//************************************************************** // Trois domaines : cercle1, cercle2, ellipse avec aero * // Auteur : M.N.I. Leblond * //************************************************************** load "iovtk"; // Chargement du module pour la sortie VTK // Chargement de la bibliothèque load "msh3"; // Définition des paramètres temporels et autres paramètres globaux real dt = 0.1; real dtau = dt/2; real L = 20; int Niter = 200; // Densité des points de frontière int NiterAero = 20; // suffisant pour un petit cercle // --------------------------- // 1) CERCLE 1 // --------------------------- real xc1 = -6.0, yc1 = 0.0, r1 = 3.0; border C1(t = 0, 2*pi) { x = xc1 + r1*cos(t); y = yc1 + r1*sin(t); } mesh Th1 = buildmesh(C1(Niter)); // --- Aéroport Cercle 1 --- real airport1x = -6.8, airport1y = 2, radius1 = 0.2; border Air1(t=0,2*pi){ x = airport1x + radius1*cos(t); y = airport1y + radius1*sin(t);} mesh ThAir1 = buildmesh(Air1(NiterAero)); // --------------------------- // 2) CERCLE 2 // --------------------------- real xc2 = 0.0, yc2 = -4.0, r2 = 3; //r2=2.5 border C2(t = 0, 2*pi) { x = xc2 + r2*cos(t); y = yc2 + r2*sin(t); } mesh Th2 = buildmesh(C2(Niter)); // --- Aéroport Cercle 2 --- real airport2x = 0.0, airport2y = -5.0, radius2 = 0.2; border Air2(t=0,2*pi){ x = airport2x + radius2*cos(t); y = airport2y + radius2*sin(t);} mesh ThAir2 = buildmesh(Air2(NiterAero)); // --------------------------- // 3) ELLIPSE // --------------------------- real xc3 = 6.0, yc3 = 0.0, a3 = 3.0, b3 = 1.5, r3=3; //border E1(t = 0, 2*pi) { x = xc3 + r3*cos(t); y = yc3 + r3*sin(t); } //mesh Th2 = buildmesh(C2(Niter)); border E1(t = 0, 2*pi) { x = xc3 + a3*cos(t); y = yc3 + b3*sin(t); } mesh Th3 = buildmesh(E1(Niter)); // --- Aéroport Ellipse --- real airport3x = 8.5, airport3y = 0.0, radius3 = 0.2; border Air3(t=0,2*pi){ x = airport3x + radius3*cos(t); y = airport3y + radius3*sin(t);} mesh ThAir3 = buildmesh(Air3(NiterAero)); // --------------------------- // Visualisation // --------------------------- plot(Th1, Th2, Th3, ThAir1, ThAir2, ThAir3, wait = true, cmm = "Domaines avec Aero"); // --- Affichage des aéroports --- // --------------------------- // Sauvegarde // --------------------------- savemesh(Th1, "cercle1.msh"); savemesh(Th2, "cercle2.msh"); savemesh(Th3, "ellipse.msh"); savemesh(ThAir1, "airport1.msh"); savemesh(ThAir2, "airport2.msh"); savemesh(ThAir3, "airport3.msh"); cout << "Trois domaines et leurs aero crees et sauves !" << endl; // --------------------------- // Définition des espaces de FE // --------------------------- fespace Uh1(Th1, P1); fespace Uh2(Th2, P1); fespace Uh3(Th3, P1); // Constantes locals real alpha1 = 0.5; real alpha2 = 0.5; real alpha3 = 0.3; real mu1 = 0.3; real mu2 = 0.3; real mu3 = 0.5; // Paramètres du modèle dans Omega1 real du1 = 0.020; // Diffusivité P1 real dv1 = 0.01; // Diffusivité N1 // Paramètres du modèle dans Omega2 real du2 = 0.02; // Diffusivité P2 real dv2 = 0.01; // Diffusivité N2 // Paramètres du modèle dans Omega2 real du3 = 0.02; // Diffusivité P3 real dv3 = 0.01; // Diffusivité N3 //coefficient de couplages real mU21 = 0.1; // depart de proie de Omega_1 vers \Omega_2 real mU31 = 0.0; // depart de proie de Omega_1 vers \Omega_3 real mU12 = 0.0; // depart de proie de \Omega_2 vers \Omega_1 real mU32 = 0.1; // depart de proie de \Omega_2 vers \Omega_3 real mU13 = 0.0; // depart de proie de \Omega_3 vers \Omega_1 real mU23 = 0.0; // depart de proie de \Omega_3 vers \Omega_2 real mV21 = 0.0; // depart de predateur de Omega_1 vers \Omega_2 real mV31 = 0.99; // depart de predateur de Omega_1 vers \Omega_3 real mV12 = 0.0; // depart de predateur de \Omega_2 vers \Omega_1 real mV32 = 0.99; // depart de \Omega_2 vers \Omega_3 real mV13 = 0.0; // depart de predateur