assema

(Not recommended) Assemble area integral contributions

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assema is not recommended. Use assembleFEMatrices instead.

Syntax

[K,M,F] = assema(model,c,a,f)
[K,M,F] = assema(p,t,c,a,f)

Description

[K,M,F] = assema(model,c,a,f) assembles the stiffness matrix K, the mass matrix M, and the load vector F using the mesh contained in model, and the PDE coefficients c, a, and f.

example

[K,M,F] = assema(p,t,c,a,f) assembles the matrices from the mesh data in p and t.

example

Examples

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Open Live Script

Assemble finite element matrices for an elliptic problem on complicated geometry.

The PDE is Poisson's equation,

-∇⋅∇u=1.

Partial Differential Equation Toolbox™ solves equations of the form

-∇⋅(c∇u)+au=f.

So, represent Poisson's equation in toolbox syntax by setting c = 1, a = 0, and f = 1.

c = 1;
a = 0;
f = 1;

Create a PDE model container. Import the ForearmLink.stl file into the model and examine the geometry.

model = createpde;
importGeometry(model,'ForearmLink.stl');
pdegplot(model,'FaceAlpha',0.5)

Figure contains an axes object. The axes object contains 6 objects of type quiver, text, patch, line.

Create a mesh for the model.

generateMesh(model);

Create the finite element matrices from the mesh and the coefficients.

[K,M,F] = assema(model,c,a,f);

The returned matrix K is quite sparse. M has no nonzero entries.

disp(['Fraction of nonzero entries in K is ',num2str(nnz(K)/numel(K))])
Fraction of nonzero entries in K is 0.00046964

disp(['Number of nonzero entries in M is ',num2str(nnz(M))])
Number of nonzero entries in M is 0
Open Live Script

Assemble finite element matrices for the 2-D L-shaped region, using the [p,e,t] mesh representation.

Define the geometry using the lshapeg function included your software.

g = @lshapeg;

Use coefficients c = 1, a = 0, and f = 1.

c = 1;
a = 0;
f = 1;

Create a mesh and assemble the finite element matrices.

[p,e,t] = initmesh(g);
[K,M,F] = assema(p,t,c,a,f);

The returned matrix M has all zeros. The K matrix is quite sparse.

disp(['Fraction of nonzero entries in K is ',num2str(nnz(K)/numel(K))])
Fraction of nonzero entries in K is 0.042844

disp(['Number of nonzero entries in M is ',num2str(nnz(M))])
Number of nonzero entries in M is 0

Input Arguments

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PDE model, specified as a PDEModel object.

Example: model = createpde

PDE coefficient, specified as a scalar, matrix, character vector, character array, string scalar, string vector, or coefficient function. c represents the c coefficient in the scalar PDE

−∇⋅(c∇u)+au=f

or in the system of PDEs

−∇⋅(c⊗∇u)+au=f

Example: 'cosh(x+y.^2)'

Data Types: double | char | string | function_handle
Complex Number Support: Yes

PDE coefficient, specified as a scalar, matrix, character vector, character array, string scalar, string vector, or coefficient function. a represents the a coefficient in the scalar PDE

−∇⋅(c∇u)+au=f

or in the system of PDEs

−∇⋅(c⊗∇u)+au=f

Example: 2*eye(3)

Data Types: double | char | string | function_handle
Complex Number Support: Yes

PDE coefficient, specified as a scalar, matrix, character vector, character array, string scalar, string vector, or coefficient function. f represents the f coefficient in the scalar PDE

−∇⋅(c∇u)+au=f

or in the system of PDEs

−∇⋅(c⊗∇u)+au=f

Example: char('sin(x)';'cos(y)';'tan(z)')

Data Types: double | char | string | function_handle
Complex Number Support: Yes

Mesh points, specified as a 2-by-Np matrix of points, where Np is the number of points in the mesh. For a description of the (p,e,t) matrices, see Mesh Data as [p,e,t] Triples.

Typically, you use the p, e, and t data exported from the PDE Modeler app, or generated by initmesh or refinemesh.

Example: [p,e,t] = initmesh(gd)

Data Types: double

Mesh triangles, specified as a 4-by-Nt matrix of triangles, where Nt is the number of triangles in the mesh. For a description of the (p,e,t) matrices, see Mesh Data as [p,e,t] Triples.

Typically, you use the p, e, and t data exported from the PDE Modeler app, or generated by initmesh or refinemesh.

Example: [p,e,t] = initmesh(gd)

Data Types: double

Output Arguments

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Stiffness matrix, returned as a sparse matrix. See Elliptic Equations.

Typically, you use K in a subsequent call to assempde.

Mass matrix. returned as a sparse matrix. See Elliptic Equations.

Typically, you use M in a subsequent call to a solver such as assempde or hyperbolic.

Load vector, returned as a vector. See Elliptic Equations.

Typically, you use F in a subsequent call to assempde.

Version History

Introduced before R2006a

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See Also