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cuboids, cylinders, and spheres -凯发k8网页登录

this example shows how to create 3-d geometries formed by one or more cubic, cylindrical, and spherical cells by using the , , and functions, respectively. with these functions, you can create stacked or nested geometries. you also can create geometries where some cells are empty; for example, hollow cylinders, cubes, or spheres.

all cells in a geometry must be of the same type: either cuboids, or cylinders, or spheres. these functions do not combine cells of different types in one geometry.

single sphere

create a geometry that consists of a single sphere and include this geometry in a pde model.

use the multisphere function to create a single sphere. the resulting geometry consists of one cell.

gm = multisphere(5)
gm = 
  discretegeometry with properties:
       numcells: 1
       numfaces: 1
       numedges: 0
    numvertices: 0
       vertices: []

create a pde model.

model = createpde
model = 
  pdemodel with properties:
           pdesystemsize: 1
         istimedependent: 0
                geometry: []
    equationcoefficients: []
      boundaryconditions: []
       initialconditions: []
                    mesh: []
           solveroptions: [1x1 pde.pdesolveroptions]

include the geometry in the model.

model.geometry = gm
model = 
  pdemodel with properties:
           pdesystemsize: 1
         istimedependent: 0
                geometry: [1x1 discretegeometry]
    equationcoefficients: []
      boundaryconditions: []
       initialconditions: []
                    mesh: []
           solveroptions: [1x1 pde.pdesolveroptions]

plot the geometry.

pdegplot(model,"celllabels","on")

figure contains an axes object. the axes object contains 2 objects of type quiver, patch.

nested cuboids of same height

create a geometry that consists of three nested cuboids of the same height and include this geometry in a pde model.

create the geometry by using the multicuboid function. the resulting geometry consists of three cells.

gm = multicuboid([2 3 5],[4 6 10],3)
gm = 
  discretegeometry with properties:
       numcells: 3
       numfaces: 18
       numedges: 36
    numvertices: 24
       vertices: [24x3 double]

create a pde model.

model = createpde
model = 
  pdemodel with properties:
           pdesystemsize: 1
         istimedependent: 0
                geometry: []
    equationcoefficients: []
      boundaryconditions: []
       initialconditions: []
                    mesh: []
           solveroptions: [1x1 pde.pdesolveroptions]

include the geometry in the model.

model.geometry = gm
model = 
  pdemodel with properties:
           pdesystemsize: 1
         istimedependent: 0
                geometry: [1x1 discretegeometry]
    equationcoefficients: []
      boundaryconditions: []
       initialconditions: []
                    mesh: []
           solveroptions: [1x1 pde.pdesolveroptions]

plot the geometry.

pdegplot(model,"celllabels","on","facealpha",0.5)

figure contains an axes object. the axes object contains 3 objects of type quiver, patch, line.

stacked cylinders

create a geometry that consists of three stacked cylinders and include this geometry in a pde model.

create the geometry by using the multicylinder function with the zoffset argument. the resulting geometry consists of four cells stacked on top of each other.

gm = multicylinder(10,[1 2 3 4],"zoffset",[0 1 3 6])
gm = 
  discretegeometry with properties:
       numcells: 4
       numfaces: 9
       numedges: 5
    numvertices: 5
       vertices: [5x3 double]

create a pde model.

model = createpde
model = 
  pdemodel with properties:
           pdesystemsize: 1
         istimedependent: 0
                geometry: []
    equationcoefficients: []
      boundaryconditions: []
       initialconditions: []
                    mesh: []
           solveroptions: [1x1 pde.pdesolveroptions]

include the geometry in the model.

model.geometry = gm
model = 
  pdemodel with properties:
           pdesystemsize: 1
         istimedependent: 0
                geometry: [1x1 discretegeometry]
    equationcoefficients: []
      boundaryconditions: []
       initialconditions: []
                    mesh: []
           solveroptions: [1x1 pde.pdesolveroptions]

plot the geometry.

pdegplot(model,"celllabels","on","facealpha",0.5)

figure contains an axes object. the axes object contains 3 objects of type quiver, patch, line.

hollow cylinder

create a hollow cylinder and include it as a geometry in a pde model.

create a hollow cylinder by using the multicylinder function with the void argument. the resulting geometry consists of one cell.

gm = multicylinder([9 10],10,"void",[true,false])
gm = 
  discretegeometry with properties:
       numcells: 1
       numfaces: 4
       numedges: 4
    numvertices: 4
       vertices: [4x3 double]

create a pde model.

model = createpde
model = 
  pdemodel with properties:
           pdesystemsize: 1
         istimedependent: 0
                geometry: []
    equationcoefficients: []
      boundaryconditions: []
       initialconditions: []
                    mesh: []
           solveroptions: [1x1 pde.pdesolveroptions]

include the geometry in the model.

model.geometry = gm
model = 
  pdemodel with properties:
           pdesystemsize: 1
         istimedependent: 0
                geometry: [1x1 discretegeometry]
    equationcoefficients: []
      boundaryconditions: []
       initialconditions: []
                    mesh: []
           solveroptions: [1x1 pde.pdesolveroptions]

plot the geometry.

pdegplot(model,"celllabels","on","facealpha",0.5)

figure contains an axes object. the axes object contains 3 objects of type quiver, patch, line.

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