example23.edp

// example23.edp from examples/chapt3/sound.edp
// sound propagation and eigenvalues

verbosity = 10;  // increase informational printing
real konc2;   // (k/c)^2
if (true) {
  konc2 = 1.0;  // good solution
} else {
  konc2 = 14.6993;  // eigenvalue! => bad solution
}

func g = y*(1-y);

border a0(t=0,1) { x= 5; y= 1+2*t; }
border a1(t=0,1) { x=5-2*t; y= 3; }
border a2(t=0,1) { x= 3-2*t; y=3-2*t; }
border a3(t=0,1) { x= 1-t; y= 1; }
border a4(t=0,1) { x= 0; y= 1-t; }
border a5(t=0,1) { x= t; y= 0; }
border a6(t=0,1) { x= 1+4*t; y= t; }

mesh Th=buildmesh( a0(20) + a1(20) + a2(20)
        + a3(20) + a4(20) + a5(20) + a6(20));
fespace Vh(Th,P1);  
Vh u,v;

solve sound(u,v)=int2d(Th)(u*v * konc2 - dx(u)*dx(v) - dy(u)*dy(v))
                 - int1d(Th,a4)(g*v);

plot(u, wait=1);

Vh u1,u2;


real sigma = 1;  // value of the shift

// OP = A - sigma B ;  //  the shifted matrix
varf  op(u1,u2)= int2d(Th)(  dx(u1)*dx(u2) + dy(u1)*dy(u2) - sigma* u1*u2 );

varf b([u1],[u2]) = int2d(Th)(  u1*u2 );

matrix OP = op(Vh, Vh, solver=UMFPACK);
matrix B = b(Vh, Vh, solver=UMFPACK);


int nev=20;  // number of computed eigen value close to sigma

real[int] ev(nev); // to store the  nev eigenvalue
Vh[int] eV(nev);   // to store the nev eigenVector


int k=EigenValue(OP, B, sym=true, sigma=sigma, value=ev, vector=eV,
                   tol=1e-10, maxit=0, ncv=0);

assert(k == nev);  // k is number of eigenvalues found

for (int n=0; n<nev; n++){
  cout << "Eigenvalue " << n << " = " << ev[n] << endl;
}

for (int n=0; n<nev; n++){
  plot(eV[n],wait=1);
}