multicylinder

Create geometry formed by several cylindrical cells

Syntax

gm = multicylinder(R,H)

gm = multicylinder(R,H,Name,Value)

Description

gm = multicylinder(R,H) creates a geometry by combining several cylindrical cells.

When creating each cylinder, multicylinder uses the following coordinate system.

gm = multicylinder(R,H,Name,Value) creates a multi-cylinder geometry using one or more Name,Value pair arguments.

Examples

Nested Cylinders of Same Height

Create a geometry that consists of three nested cylinders of the same height and include this geometry in a PDE model.

Create the geometry by using the multicylinder function. The resulting geometry consists of three cells.

gm = multicylinder([5 10 15],2)

gm = 
  DiscreteGeometry with properties:

       NumCells: 3
       NumFaces: 9
       NumEdges: 6
    NumVertices: 6
       Vertices: [6x3 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)

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)

Single Cylinder

Create a geometry that consists of a single cylinder and include this geometry in a PDE model.

Use the multicylinder function to create a single cylinder. The resulting geometry consists of one cell.

gm = multicylinder(5,10)

gm = 
  DiscreteGeometry with properties:

       NumCells: 1
       NumFaces: 3
       NumEdges: 2
    NumVertices: 2
       Vertices: [2x3 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')

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)

Input Arguments

R — Cell radius

positive real number | vector of positive real numbers

Cell radius, specified as a positive real number or a vector of positive real numbers. If R is a vector, then R(i) specifies the radius of the ith cell.

Radius R and height H can be scalars or vectors of the same length. For a combination of scalar and vector inputs, multicylinder replicates the scalar arguments into vectors of the same length.

Note

Either radius or height must be the same for all cells in the geometry.

Example: gm = multicylinder([1 2 3],1)

H — Cell height

positive real number | vector of positive real numbers

Cell height, specified as a positive real number or a vector of positive real numbers. If H is a vector, then H(i) specifies the height of the ith cell.

Radius R and height H can be scalars or vectors of the same length. For a combination of scalar and vector inputs, multicylinder replicates the scalar arguments into vectors of the same length.

Note

Either radius or height must be the same for all cells in the geometry.

Example: gm = multicylinder(1,[1 2 3],'Zoffset',[0 1 3])

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: gm = multicylinder([1 2],1,'Void',[true,false])

ZOffset — Z-offset for each cell

vector of 0 values (default) | vector of real numbers

Z-offset for each cell, specified as a vector of real numbers. ZOffset(i) specifies the Z-offset of the ith cell. This vector must have the same length as the radius vector R or height vector H.

Note

The ZOffset argument is valid only if the radius is the same for all cells in the geometry.

Example: gm = multicylinder(20,[10 10],'ZOffset',[0 10])

Data Types: double

Void — Empty cell indicator

vector of logical false values (default) | vector of logical true or false values

Empty cell indicator, specified as a vector of logical true or false values. This vector must have the same length as the radius vector R or the height vector H.

The value true corresponds to an empty cell. By default, multicylinder assumes that all cells are not empty.

Example: gm = multicylinder([1 2],1,'Void',[true,false])

Data Types: double

Output Arguments

gm — Geometry object

DiscreteGeometry object

Geometry object, returned as a DiscreteGeometry Properties object.

Tip

A cylinder has one cell, three faces, and two edges. Also, since every edge has a start and an end vertex, a cylinder has vertices. Both edges are circles, their start and end vertices coincide. Thus, a cylinder has two vertices - one for each edge.

Limitations

• multicylinder lets you create only geometries consisting of stacked or nested cylinders. For nested cylinders, the height must be the same for all cells in the geometry. For stacked cylinders, the radius must be the same for all cells in the geometry. Use the ZOffset argument to stack the cells on top of each over without overlapping them.

• multicylinder does not let you create nested cylinders of the same radius. The call multicylinder(r,[h1,h2,...]) is not supported.