From: Sean Ingimarson Date: Thu, 1 Apr 2021 14:33:32 +0000 (-0700) Subject: step-49 gmsh X-Git-Tag: v9.4.0-rc1~954^2~2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=4087d43c205ea32df78d9b6879417afc40c55d5e;p=dealii.git step-49 gmsh --- diff --git a/examples/step-49/doc/intro.dox b/examples/step-49/doc/intro.dox index 881c2281f0..83121c5ccf 100644 --- a/examples/step-49/doc/intro.dox +++ b/examples/step-49/doc/intro.dox @@ -99,12 +99,220 @@ many cases it is best to combine both approaches. The file can be easily reloaded by pressing "reload" under the "Geometry" tab if you want to write it by hand and see the effects in the graphical user interface of gmsh. + + This tutorial contains an example .geo file that describes a box -with two objects cut out in the interior. This is how +with two circles cut out in the interior and several slits on the sides. This is how example.geo looks like in %Gmsh (displaying the boundary indicators as well as the mesh discussed further down below): - + + +We will go through the basics of %Gmsh and show how we can obtain a mesh like this. + +It's also worth mentioning this video (which can be found here https://www.youtube.com/watch?v=xL2LmDsDLYw&t=921s) +which does a good job of explaining how to use gmsh to create basic shapes and meshes. +Let us first go through the documented example.geo file that describes the geometry. + +We will now go through the main parts of example.geo file that defines the mesh. + +
Point declaration
+ +In this section we create the points that make up the domain. + +The points can either be typed in the .geofile manually or +found via Geometry -> Elementary Entities -> Add -> +Point where you simply enter the coordinates in the prompt or use the mouse to place them. + +@code +Point(1) = {-3.5, -3.36, 0, 1.0}; +Point(2) = {3.5, -3.36, 0, 1.0}; +Point(3) = {3.5, 3.36, 0, 1.0}; +Point(4) = {-3.5, 3.36, 0, 1.0}; +Point(5) = {-3.5, 0.2, 0, 1.0}; +Point(6) = {-0.98 - b, 0.2, 0, 1.0}; +... +@endcode + +
Lines on outer domain
+ +To create lines of the mesh, go to Geometry -> Elementary +entities -> Add -> Line. You do not get a prompt to enter in +specific coordinates, rather you simply click a starting point and +ending point for each line. + +The generated code in the geo file then looks like this: + +@code +Line(4) = {4, 5}; +Line(5) = {5, 6}; +Line(6) = {6, 7}; +Line(7) = {7, 8}; +Line(8) = {8, 9}; +... +@endcode + +
Creating holes in domain
+ +Here are the points and lines that create the two holes in the domain. +We start by defining the relevant points for bottom left hole: + +@code +Point(31) = {-2.1, -1.54, 0, 1.0}; // origin +Point(32) = {-2.1, -0.84, 0, 1.0}; // top point +Point(33) = {-2.1, -2.24, 0, 1.0}; // bottom point +Point(103) = {-1.4, -1.54, 0, 1.0}; // right point +Point(104) = {-2.8, -1.54, 0, 1.0}; // left point +@endcode + +Then we use the Circle arc entity, which is found in the same category as +Point<\code> and Lines. The file reads "Circle" +but the difference to note is that this function uses three points to +make an arc of a circle, namely the starting point, center, and ending point. +Splitting the circle into four arcs like this allows for more freedom when declaring the +boundary IDs. + +@code +Circle(48) = {103, 31, 32}; +Circle(49) = {32, 31, 104}; +Circle(50) = {104, 31, 33}; +Circle(51) = {33, 31, 103}; +@endcode + +For the second circle, we use the alternate Circle entity, which requires the origin, radius, +and starting and ending angle respectively. + +@code +radius1 = .5; +Circle(12) = {0.42, 2.0, 0, radius1, 0, 2*Pi}; +@endcode + +
Plane surfaces
+ +This section describes the "Plane Surfaces", i.e., the 2D surfaces for meshing. +This can be found in Elementary entities as Plane Surface. +The purpose of this entity is to specify the domain in 2D. Because we have our +mesh split into 4 sections, we must have 4 plane surfaces. + +To make a plane surface, simply click Plane surface and click on all +the relevant borders for the mesh. This includes holes or other objects contained +in the mesh. Again, since we have 4 different meshes, we will do this 4 times. + +The code below is for the top right mesh. Notice we have 2 instances of +Curve Loop. The first one is the boundary for the outer domain +and the second one is for the hole. This can easily be traced back by following +along with the numbers in the brackets. + +@code +Curve Loop(1) = {40, -43, 14, 57, 59, 60, 58}; +Curve Loop(2) = {12}; +Plane Surface(1) = {1, 2}; +@endcode + +The other 4 surfaces are then declared in a similar way + +Next we define the physical surface itself. This line is what makes our mesh 2D. +The values in the bracket on the right hand side are the tags for the Plane Surfaces +we declared above. + +@code +Physical Surface(2) = {1, 2, 3, 4}; +@endcode + +
