1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
|
// -----------------------------------------------------------------------------
//
// Gmsh C++ extended tutorial 6
//
// Additional mesh data: integration points, Jacobians and basis functions
//
// -----------------------------------------------------------------------------
#include <iostream>
#include <gmsh.h>
int main(int argc, char **argv)
{
gmsh::initialize(argc, 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:
int elementOrder = 1, interpolationOrder = 2;
gmsh::model::mesh::setOrder(elementOrder);
auto pp = [](const std::string &label, const std::vector<double> &v, int mult)
{
std::cout << " * " << v.size() / mult << " " << label << ": ";
for(auto c : v) std::cout << c << " ";
std::cout << "\n";
};
// Iterate over all the element types present in the mesh:
std::vector<int> elementTypes;
gmsh::model::mesh::getElementTypes(elementTypes);
for(auto t : elementTypes) {
// Retrieve properties for the given element type
std::string elementName;
int dim, order, numNodes, numPrimNodes;
std::vector<double> localNodeCoord;
gmsh::model::mesh::getElementProperties
(t, elementName, dim, order, numNodes, localNodeCoord, numPrimNodes);
std::cout << "\n** " << elementName << " **\n\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.
std::vector<double> localCoords, weights;
gmsh::model::mesh::getIntegrationPoints
(t, "Gauss" + std::to_string(interpolationOrder), localCoords, weights);
pp("integration points to integrate order " +
std::to_string(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".
int numComponents, numOrientations;
std::vector<double> basisFunctions;
gmsh::model::mesh::getBasisFunctions
(t, localCoords, "Lagrange", numComponents, basisFunctions,
numOrientations);
pp("basis functions at integration points", basisFunctions, 1);
gmsh::model::mesh::getBasisFunctions
(t, localCoords, "GradLagrange", numComponents, basisFunctions,
numOrientations);
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.
std::vector<double> jacobians, determinants, coords;
gmsh::model::mesh::getJacobians
(t, localCoords, jacobians, determinants, coords);
pp("Jacobian determinants at integration points", determinants, 1);
}
gmsh::finalize();
return 0;
}
|
