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# -----------------------------------------------------------------------------
#
# Gmsh Python extended tutorial 6
#
# Additional mesh data: integration points, Jacobians and basis functions
#
# -----------------------------------------------------------------------------
import gmsh
import sys
gmsh.initialize(sys.argv)
gmsh.model.add("x6")
# The API provides access to all the elementary building blocks required to
# implement finite-element-type numerical methods. Let's create a simple 2D
# model and mesh it:
gmsh.model.occ.addRectangle(0, 0, 0, 1, 0.1)
gmsh.model.occ.synchronize()
gmsh.model.mesh.setTransfiniteAutomatic()
gmsh.model.mesh.generate(2)
# Set the element order and the desired interpolation order:
elementOrder = 1
interpolationOrder = 2
gmsh.model.mesh.setOrder(elementOrder)
def pp(label, v, mult):
print(" * " + str(len(v) / mult) + " " + label + ": " + str(v))
# Iterate over all the element types present in the mesh:
elementTypes = gmsh.model.mesh.getElementTypes()
for t in elementTypes:
# Retrieve properties for the given element type
elementName, dim, order, numNodes, localNodeCoord, numPrimNodes =\
gmsh.model.mesh.getElementProperties(t)
print("\n** " + elementName + " **\n")
# Retrieve integration points for that element type, enabling exact
# integration of polynomials of order "interpolationOrder". The "Gauss"
# integration family returns the "economical" Gauss points if available, and
# defaults to the "CompositeGauss" (tensor product) rule if not.
localCoords, weights =\
gmsh.model.mesh.getIntegrationPoints(t, "Gauss" + str(interpolationOrder))
pp("integration points to integrate order " +
str(interpolationOrder) + " polynomials", localCoords, 3)
# Return the basis functions evaluated at the integration points. Selecting
# "Lagrange" and "GradLagrange" returns the isoparamtric basis functions and
# their gradient (in the reference space of the given element type). A
# specific interpolation order can be requested using "LagrangeN" and
# "GradLagrangeN" with N = 1, 2, ... Other supported function spaces include
# "H1LegendreN", "GradH1LegendreN", "HcurlLegendreN", "CurlHcurlLegendreN".
numComponents, basisFunctions, numOrientations =\
gmsh.model.mesh.getBasisFunctions(t, localCoords, "Lagrange")
pp("basis functions at integration points", basisFunctions, 1)
numComponents, basisFunctions, numOrientations =\
gmsh.model.mesh.getBasisFunctions(t, localCoords, "GradLagrange")
pp("basis function gradients at integration points", basisFunctions, 3)
# Compute the Jacobians (and their determinants) at the integration points
# for all the elements of the given type in the mesh. Beware that the
# Jacobians are returned "by column": see the API documentation for details.
jacobians, determinants, coords =\
gmsh.model.mesh.getJacobians(t, localCoords)
pp("Jacobian determinants at integration points", determinants, 1)
gmsh.finalize()
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