multicuboid

Create geometry formed by several cubic cells

Syntax

gm = multicuboid(W,D,H)

gm = multicuboid(W,D,H,Name,Value)

Description

gm = multicuboid(W,D,H) creates a geometry by combining several cubic cells.

When creating each cuboid, multicuboid uses the following coordinate system.

gm = multicuboid(W,D,H,Name,Value) creates a multi-cuboid geometry using one or more Name,Value pair arguments.

Examples

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)

Stacked Cuboids

Create a geometry that consists of four stacked cuboids and include this geometry in a PDE model.

Create the geometry by using the multicuboid function with the ZOffset argument. The resulting geometry consists of four cells stacked on top of each other.

gm = multicuboid(5,10,[1 2 3 4],'ZOffset',[0 1 3 6])

gm = 
  DiscreteGeometry with properties:

       NumCells: 4
       NumFaces: 21
       NumEdges: 36
    NumVertices: 20
       Vertices: [20x3 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 Cuboid

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

Use the multicuboid function to create a single cuboid. The resulting geometry consists of one cell.

gm = multicuboid(5,10,7)

gm = 
  DiscreteGeometry with properties:

       NumCells: 1
       NumFaces: 6
       NumEdges: 12
    NumVertices: 8
       Vertices: [8x3 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 Cube

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

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

gm = multicuboid([6 10],[6 10],10,'Void',[true,false])

gm = 
  DiscreteGeometry with properties:

       NumCells: 1
       NumFaces: 10
       NumEdges: 24
    NumVertices: 16
       Vertices: [16x3 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

W — Cell width

positive real number | vector of positive real numbers

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

Width W, depth D, and height H can be scalars or vectors of the same length. For a combination of scalar and vector inputs, multicuboid replicates the scalar arguments into vectors of the same length.

Note

All cells in the geometry either must have the same height, or must have both the same width and the same depth.

Example: gm = multicuboid([1 2 3],[2.5 4 5.5],5)

D — Cell depth

positive real number | vector of positive real numbers

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

Width W, depth D, and height H can be scalars or vectors of the same length. For a combination of scalar and vector inputs, multicuboid replicates the scalar arguments into vectors of the same length.

Note

All cells in the geometry either must have the same height, or must have both the same width and the same depth.

Example: gm = multicuboid([1 2 3],[2.5 4 5.5],5)

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.

Width W, depth D, and height H can be scalars or vectors of the same length. For a combination of scalar and vector inputs, multicuboid replicates the scalar arguments into vectors of the same length.

Note

All cells in the geometry either must have the same height, or must have both the same width and the same depth.

Example: gm = multicuboid(4,5,[1 2 3],'ZOffset',[0 1 3])

Name-Value Pair 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 = multicuboid([1 2],[1 2],[3 3],'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 width vector W, depth vector D, or height vector H.

Note

The ZOffset argument is valid only if the width and depth are constant for all cells in the geometry.

Example: gm = multicuboid(20,30,[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 width vector W, depth vector D, or the height vector H.

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

Example: gm = multicuboid([1 2],[1 2],[3 3],'Void',[true,false])

Data Types: double

Output Arguments

gm — Geometry object

DiscreteGeometry object

Geometry object, returned as a DiscreteGeometry Properties object.

Limitations

• multicuboid lets you create only geometries consisting of stacked or nested cuboids. For nested cuboids, the height must be the same for all cells in the geometry. For stacked cuboids, the width and depth must be the same for all cells in the geometry. Use the ZOffset argument to stack the cells on top of each other without overlapping them.

• multicuboid does not let you create nested cuboids of the same width and depth. The call multicuboid(w,d,[h1,h2,...]) is not supported.