Creating a mesh

We start with setting the Feel++ environment and loading the Feel++ library.

Set the Feel++ environment with local repository
import feelpp.core as fppc
import sys
app = fppc.Environment(["myapp"],config=fppc.localRepository(""))
Results 
















1. Load a mesh from a geo or msh file






fppc.mesh(dim=2, geo=1, realdim=2, worldComm=None) : create a mesh.
The mesh is of topological dimension dim, in real dimension realdim with geometric order geo.
The mesh is configured with a WorldComm which provides the parallel process layout.






Keyword arguments:






    

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    dim : the topological dimension (default: 2)
    

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    geo : the geometrical order (default: 1)
    

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    realdim : the real dimension (default: 2)
    

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    worldComm : the parallel communicator for the mesh (default:  Environment::worldCommPtr())
    

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fppc.load(m, path, size) → fppc._mesh.Mesh_S1DG1R1 : load a mesh from a file






    

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    m declared with the function mesh above
    

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    path (string) path to the geometry (with geo or msh format)
    

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    size (float) size of the meshed geometry (if it is not meshed yet)
    

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Example




geo=fppc.download( "github:{repo:feelpp,path:feelpp/quickstart/laplacian/cases/feelpp2d/feelpp2d.geo}", worldComm=app.worldCommPtr() )[0]
print("geo file: {}".format(geo))
mesh = fppc.load(fppc.mesh(dim=2,realdim=2), geo, 0.1)







Results







geo file: /scratch/prudhomm/actions-runner/_work/book.feelpp.org/book.feelpp.org/feelppdb/downloads/feelpp2d.geo
















2. Usage






The mesh provides the Feel++ data structures in Python:
The following methods are to use on the mesh object (mesh in the previous example) :






2.1. Mesh information :




    

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    dimension(self) → int : get topological dimension
    

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    hAverage(self) → float : get the average edge length of the mesh
    

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    hMax(self) → float : get the maximum edge length of the mesh
    

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    hMin(self) → float : get the minimum edge length of the mesh
    

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    measure(self, parallel: bool = True) → float : get the measure of the mesh (which is equal to \(\int_\Omega 1\))
    

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    measureBoundary(self) → float : get the measure of the boundary of the mesh (which is equal to \(???\))
    

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    numGlobalEdges(self) → int : get the number of edges over the whole mesh, requires communication if the mesh is parallel
    

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    numGlobalElements(self) → int : get the number of elements over the whole mesh, requires communication if the mesh is parallel
    

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    numGlobalFaces(self) → int : get the number of faces over the whole mesh, requires communication if the mesh is parallel
    

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    numGlobalPoints(self) → int : get the number of points over the whole mesh, requires communication if the mesh is parallel
    

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    realDimension(self) → int : get real dimension
    

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    updateMeasures(self) → None : update the measures of the mesh
    

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Here is an example of how to use the mesh information:






Query the mesh information




print(f"dimention: {mesh.dimension()}")
print(f"number of elements: {mesh.numGlobalElements()}")
print(f"number of faces: {mesh.numGlobalFaces()}")
print(f"hmin: {mesh.hMin()}")
print(f"havg: {mesh.hAverage()}")
print(f"hmax: {mesh.hMax()}")
print(f"measure: {mesh.measure()}")
print(f"measure of boundary: {mesh.measureBoundary()}")







Results







dimention: 2
number of elements: 5130
number of faces: 8000
hmin: 0.07738894997584338
havg: 0.10266129894318482
hmax: 0.13695416558140552
measure: 20.79999999999995
measure of boundary: 1496.2887158543454














2.2. Test relation between meshes :




    

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    isParentMeshOf(self: fppc._mesh.Mesh_S3DG1R3, arg0: fppc._mesh.Mesh_S3DG1R3) → bool : is the mesh the parent mesh of another mesh
    

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    isRelatedTo(self: fppc._mesh.Mesh_S3DG1R3, arg0: fppc._mesh.Mesh_S3DG1R3) → bool : is the mesh related to another mesh
    

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    isSiblingOf(self: fppc._mesh.Mesh_S3DG1R3, arg0: fppc._mesh.Mesh_S3DG1R3) → bool: is the mesh a sibling of another mesh
    

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    isSubMeshFrom(self: fppc._mesh.Mesh_S3DG1R3, arg0: fppc._mesh.Mesh_S3DG1R3) → bool : is the mesh a sub mesh of another mesh
    

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2.3. Export and load mesh on HDF5 format




    

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    saveHDF5(self, name: str) → None : save mesh to H5 file
    

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    loadHDF5(self, name: str) → None : load mesh from H5 file
    

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3. Ranges








elements




fppc.elements(mesh) : get iterator over the elements of the mesh




markedelements






    

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    fppc.markedelements(mesh, tag: str) : get iterator over the marked elements of the mesh
    

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    fppc.markedelements(mesh, marker: str) :  return the range of elements of the mesh with marker
    

    3. 

  3. 

    fppc.markedelements(mesh, markers: List[str]) : return the range of elements of the mesh with markers
    

    4. 







faces




fppc.faces(mesh) : get iterator over the faces of the mesh




markedfaces






    

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    fppc.markedfaces(mesh, marker: str) : return the range of facets of the mesh with marker
    

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    markedfaces(mesh, markers: List[str]) : return the range of facets of the mesh with marker
    

    3. 







boundaryfaces




fppc.boundaryfaces(mesh): get iterator over the boundary faces of the mesh










A first example with ranges:








r = fppc.elements(mesh)
print("mesh elts:", fppc.nelements(r))
r = fppc.boundaryfaces(mesh)
print("mesh boundary faces:", fppc.nelements(r))







Results







mesh elts: 5130
mesh boundary faces: 610












A second more interesting example with ranges uses integrate to compute integrals of expressions over the mesh:






Example : compute integrals




from feelpp.core.integrate  import integrate

i1 = integrate(range=fppc.elements(mesh),expr="sin(x+y):x:y")
i2 = integrate(range=fppc.boundaryfaces(mesh),expr="x*nx+y*ny+z*nz:x:y:z:nx:ny:nz")
i3 = integrate(range=fppc.markedelements(mesh, "marker"), expr="1")

print(f"i1 = {i1}, i2 = {i2}, i3 = {i3}")







Results







i1 = [3.24283419], i2 = [41.6], i3 = [0.]
















4. Next steps