Physical IDs
+ +This section is for assigning physical IDs as these become boundary IDs in deal.II. Here you press +Geometry -> Physical groups -> Add -> Curve. You may do this +for points as well, but we will only be needing to use curves. + +We assign boundary ID 0 to the outer boundary. This is usually here by default +but we include it anyway: + +@code +Physical Curve(0) = {38, 39, 52:57, 59, 60, 58, 40, 41, 4:9}; +@endcode + +We then assign boundary ID of 1 top right circle; + +@code +Physical Curve(1) = {12}; +@endcode + +Finally, we assign boundary IDs of 2 and 3 to the top and bottom half of the bottom left +hole, respectively. We can see here that we needed to pick two boundaries +to make both of the physical curves. Recall this circle is comprised of +four circle arcs, so Physical Curve(2) is the top left and top right quarter +of the circle, and Physical Curve(3) is the bottom left and bottom right quarter +of the circle. + +@code +Physical Curve(2) = {48, 49}; +Physical Curve(3) = {50, 51}; +@endcode + +
Meshing Parameters
+ +Finally, the .geo file contains meshing parameters that can all be adjusted in the GMSH UI. We include it +at the bottom of our .geo file to keep the changes when creating our +.msh file. + +@code +Mesh.Algorithm = 3; +Mesh.RecombineAll = 1; +Mesh.CharacteristicLengthFactor = .6; +Mesh.SubdivisionAlgorithm = 1; +Mesh.Smoothing = 20; +Show "*"; +@endcode + +To view what each of these do, press Tools -> Options -> Mesh. + +You may change the algorithm used for meshing in 2D algorithm. + +CharacteristicLengthFactor can be thought of the distance between +nodes on the boundaries of the mesh. This sets the initial size of the nodes +of the mesh. If we want a finer mesh we want a smaller characteristic length. +For this examples purposes we would like to do more refinement in deal.ii so +we pick a relatively coarse mesh. This can also be adjusted in the Options +menu. + +SubdivisionAlgorithm is set to 1 in our file because we want to +use "All Quads" for subdivision. In the options menu the default is "None", +but we use "All Quads" for reasons mentioned earlier. + +Smoothing is a post-processing step that iteratively improves mesh quality (for example by moving inner vertices). The number of steps is not crucial in this example. +For our example we pick 20, however this value can be adjusted +accordingly, as it's not the most important step in mesh building. + + + +@note That ends the code for example.geo. It's important to note that + the .geo file did not come out as organized as it appears here. It + was edited after creating the mesh and geometry to be more readable. + +Before loading this into deal.II, we need to create the .msh +file. If everything was set up correctly, we can press Mesh -> 2D. +If all this goes well, then we +should see something similar to the following output: + + + +It behooves us at this point to also make sure our boundaries were declared +correctly. So in the Options menu go to Mesh -> Visibility. +In the dropdown menu labeled "Label type" we may choose a label for our boundaries. +We wish to check physical IDs, so we would like to have "Physical tag" picked. +Now we check "1D element labels" and we should see the numbers assigned to the +specified boundaries. + + + +Finally, we can choose Mesh -> Save to save the .msh file, which +deal.II's GridIn class can read. You can also generate the .msh from the +.geo file by running the command + +@code +gmsh -2 example.geo. +@endcode You might want to open the example.geo file in a text editor (it is located in the same directory as the step-49.cc source