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Source: examples/poisson

Poisson examples

The upstream examples/poisson folder collects static scalar-field problems built around the "poisson" element. The shipped cases cover generated meshes, imported Gmsh meshes, analytic benchmark materials, mixed Dirichlet/Neumann boundary conditions, and nonlinear Poisson materials.

Files in this folder

• poisson-1d.json: generated 1D edge2 mesh with constpoisson material and Dirichlet values on both ends.
• poisson-1d-benchmark.json: 1D benchmark case using poisson1d-benchmark, projection of "exactsolution", and the companion plotting script plot-poisson1dbenchmark.py.
• poisson-2d.json: generated 2D quad4 mesh with a constant source term.
• poisson-2d-quad8.json: the same problem on a higher-order quad8 mesh.
• poisson-2d-benchmark.json: generated 2D benchmark with poisson2d-benchmark material and the dedicated poisson2dbenchmark boundary condition.
• poisson-2d-cookmembrane.json: the same 2D benchmark on an imported Gmsh mesh from cookmembrane2d.msh.
• poisson-2d-msh-neumann.json: imported mesh with mixed Dirichlet and Neumann boundary conditions.
• poisson-2d-nonlinear.json: nonlinear 2D Poisson case using nonlinear-poisson2d on an imported Gmsh cube slice.
• poisson-3d-nonlinear.json: nonlinear 3D Poisson case using nonlinear-poisson3d.
• Geometry helpers: cookmembrane2d.geo and cubic.geo.

Representative input

The simplest generated-mesh case is poisson-2d.json:

json { "mesh": { "type": "asfem", "dim": 2, "nx": 20, "ny": 20, "meshtype": "quad4", "savemesh": true }, "dofs": { "names": ["phi"] }, "elements": { "elmt1": { "type": "poisson", "dofs": ["phi"], "material": { "type": "constpoisson", "parameters": { "sigma": 1.0, "f": 0.1 } } } }, "projection": { "type": "default", "vectormate": ["gradu"] }, "bcs": { "left": { "type": "dirichlet", "dofs": ["phi"], "bcvalue": 0.0, "side": ["left"] } }, "job": { "type": "static", "print": "dep" } }

Notes

• All Poisson examples use the single DoF name "phi" and the "poisson" element type.
• Benchmark inputs use the materials poisson1d-benchmark or poisson2d-benchmark, and the 2D benchmark cases also use the special boundary condition "type":"poisson2dbenchmark".
• Nonlinear cases switch the material to nonlinear-poisson2d or nonlinear-poisson3d and use "nlsolver":{"type":"newton"}.
• Several upstream files still include "restart": true inside "job", but the current ReadJobBlock.cpp only reads "type" and "print".