The Poisson problem is solved using matrices
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Solution and mesh |
download example: lap_mat.edp or return to 2D examples
// laplace with matrix verbosity=10; mesh Th=square(10,10); fespace Vh(Th,P1); Vh u1,u2; varf a(u1,u2)= int2d(Th)( dx(u1)*dx(u2) + dy(u1)*dy(u2) ) + on(1,2,3,4,u1=1); varf b([u1],[u2]) = int2d(Th)( u1*u2 ); matrix A= a(Vh,Vh,solver=CG); matrix B= b(Vh,Vh,solver=CG,eps=1e-20); Vh bb ,bc,rhs; bc[]= a(0,Vh); // to save the u1=x; bb[] = bc[] .* u1[]; u1[] = A^-1*bb[]; //plot(u1,cmm="solution = x ",wait=1,value=1); u1=x*y; bb[] = bc[] .* u1[]; u1[] = A^-1*bb[]; //plot(u1,cmm="solution = x*y ",wait=1,value=1); u1=-4; // $-\Delta (x^2 + y^2) $ bb[] = B*u1[]; u1= x^2 + y^2 ; bb[] += bc[] .* u1[]; u1[] = A^-1*bb[]; u2= x^2 + y^2; cout << " u1(1,2) =" << u1(.1,.2) << " ~= " << u2(.1,.2) << " == " << .1^2+.2^2 << endl; plot(u1,cmm="solution = $x^2 + y^2$ ",wait=1,value=1);