file) to diff --git a/examples/step-49/example.geo b/examples/step-49/example.geo index 95e422dc86..050931a65f 100644 --- a/examples/step-49/example.geo +++ b/examples/step-49/example.geo @@ -1,56 +1,136 @@ -cl1 = 1; - -Point(1) = {-1, 0.3, 0, 1}; -Point(2) = {0.5, 0.3, 0, 1}; -Point(3) = {-1, -0.5, 0, 1}; -Point(4) = {0.5, -0.5, 0, 1}; - -Point(7) = {-0.3, -0.1, 0, 1}; -Point(8) = {-0.2, -0.1, 0, 1}; -Point(9) = {-0.3, 0.1, -0, 1}; -Point(10) = {-0.4, -0.1, 0, 1}; -Point(11) = {-0.3, -0.3, 0, 1}; - -Point(12) = {0.1, -0.1, 0, 1}; -Point(13) = {0.2, 0.0, 0, 1}; -Point(14) = {0.3, -0.1, 0, 1}; - -// lines of the outer box: -Line(1) = {1, 2}; -Line(2) = {4, 2}; -Line(3) = {1, 3}; -Line(4) = {3, 4}; - -// the first cutout: -Ellipse(5) = {8, 7, 11, 9}; -Ellipse(6) = {9, 7, 11, 10}; -Ellipse(7) = {8, 7, 10, 11}; -Ellipse(8) = {11, 7, 8, 10}; - -// the second cutout: -Line(9) = {12, 13}; -Line(10) = {13, 14}; -Line(11) = {14, 12}; - -// loops of the outside and the two cutouts -Line Loop(12) = {1, -2, -4, -3}; -Line Loop(14) = {5, 6, -8, -7}; -Line Loop(15) = {9,10,11}; - -// these define the boundary indicators in deal.II: -Physical Line(0) = {1, 2, 4, 3}; -Physical Line(1) = {6, 5, 8, 7}; -Physical Line(2) = {9, 10, 11}; - - -// you need the physical surface, because that is what deal.II reads in -Plane Surface(16) = {12, 14, 15}; -Physical Surface(17) = {16}; - -// some parameters for the meshing: -Mesh.Algorithm = 8; +//--------------------------------------------------------------------------- +// In this section we create the points that make up the outer domain + +// Compute the length of the line closest to the edge of the slit: +b = .2 * Tan((60 * Pi)/180); + +// Points on the outer domain +Point(1) = {-3.5, -3.36, 0, 1.0}; +Point(2) = {3.5, -3.36, 0, 1.0}; +Point(3) = {3.5, 3.36, 0, 1.0}; +Point(4) = {-3.5, 3.36, 0, 1.0}; +Point(5) = {-3.5, 0.2, 0, 1.0}; +Point(6) = {-0.98 - b, 0.2, 0, 1.0}; +Point(7) = {-0.98, 0, 0, 1.0}; +Point(8) = {-0.98 - b, -0.2, 0, 1.0}; +Point(9) = {-3.5, -0.2, 0, 1.0}; +Point(14) = {3.5, 0, 0, 1.0}; // Tip of slit on left hand side + +// The 2 points below are for separating the left and right side of the mesh +Point(36) = {-0.98, 3.36, 0, 1.0}; +Point(37) = {-0.98, -3.36, 0, 1.0}; + +// Points for the right hand side slit +Point(107) = {3.5, -1.88, 0, 1.0}; +Point(108) = {3.5, -1.48, 0, 1.0}; +Point(109) = {1.2, -1.88, 0, 1.0}; +Point(110) = {1.8, -1.48, 0, 1.0}; + +// Points for the triangle on the right hand side +Point(111) = {3.5, 1.18, 0, 1.0}; +Point(112) = {3.5, 2.18, 0, 1.0}; +Point(113) = {3, 1.68, 0, 1.0}; + +//--------------------------------------------------------------------------- +// This section contains the lines that make up the outer domain + +// Lines for the left hand side of the domain +Line(4) = {4, 5}; +Line(5) = {5, 6}; +Line(6) = {6, 7}; +Line(7) = {7, 8}; +Line(8) = {8, 9}; +Line(9) = {9, 1}; +Line(14) = {7, 14}; // Line that bisects domain from top/bottom + +// Lines on the bottom/top domain +Line(38) = {1, 37}; +Line(39) = {37, 2}; +Line(40) = {3, 36}; +Line(41) = {36, 4}; + +// Lines that bisect the domain from left/right +Line(42) = {37, 7}; +Line(43) = {7, 36}; + +// Lines on the right hand side of the domain +Line(52) = {2, 107}; +Line(53) = {107, 109}; +Line(54) = {109, 110}; +Line(55) = {110, 108}; +Line(56) = {108, 14}; +Line(57) = {14, 111}; +Line(58) = {112, 3}; +Line(59) = {111, 113}; +Line(60) = {113, 112}; + +//--------------------------------------------------------------------------- +// Here are the points and lines that create the two holes in the domain + +// Relevant points for bottom left hole +Point(31) = {-2.1, -1.54, 0, 1.0}; // origin +Point(32) = {-2.1, -0.84, 0, 1.0}; // top point +Point(33) = {-2.1, -2.24, 0, 1.0}; // bottom point +Point(103) = {-1.4, -1.54, 0, 1.0}; // right point +Point(104) = {-2.8, -1.54, 0, 1.0}; // left point + +// Bottom left hole +Circle(48) = {103, 31, 32}; +Circle(49) = {32, 31, 104}; +Circle(50) = {104, 31, 33}; +Circle(51) = {33, 31, 103}; + +// The upper right circle +radius1 = .5; +Point(19) = {0.42, 2.0, 0, 1.0}; // origin +Point(22) = {0.42, 2.0 + radius1, 0, 1.0}; // top point +Point(23) = {0.42, 2.0 - radius1, 0, 1.0}; // bottom