EigenResults

PDE eigenvalue solution and derived quantities

Description

An EigenResults object contains the solution of a PDE eigenvalue problem in a form convenient for plotting and postprocessing.

• Eigenvector values at the nodes appear in the Eigenvectors property.

• The eigenvalues appear in the Eigenvalues property.

Creation

There are several ways to create an EigenResults object:

• Solve an eigenvalue problem using the solvepdeeig function. This function returns a PDE eigenvalue solution as an EigenResults object. This is the recommended approach.

• Solve an eigenvalue problem using the pdeeig function. Then use the createPDEResults function to obtain an EigenResults object from a PDE eigenvalue solution returned by pdeeig. Note that pdeeig is a legacy function. It is not recommended for solving eigenvalue problems.

Properties

Mesh — Finite element mesh

FEMesh object

Finite element mesh, returned as a FEMesh Properties object.

Eigenvectors — Solution eigenvectors

matrix | 3-D array

Solution eigenvectors, returned as a matrix or 3-D array. The solution is a matrix for scalar eigenvalue problems, and a 3-D array for eigenvalue systems. For details, see Dimensions of Solutions, Gradients, and Fluxes.

Data Types: double

Eigenvalues — Solution eigenvalues

vector

Solution eigenvalues, returned as a vector. The vector is in order by the real part of the eigenvalues from smallest to largest.

Data Types: double

Object Functions

interpolateSolution

Interpolate PDE solution to arbitrary points

Examples

Results from an Eigenvalue Problem

Obtain an EigenResults object from solvepdeeig.

Create the geometry for the L-shaped membrane. Apply zero Dirichlet boundary conditions to all edges.

model = createpde;
geometryFromEdges(model,@lshapeg);
applyBoundaryCondition(model,'dirichlet', ...
                             'Edge',1:model.Geometry.NumEdges, ...
                             'u',0);

Specify coefficients c = 1, a = 0, and d = 1.

specifyCoefficients(model,'m',0,'d',1,'c',1,'a',0,'f',0);

Create the mesh and solve the eigenvalue problem for eigenvalues from 0 through 100.

generateMesh(model,'Hmax',0.05);
ev = [0,100];
results = solvepdeeig(model,ev)

              Basis= 10,  Time=   0.15,  New conv eig=  0
              Basis= 11,  Time=   0.18,  New conv eig=  0
              Basis= 12,  Time=   0.19,  New conv eig=  0
              Basis= 13,  Time=   0.19,  New conv eig=  0
              Basis= 14,  Time=   0.23,  New conv eig=  0
              Basis= 15,  Time=   0.23,  New conv eig=  0
              Basis= 16,  Time=   0.23,  New conv eig=  0
              Basis= 17,  Time=   0.24,  New conv eig=  0
              Basis= 18,  Time=   0.25,  New conv eig=  1
              Basis= 19,  Time=   0.26,  New conv eig=  1
              Basis= 20,  Time=   0.26,  New conv eig=  1
              Basis= 21,  Time=   0.27,  New conv eig=  1
              Basis= 22,  Time=   0.28,  New conv eig=  3
              Basis= 23,  Time=   0.28,  New conv eig=  3
              Basis= 24,  Time=   0.29,  New conv eig=  4
              Basis= 25,  Time=   0.40,  New conv eig=  5
              Basis= 26,  Time=   0.42,  New conv eig=  6
              Basis= 27,  Time=   0.43,  New conv eig=  6
              Basis= 28,  Time=   0.43,  New conv eig=  6
              Basis= 29,  Time=   0.44,  New conv eig=  7
              Basis= 30,  Time=   0.45,  New conv eig=  7
              Basis= 31,  Time=   0.46,  New conv eig= 10
              Basis= 32,  Time=   0.46,  New conv eig= 10
              Basis= 33,  Time=   0.47,  New conv eig= 11
              Basis= 34,  Time=   0.47,  New conv eig= 11
              Basis= 35,  Time=   0.48,  New conv eig= 14
              Basis= 36,  Time=   0.50,  New conv eig= 14
              Basis= 37,  Time=   0.50,  New conv eig= 14
              Basis= 38,  Time=   0.51,  New conv eig= 14
              Basis= 39,  Time=   0.52,  New conv eig= 14
              Basis= 40,  Time=   0.52,  New conv eig= 14
              Basis= 41,  Time=   0.65,  New conv eig= 15
              Basis= 42,  Time=   0.68,  New conv eig= 15
              Basis= 43,  Time=   0.68,  New conv eig= 15
              Basis= 44,  Time=   0.69,  New conv eig= 16
              Basis= 45,  Time=   0.70,  New conv eig= 16
              Basis= 46,  Time=   0.70,  New conv eig= 16
              Basis= 47,  Time=   0.72,  New conv eig= 16
              Basis= 48,  Time=   0.74,  New conv eig= 17
              Basis= 49,  Time=   0.77,  New conv eig= 18
              Basis= 50,  Time=   0.78,  New conv eig= 18
              Basis= 51,  Time=   0.79,  New conv eig= 18
              Basis= 52,  Time=   0.80,  New conv eig= 18
              Basis= 53,  Time=   1.06,  New conv eig= 18
              Basis= 54,  Time=   1.11,  New conv eig= 21
End of sweep: Basis= 54,  Time=   1.11,  New conv eig= 21
              Basis= 31,  Time=   1.15,  New conv eig=  0
              Basis= 32,  Time=   1.16,  New conv eig=  0
              Basis= 33,  Time=   1.16,  New conv eig=  0
End of sweep: Basis= 33,  Time=   1.16,  New conv eig=  0

results = 
  EigenResults with properties:

    Eigenvectors: [5597x19 double]
     Eigenvalues: [19x1 double]
            Mesh: [1x1 FEMesh]

Plot the solution for mode 10.

pdeplot(model,'XYData',results.Eigenvectors(:,10))