eqHelm.edp

include "gmshExport.idp";

real k = 6;
real alpha = pi/6;
func uinc = exp(1i*k*(x*cos(alpha) + y*sin(alpha)));

real R1 = 1;
real R2 = 3;

border C1(t=0,2*pi){x=R1*cos(t); y = R1*sin(t);}
border C2(t=0,2*pi){x=R2*cos(t); y = R2*sin(t);}

int nlambda = 20;
int nc1 = floor(k*nlambda*R1);
int nc2 = floor(k*nlambda*R2);


mesh Th = buildmesh(C1(-nc1) + C2(nc2));

fespace Vh(Th, P1);
Vh<complex> uh,vh;
solve Helmholtz (uh , vh, solver=LU) = int2d ( Th ) ( dx ( uh ) * dx ( vh ) ) + int2d ( Th ) ( dy ( uh ) * dy ( vh ) )  -  int2d ( Th ) ( k*k*uh  * vh  ) - int1d ( Th, C2 ) (  1i*k*uh* vh ) + on(C1,uh=uinc);

Vh<complex> uabs = abs(uh + uinc);
Vh<complex> ure = real(uh);
plot(ure, wait = true, cmm = "Solution", value = true, fill = true, dim = 2);
gmshExport(Th, uh[], "uh.pos");
gmshExport(Th, ure[], "ure.pos");
gmshExport(Th, uabs[], "uabs.pos");