point +Circle(12) = {0.42, 2.0, 0, radius1, 0, 2*Pi}; + +//--------------------------------------------------------------------------- +// This section describes the "Plane Surfaces", i.e., the 2D surfaces for meshing + +// The surface of the top right partition +Curve Loop(1) = {40, -43, 14, 57, 59, 60, 58}; +Curve Loop(2) = {12}; +Plane Surface(1) = {1, 2}; + +// Surface of the bottom right partition +Curve Loop(3) = {39, 52, 53, 54, 55, 56, -14, -42}; +Plane Surface(2) = {3}; + +// Surface of bottem left mesh +Curve Loop(4) = {42, 7, 8, 9, 38}; +Curve Loop(5) = {49, 50, 51, 48}; +Plane Surface(3) = {4, 5}; + +// Surface of top left mesh +Curve Loop(6) = {6, 43, 41, 4, 5}; +Plane Surface(4) = {6}; + +// Creates a physical surface. The expression list on the right hand side is the list +// of elementary surfaces created above. This is what makes our mesh 2D. +Physical Surface(2) = {1, 2, 3, 4}; + +//--------------------------------------------------------------------------- +// This section describes the physical IDs of certain objects. + +// Assign boundary ID of 0 to outer boundary +Physical Curve(0) = {38, 39, 52, 53, 54, 55, 56, 57, 59, 60, 58, 40, 41, 4, 5, 6, 7, 8, 9}; + +// Assign boundary ID of 1 top right circle +Physical Curve(1) = {12}; + +// Assign boundary IDs of 2 & 3 to the top & bottom half of the bottom left +Physical Curve(2) = {48, 49}; +Physical Curve(3) = {50, 51}; + +//--------------------------------------------------------------------------- +// Parameters for the meshing + +Mesh.Algorithm = 3; Mesh.RecombineAll = 1; -Mesh.CharacteristicLengthFactor = 0.09; +Mesh.CharacteristicLengthFactor = .6; Mesh.SubdivisionAlgorithm = 1; Mesh.Smoothing = 20; Show "*"; diff --git a/examples/step-49/example.msh b/examples/step-49/example.msh index c98a09951f..175032a3df 100644 --- 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e4f2ccaf5b..4a81613d77 100644 --- a/examples/step-49/step-49.cc +++ b/examples/step-49/step-49.cc @@ -29,6 +29,8 @@ // @sect3{Include files} #include +#include +#include #include #include #include @@ -99,8 +101,31 @@ void print_mesh_info(const Triangulation &triangulation, // discussed in the introduction how to generate it. This follows the same // pattern as used in step-5 to load a mesh, although there it was written in // a different file format (UCD instead of MSH). +// +// It's worth noting that it is possible to save manifold ids when using +// the gmsh api. If we specify +// +// @code +// GMSH_INCLUDE_DIR +// GMSH_LIBRARY +// @endcode +// +// when building deal.II, then DEAL_II_GMSH_WITH_API gets defined and +// and we can use GridIn::read_msh(). More details on the function +// can be found in its deal.II documentation. +// +// We will be utilizing the SphericalManifold class for the holes. We need to +// assign manifold IDs for this purpose. As physical IDs from Gmsh are assigned +// to boundary IDs in deal.II, we will assign manifold IDs based on the boundary IDs loaded +// from the file. void grid_1() { + const Point<2> Top_right_hole_origin(0.42, 2.0); + const Point<2> Bottom_left_hole_origin(-2.1, -1.54); + + const SphericalManifold<2> Top_right_manifold(Top_right_hole_origin); + const SphericalManifold<2> Bottom_left_manifold(Bottom_left_hole_origin); + Triangulation<2> triangulation; GridIn<2> gridin; @@ -108,6 +133,20 @@ void grid_1() std::ifstream f("example.msh"); gridin.read_msh(f); + // Here is where we get the boundary IDs made in gmsh, which are in the first + // coordinate position, and assign them to manifold ids. With our example, we + // have boundary ID 1 on the top right hole and 2 and 3 for the bottom left + // hole. We assign both of these boundary IDs 2 because together they make a + // circle to match the manifold we assign it later. + triangulation.set_all_manifold_ids_on_boundary(1, 1); // top right hole + triangulation.set_all_manifold_ids_on_boundary(2, 2); // top of bottom left hole + triangulation.set_all_manifold_ids_on_boundary(3, 2); // bottom of bottom left hole + + triangulation.set_manifold(1, Top_right_manifold); + triangulation.set_manifold(2, Bottom_left_manifold); + + triangulation.refine_global(2); + print_mesh_info(triangulation, "grid-1.vtu"); }