1load "Morley" 2macro DD(f,hx,hy) ( (f(x1+hx,y1+hy)-f(x1-hx,y1-hy))/(2*(hx+hy))) // 3macro dn(f) ( N.x*dx(f)+N.y*dy(f)) // 4macro dnn(f) ( N.x*f#2+N.y*f#3) // 5mesh Th=square(1,1,[10*(x+y/3),10*(y-x/3)]); 6 7real x1=0.7,y1=0.9, h=1e-6; 8int it1=Th(x1,y1).nuTriangle; 9 10func ff = 2*x*x + 3*y*y + 4.5*y*x + 5*x + 6*y + 7; 11func ffx = 4*x + 4.5*y + 5; 12func ffy = 6*y + 4.5*x + 6; 13func ffxx = 4.; 14func ffyy = 6.; 15func ffxy =4.5; 16 17fespace Vh(Th,P2Morley); 18fespace Eh(Th,P0edge); 19 20Eh edges; 21 22Vh [a1,a2,a3],[b1,b2,b3],[c1,c2,c3]; 23 24[a1,a2,a3] = [ ff,ffx,ffy]; 25 26 cout << a1(0.6,0.2) << " == " << ff(0.6,0.2) << endl; 27 cout << a2(0.6,0.2) << " == " << ffx(0.6,0.2) << endl; 28 cout << a3(0.6,0.2) << " == " << ffy(0.6,0.2) << endl; 29 cout << dxx(a1)(0.6,0.2) << " xx== " << ffxx(0.6,0.2) << endl; 30 cout << dyy(a1)(0.6,0.2) << " yy== " << ffyy(0.6,0.2) << endl; 31 cout << dxy(a1)(0.6,0.2) << " xy== " << ffxy(0.6,0.2) << endl; 32 cout << dyx(a1)(0.6,0.2) << " yx== " << ffxy(0.6,0.2) << endl; 33 cout << a1(0.2,0.6) << " == " << ff(0.2,0.6) << endl; 34 cout << a2(0.2,0.6) << " == " << ffx(0.2,0.6) << endl; 35 cout << a3(0.2,0.6) << " == " << ffy(0.2,0.6) << endl; 36 cout << " 00 = " << int2d(Th)(square(a1-ff)) << endl; 37 cout << " 00 = " << int2d(Th)(square(a2-ffx)) << endl; 38 cout << " 00 = " << int2d(Th)(square(a3-ffy)) << endl; 39plot(a1,wait=1); 40 41Th=square(1,1,[10*(x+y/3),10*(y-x/3)]); 42 43varf vFlux([a],[e]) = intalledges(Th)( dn(a1)*e*(jump(real(nuTriangle))<= 0)); 44varf vMean([a],[e]) = intalledges(Th)( (a1)*e*(jump(real(nuTriangle))<= 0)/lenEdge); 45 46 47for (int i=0;i<Vh.ndofK;++i) 48 cout << i << " -> " << Vh(0,i) << endl; 49for (int i=0;i<Vh.ndofK;++i) 50{ 51 cout << " *** node " << i << " of Traingle " << it1 << endl; 52 a1[]=0; 53 int j=Vh(it1,i); 54 a1[][j]=1; 55 edges[]=vFlux(0,Eh); 56 cout << "Flux edges = " << edges[] << endl; 57 edges[]=vMean(0,Eh); 58 cout << " Mean edges = " << edges[] << endl; 59 60 plot(a1, wait=1,cmm="w_"+i); 61 [b1,b2,b3]=[a1,a2,a3]; 62 63 plot(a1,b1,cmm="w"+i, wait=1); 64 65 c1[] = a1[] - b1[]; 66 cout << " int_1 " << int1d(Th,1) (dn(a1)) << endl; 67 cout << " int_3 " << int1d(Th,3) (dn(a1)) << endl; 68 cout << " int_2 " << int1d(Th,2) (dn(a1)) << endl; 69 cout << " int_4 " << int1d(Th,4) (dn(a1)) << endl; 70 71 cout << " int_1 " << int1d(Th,1) (dnn(a)) << endl; 72 cout << " int_3 " << int1d(Th,3) (dnn(a)) << endl; 73 cout << " int_2 " << int1d(Th,2) (dnn(a)) << endl; 74 cout << " int_4 " << int1d(Th,4) (dnn(a)) << endl; 75 76 cout << " ---------" << i << " " << c1[].max << " " << c1[].min << endl; 77 cout << " a = " << a1[] <<endl; 78 cout << " b = " << b1[] <<endl; 79 80 assert(c1[].max < 1e-5 && c1[].min > -1e-9); 81 82 cout << " dx(a1)(x1,y1) = " << dx(a1)(x1,y1) << " == " << DD(a1,h,0) << " == " << a2(x1,y1) << endl; 83 cout << " dy(a1)(x1,y1) = " << dy(a1)(x1,y1) << " == " << DD(a1,0,h) << " == " << a3(x1,y1) << endl; 84 85 cout << " dx(a2)(x1,y1) = " << dx(a2)(x1,y1) << " == " << DD(a2,h,0) << " == " << dxx(a1) << endl; 86 cout << " dy(a2)(x1,y1) = " << dy(a2)(x1,y1) << " == " << DD(a2,0,h) << " == " << dxy(a1) << endl; 87 cout << " dx(a3)(x1,y1) = " << dx(a3)(x1,y1) << " == " << DD(a3,h,0) << " == " << dxy(a1) << endl; 88 cout << " dy(a3)(x1,y1) = " << dy(a3)(x1,y1) << " == " << DD(a3,0,h) << " == " << dyy(a1) << endl; 89 90 assert( abs(dx(a1)(x1,y1)-DD(a1,h,0) ) < 1e-4); 91 assert( abs((a2)(x1,y1)-DD(a1,h,0) ) < 1e-4); 92 assert( abs((a3)(x1,y1)-DD(a1,0,h) ) < 1e-4); 93 assert( abs(dx(a2)(x1,y1)-DD(a2,h,0) ) < 1e-4); 94 assert( abs(dy(a1)(x1,y1)-DD(a1,0,h) ) < 1e-4); 95 assert( abs(dy(a2)(x1,y1)-DD(a2,0,h) ) < 1e-4); 96 97 98} 99 100