Problem
So I took this example and my goal is to rewrite it using varf
functionality and get the same results.
Note
The usage of varf
is explained here on a 2D and 3D Poisson problem.
load "msh3" //import three-dimensional meshing tools
mesh3 T = cube(10, 10, 10);
fespace V(T, P1);
varf a(u, v) = int3d(T)( dx(u)*dx(v) + dy(u)*dy(v) + dz(u)*dz(v) )
+ on(1, 2, u = 0.0);
varf l(u, v) = int3d(T)( x*v ) + on(1, 2, u = 0.0);
matrix A = a(V, V);
real[int] b = l(0, V);
V u;
u[] = A^-1*b;
plot(u, value = true, fill = true, nbiso = 64, wait = true);
Attempt at solution
So my attempt to rewrite the example is as follows
load "medit"
include "cube.idp"
int[int] Nxyz=[20,5,5];
real [int,int] Bxyz=[[0.,5.],[0.,1.],[0.,1.]];
int [int,int] Lxyz=[[1,2],[2,2],[2,2]];
mesh3 Th=Cube(Nxyz,Bxyz,Lxyz);
real E = 21.5e4;
real sigma = 0.29;
real mu = E/(2*(1+sigma));
real lambda = E*sigma/((1+sigma)*(1-2*sigma));
real gravity = -0.05;
fespace Vh(Th,[P1,P1,P1]);
Vh [u1,u2,u3], [v1,v2,v3];
real sqrt2=sqrt(2.);
macro epsilon(u1,u2,u3) [dx(u1),dy(u2),dz(u3),(dz(u2)+dy(u3))/sqrt2,(dz(u1)+dx(u3))/sqrt2,(dy(u1)+dx(u2))/sqrt2] // EOM
macro div(u1,u2,u3) ( dx(u1)+dy(u2)+dz(u3) ) // EOM
// ******************** Modification below.
varf a([u1,u2,u3],[v1,v2,v3]) =
int3d(Th)(
lambda*div(u1,u2,u3)*div(v1,v2,v3)
+2.*mu*( epsilon(u1,u2,u3)'*epsilon(v1,v2,v3) ) //')
)
+ on(1,u1=0,u2=0,u3=0)
;
varf l([u1,u2,u3],[v1,v2,v3]) = int3d(Th) (gravity*v3);
matrix A = a(Vh, Vh);
real[int] b = l(0, Vh);
// The following lines break but I do not know why!
Vh [uu1, uu2, uu3];
[uu1[, uu2, uu3]] = A^-1*b;
As marked above, the final couple of lines break at compile time but I can not figure out why. Could anybody help?