area

Area of 2-D mesh elements

Syntax

A = area(mesh)

[A,AE] = area(mesh)

A = area(mesh,elements)

Description

A = area(mesh) returns the area A of the entire mesh.

[A,AE] = area(mesh) also returns a row vector AE containing areas of each individual element of the mesh.

A = area(mesh,elements) returns the combined area of the specified elements of the mesh.

Examples

Area of Entire 2-D Mesh

Generate a 2-D mesh and find its area.

Create a PDE model.

model = createpde;

Include the geometry of the built-in function lshapeg. Plot the geometry.

geometryFromEdges(model,@lshapeg);
pdegplot(model,'FaceLabels','on')

Generate a mesh and plot it.

mesh = generateMesh(model);
figure
pdemesh(model)

Compute the area of the entire mesh.

ma = area(mesh)

ma = 3.0000

Area of Individual Elements of 2-D Mesh

Generate a 2-D mesh and find the area of each element.

Create a PDE model.

model = createpde;

Include the geometry of the built-in function lshapeg. Plot the geometry.

geometryFromEdges(model,@lshapeg);
pdegplot(model,'FaceLabels','on')

Generate a mesh and plot it.

mesh = generateMesh(model);
figure
pdemesh(model)

Compute the area of the entire mesh and the area of each individual element of the mesh. Display the areas of the first 5 elements.

[ma,mi] = area(mesh);
mi(1:5)

ans = 1×5

    0.0047    0.0054    0.0053    0.0048    0.0061

Total Area of Group of Elements

Find the combined area of the elements associated with a particular face of a 2-D mesh.

Create a PDE model.

model = createpde;

Include the geometry of the built-in function lshapeg. Plot the geometry.

geometryFromEdges(model,@lshapeg);
pdegplot(model,'FaceLabels','on')

Generate a mesh and plot it.

mesh = generateMesh(model);
figure
pdemesh(model)

Find the elements associated with face 1 and compute the total area of these elements.

Ef1 = findElements(mesh,'region','Face',1);
maf1 = area(mesh,Ef1)

maf1 = 1.0000

Find how much of the total mesh area belongs to these elements. Return the result as a percentage.

maf1_percent = maf1/area(mesh)*100

maf1_percent = 33.3333

Input Arguments

mesh — Mesh object

Mesh property of a PDEModel object | output of generateMesh

Mesh object, specified as the Mesh property of a PDEModel object or as the output of generateMesh.

Example: model.Mesh

elements — Element IDs

positive integer | matrix of positive integers

Element IDs, specified as a positive integer or a matrix of positive integers.

Example: [10 68 81 97 113 130 136 164]

Output Arguments

A — Area

positive number

Area of the entire mesh or the combined area of the specified elements of the mesh, returned as a positive number.

AE — Areas of individual elements

row vector of positive numbers

Areas of individual elements, returned as a row vector of positive numbers.