eigenvalues and eigenmodes of l-pg电子麻将胡了
this example shows how to calculate eigenvalues and eigenvectors. the eigenvalue problem is . this example computes all eigenmodes with eigenvalues smaller than 100.
create a model and include this geometry. the geometry of the l-shaped membrane is described in the file lshapeg.
model = createpde(); geometryfromedges(model,@lshapeg);
set zero dirichlet boundary conditions on all edges.
applyboundarycondition(model,"dirichlet", ... "edge",1:model.geometry.numedges, ... "u",0);
specify the coefficients for the problem: d = 1 and c = 1. all other coefficients are equal to zero.
specifycoefficients(model,"m",0,"d",1,"c",1,"a",0,"f",0);
set the interval [0 100] as the region for the eigenvalues in the solution.
r = [0 100];
create a mesh and solve the problem.
generatemesh(model,"hmax",0.05);
results = solvepdeeig(model,r); basis= 10, time= 0.12, new conv eig= 0
basis= 11, time= 0.16, new conv eig= 0
basis= 12, time= 0.17, new conv eig= 0
basis= 13, time= 0.18, new conv eig= 0
basis= 14, time= 0.19, new conv eig= 0
basis= 15, time= 0.21, new conv eig= 0
basis= 16, time= 0.21, new conv eig= 0
basis= 17, time= 0.22, new conv eig= 0
basis= 18, time= 0.22, new conv eig= 1
basis= 19, time= 0.23, new conv eig= 1
basis= 20, time= 0.23, new conv eig= 1
basis= 21, time= 0.24, new conv eig= 2
basis= 22, time= 0.26, new conv eig= 3
basis= 23, time= 0.27, new conv eig= 3
basis= 24, time= 0.28, new conv eig= 3
basis= 25, time= 0.30, new conv eig= 3
basis= 26, time= 0.31, new conv eig= 3
basis= 27, time= 0.32, new conv eig= 3
basis= 28, time= 0.32, new conv eig= 4
basis= 29, time= 0.33, new conv eig= 4
basis= 30, time= 0.33, new conv eig= 4
basis= 31, time= 0.34, new conv eig= 5
basis= 32, time= 0.34, new conv eig= 5
basis= 33, time= 0.35, new conv eig= 5
basis= 34, time= 0.36, new conv eig= 5
basis= 35, time= 0.36, new conv eig= 6
basis= 36, time= 0.63, new conv eig= 6
basis= 37, time= 0.66, new conv eig= 6
basis= 38, time= 0.67, new conv eig= 7
basis= 39, time= 0.70, new conv eig= 7
basis= 40, time= 0.71, new conv eig= 7
basis= 41, time= 0.72, new conv eig= 7
basis= 42, time= 0.73, new conv eig= 7
basis= 43, time= 0.75, new conv eig= 8
basis= 44, time= 0.77, new conv eig= 8
basis= 45, time= 0.78, new conv eig= 9
basis= 46, time= 0.79, new conv eig= 11
basis= 47, time= 0.81, new conv eig= 11
basis= 48, time= 0.83, new conv eig= 11
basis= 49, time= 0.85, new conv eig= 11
basis= 50, time= 1.03, new conv eig= 13
basis= 51, time= 1.08, new conv eig= 13
basis= 52, time= 1.11, new conv eig= 14
basis= 53, time= 1.13, new conv eig= 14
basis= 54, time= 1.16, new conv eig= 14
basis= 55, time= 1.18, new conv eig= 14
basis= 56, time= 1.19, new conv eig= 14
basis= 57, time= 1.21, new conv eig= 14
basis= 58, time= 1.22, new conv eig= 14
basis= 59, time= 1.23, new conv eig= 15
basis= 60, time= 1.24, new conv eig= 15
basis= 61, time= 1.40, new conv eig= 15
basis= 62, time= 1.44, new conv eig= 16
basis= 63, time= 1.46, new conv eig= 16
basis= 64, time= 1.48, new conv eig= 16
basis= 65, time= 1.50, new conv eig= 17
basis= 66, time= 1.53, new conv eig= 17
basis= 67, time= 1.54, new conv eig= 18
basis= 68, time= 1.56, new conv eig= 18
basis= 69, time= 1.58, new conv eig= 18
basis= 70, time= 1.60, new conv eig= 19
basis= 71, time= 1.62, new conv eig= 20
basis= 72, time= 1.63, new conv eig= 21
basis= 73, time= 1.65, new conv eig= 21
basis= 74, time= 1.65, new conv eig= 22
end of sweep: basis= 74, time= 1.65, new conv eig= 22
basis= 32, time= 1.67, new conv eig= 0
basis= 33, time= 1.69, new conv eig= 0
basis= 34, time= 1.70, new conv eig= 0
basis= 35, time= 1.71, new conv eig= 0
basis= 36, time= 1.72, new conv eig= 0
basis= 37, time= 1.73, new conv eig= 0
basis= 38, time= 1.74, new conv eig= 0
basis= 39, time= 1.74, new conv eig= 0
basis= 40, time= 1.74, new conv eig= 0
basis= 41, time= 1.75, new conv eig= 0
basis= 42, time= 1.75, new conv eig= 0
end of sweep: basis= 42, time= 1.75, new conv eig= 0
there are 19 eigenvalues smaller than 100.
length(results.eigenvalues)
ans = 19
plot the first eigenmode and compare it to the matlab's membrane function.
u = results.eigenvectors; pdeplot(model,"xydata",u(:,1),"zdata",u(:,1));
figure membrane(1,20,9,9)
eigenvectors can be multiplied by any scalar and remain eigenvectors. this explains the difference in scale that you see.
membrane can produce the first 12 eigenfunctions for the l-shaped membrane. compare the 12th eigenmodes.
figure pdeplot(model,"xydata",u(:,12),"zdata",u(:,12));
figure membrane(12,20,9,9)
select a web site
choose a web site to get translated content where available and see local events and offers. based on your location, we recommend that you select: .
you can also select a web site from the following list: