# multicylinder

Create geometry formed by several cylindrical cells

## Description

## 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

Include the geometry in the model.

model.Geometry = gm

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 `i`

th 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 `i`

th 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 pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**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 `i`

th 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`

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.

## Version History

**Introduced in R2017a**

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