// -----------------------------------------------------------------------------
//
// Gmsh C++ tutorial 10
//
// Mesh size fields
//
// -----------------------------------------------------------------------------
// In addition to specifying target mesh sizes at the points of the geometry
// (see `t1.cpp') or using a background mesh (see `t7.cpp'), you can use general
// mesh size "Fields".
#include <set>
#include <sstream>
#include <gmsh.h>
int main(int argc, char **argv)
{
gmsh::initialize(argc, argv);
gmsh::model::add("t10");
// Let's create a simple rectangular geometry:
double lc = .15;
gmsh::model::geo::addPoint(0.0, 0.0, 0, lc, 1);
gmsh::model::geo::addPoint(1, 0.0, 0, lc, 2);
gmsh::model::geo::addPoint(1, 1, 0, lc, 3);
gmsh::model::geo::addPoint(0, 1, 0, lc, 4);
gmsh::model::geo::addPoint(0.2, .5, 0, lc, 5);
gmsh::model::geo::addLine(1, 2, 1);
gmsh::model::geo::addLine(2, 3, 2);
gmsh::model::geo::addLine(3, 4, 3);
gmsh::model::geo::addLine(4, 1, 4);
gmsh::model::geo::addCurveLoop({1, 2, 3, 4}, 5);
gmsh::model::geo::addPlaneSurface({5}, 6);
gmsh::model::geo::synchronize();
// Say we would like to obtain mesh elements with size lc/30 near curve 2 and
// point 5, and size lc elsewhere. To achieve this, we can use two fields:
// "Distance", and "Threshold". We first define a Distance field (`Field[1]')
// on points 5 and on curve 2. This field returns the distance to point 5 and
// to (100 equidistant points on) curve 2.
gmsh::model::mesh::field::add("Distance", 1);
gmsh::model::mesh::field::setNumbers(1, "PointsList", {5});
gmsh::model::mesh::field::setNumbers(1, "CurvesList", {2});
gmsh::model::mesh::field::setNumber(1, "NumPointsPerCurve", 100);
// We then define a `Threshold' field, which uses the return value of the
// `Distance' field 1 in order to define a simple change in element size
// depending on the computed distances
//
// SizeMax - /------------------
// /
// /
// /
// SizeMin -o----------------/
// | | |
// Point DistMin DistMax
gmsh::model::mesh::field::add("Threshold", 2);
gmsh::model::mesh::field::setNumber(2, "InField", 1);
gmsh::model::mesh::field::setNumber(2, "SizeMin", lc / 30);
gmsh::model::mesh::field::setNumber(2, "SizeMax", lc);
gmsh::model::mesh::field::setNumber(2, "DistMin", 0.15);
gmsh::model::mesh::field::setNumber(2, "DistMax", 0.5);
// Say we want to modulate the mesh element sizes using a mathematical
// function of the spatial coordinates. We can do this with the MathEval
// field:
gmsh::model::mesh::field::add("MathEval", 3);
gmsh::model::mesh::field::setString(
3, "F", "Cos(4*3.14*x) * Sin(4*3.14*y) / 10 + 0.101");
// We could also combine MathEval with values coming from other fields. For
// example, let's define a `Distance' field around point 1
gmsh::model::mesh::field::add("Distance", 4);
gmsh::model::mesh::field::setNumbers(4, "PointsList", {1});
// We can then create a `MathEval' field with a function that depends on the
// return value of the `Distance' field 4, i.e., depending on the distance to
// point 1 (here using a cubic law, with minimum element size = lc / 100)
gmsh::model::mesh::field::add("MathEval", 5);
std::stringstream stream;
stream << "F4^3 + " << lc / 100;
gmsh::model::mesh::field::setString(5, "F", stream.str());
// We could also use a `Box' field to impose a step change in element sizes
// inside a box
gmsh::model::mesh::field::add("Box", 6);
gmsh::model::mesh::field::setNumber(6, "VIn", lc / 15);
gmsh::model::mesh::field::setNumber(6, "VOut", lc);
gmsh::model::mesh::field::setNumber(6, "XMin", 0.3);
gmsh::model::mesh::field::setNumber(6, "XMax", 0.6);
gmsh::model::mesh::field::setNumber(6, "YMin", 0.3);
gmsh::model::mesh::field::setNumber(6, "YMax", 0.6);
// Many other types of fields are available: see the reference manual for a
// complete list. You can also create fields directly in the graphical user
// interface by selecting `Define->Size fields' in the `Mesh' module.
// Finally, let's use the minimum of all the fields as the background mesh
// field:
gmsh::model::mesh::field::add("Min", 7);
gmsh::model::mesh::field::setNumbers(7, "FieldsList", {2, 3, 5, 6});
gmsh::model::mesh::field::setAsBackgroundMesh(7);
// The API also allows to set a global mesh size callback, which is called
// each time the mesh size is queried
auto meshSizeCallback = [](int dim, int tag, double x, double y, double z) {
return 0.02 * x + 0.01;
};
gmsh::model::mesh::setSizeCallback(meshSizeCallback);
// To determine the size of mesh elements, Gmsh locally computes the minimum
// of
//
// 1) the size of the model bounding box;
// 2) if `Mesh.MeshSizeFromPoints' is set, the mesh size specified at
// geometrical points;
// 3) if `Mesh.MeshSizeFromCurvature' is positive, the mesh size based on
// curvature (the value specifying the number of elements per 2 * pi rad);
// 4) the background mesh field;
// 5) any per-entity mesh size constraint;
// 6) the mesh size returned by the mesh size callback, if any.
//
// This value is then constrained in the interval [`Mesh.MeshSizeMin',
// `MeshMeshSizeMax'] and multiplied by `Mesh.MeshSizeFactor'. In addition,
// boundary mesh sizes (on curves or surfaces) are interpolated inside the
// enclosed entity (surface or volume, respectively) if the option
// `Mesh.MeshSizeExtendFromBoundary' is set (which is the case by default).
//
// When the element size is fully specified by a background mesh (as it is in
// this example), it is thus often desirable to set
gmsh::option::setNumber("Mesh.MeshSizeExtendFromBoundary", 0);
gmsh::option::setNumber("Mesh.MeshSizeFromPoints", 0);
gmsh::option::setNumber("Mesh.MeshSizeFromCurvature", 0);
// This will prevent over-refinement due to small mesh sizes on the boundary.
gmsh::model::mesh::generate(2);
gmsh::write("t10.msh");
// Launch the GUI to see the results:
std::set<std::string> args(argv, argv + argc);
if(!args.count("-nopopup")) gmsh::fltk::run();
gmsh::finalize();
return 0;
}