral cell block; accompanying triangle/line blocks are ignored, and mixed-element meshes are not supported.

  • The per-cell material id comes from a cell-data array, mapped to 0-based rows as described above. Provide one sigmas.txt row per distinct region code, ordered by ascending code.

  • Reading is done with meshio, already a preprocess dependency.