multisphere

Create geometry formed by several spherical cells

Syntax

gm = multisphere(R)

gm = multisphere(R,"Void",eci)

Description

gm = multisphere(R) creates a geometry by combining several spherical cells.

When creating each sphere, multisphere uses the following coordinate system.

gm = multisphere(R,"Void",eci) creates a multi-sphere geometry with empty cells.

Examples

Nested Spheres

Create a geometry that consists of three nested spheres and include this geometry in a PDE model.

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

gm = multisphere([5 10 15])

gm = 
  DiscreteGeometry with properties:

       NumCells: 3
       NumFaces: 3
       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","FaceAlpha",0.2)

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")

Hollow Sphere

Create a hollow sphere and include it as a geometry in a PDE model.

Create a hollow sphere by using the multisphere function with the Void argument. The resulting geometry consists of one cell.

gm = multisphere([9 10],"Void",[true,false])

gm = 
  DiscreteGeometry with properties:

       NumCells: 1
       NumFaces: 2
       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]

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.

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

eci — Empty cell indicator

vector of logical true or false values

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

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

Example: gm = multisphere([1,2,3],"Void",[false,true,false])

Output Arguments

gm — Geometry object

DiscreteGeometry object

Geometry object, returned as a DiscreteGeometry object.

Version History

Introduced in R2017a