de \Omega_3 vers \Omega_1 real mV23 = 0.0; // depart de predateur de \Omega_3 vers \Omega_2 macro fu1(u1, v1) (u1*(1-u1)-alpha1*u1*v1) // EOM macro fu2(u2, v2) (u2*(1-u2)-alpha2*u2*v2) // EOM macro fu3(u3, v3) (u3*(1-u3)-alpha3*u3*v3) // EOM macro fv1(u1, v1) (alpha1*u1*v1-mu1*v1) // EOM macro fv2(u2, v2) (alpha2*u2*v2-mu2*v2) // EOM macro fv3(u3, v3) (alpha3*u3*v3-mu3*v3) // EOM // ============================================================ // CONDITIONS INITIALES AVEC CONTROLE DE LA MASSE TOTALE // ============================================================ // ------------------------------------------------------------ // Domaine 1 : Populations P1 (proies) et N1 (prédateurs) // ------------------------------------------------------------ real xcP1 = -6.0, ycP1 = 0.0, rP1 = 0.5; real xcN1 = -5.5, ycN1 = 0.0, rN1 = 0.3; // Masses totales désirées real M0P1 = 0.1; // masse totale voulue pour U1 real M0N1 = 0.2; // masse totale voulue pour V1 // Amplitudes correspondantes real AP1 = M0P1 / (pi * rP1^2); real AN1 = M0N1 / (pi * rN1^2); // Conditions initiales Uh1 u10 = AP1 * ((x - xcP1)^2 + (y - ycP1)^2 <= rP1^2); Uh1 v10 = AN1 * ((x - xcN1)^2 + (y - ycN1)^2 <= rN1^2); // ------------------------------------------------------------ // Domaine 2 : Populations P2 et N2 // ------------------------------------------------------------ real xcP2 = 0.0, ycP2 = -4.0, rP2 = 0.5; real xcN2 = 0.2, ycN2 = -4.2, rN2 = 0.3; real M0P2 = 0.1; // masse totale voulue pour U2 real M0N2 = 0.2; // masse totale voulue pour V2 real AP2 = M0P2 / (pi * rP2^2); real AN2 = M0N2 / (pi * rN2^2); Uh2 u20 = 0;//AP2 * ((x - xcP2)^2 + (y - ycP2)^2 <= rP2^2); Uh2 v20 = AN2 * ((x - xcN2)^2 + (y - ycN2)^2 <= rN2^2); // ------------------------------------------------------------ // Domaine 3 : Populations P3 et N3 // ------------------------------------------------------------ real xcP3 = 6.0, ycP3 = 0.0, rP3 = 0.5; real xcN3 = 6.5, ycN3 = 0.0, rN3 = 0.5; real M0P3 = 0.1; // masse totale voulue pour U3 real M0N3 = 0.2; // masse totale voulue pour V3 real AP3 = M0P3 / (pi * rP3^2); real AN3 = M0N3 / (pi * rN3^2); Uh3 u30 = 0;//AP3 * ((x - xcP3)^2 + (y - ycP3)^2 <= rP3^2); Uh3 v30 =0; // AN3 * ((x - xcN3)^2 + (y - ycN3)^2 <= rN3^2); // ============================================================ // DIAGNOSTIC : VERIFICATION DES MASSES INITIALES // ============================================================ cout << endl; cout << "============================================================" << endl; cout << " DIAGNOSTIC DES CONDITIONS INITIALES " << endl; cout << "============================================================" << endl; real Iu1 = int2d(Th1)(u10); real Iv1 = int2d(Th1)(v10); real Iu2 = int2d(Th2)(u20); real Iv2 = int2d(Th2)(v20); real Iu3 = int2d(Th3)(u30); real Iv3 = int2d(Th3)(v30); cout << " Domaine Omega1 : " << endl; cout << " Masse P1 (attendue = " << M0P1 << ") -> obtenue = " << Iu1 << endl; cout << " Masse N1 (attendue = " << M0N1 << ") -> obtenue = " << Iv1 << endl; cout << "\n Domaine Omega2 : " << endl; cout << " Masse P2 (attendue = " << M0P2 << ") -> obtenue = " << Iu2 << endl; cout << " Masse N2 (attendue = " << M0N2 << ") -> obtenue = " << Iv2 << endl; cout << "\n Domaine Omega3 : " << endl; cout << " Masse P3 (attendue = " << M0P3 << ") -> obtenue = " << Iu3 << endl; cout << " Masse N3 (attendue = " << M0N3 << ") -> obtenue = " << Iv3 << endl; cout << "============================================================" << endl; cout << endl; // Affichage de toutes les populations u (P1, P2, P3) plot(u10, u20, u30, fill=true, value=true, wait=true, cmm="Conditions initiales : u (P1, P2, P3)"); // Affichage de toutes les populations v (N1, N2, N3) plot(v10, v20, v30, fill=true, value=true, wait=true, cmm="Conditions initiales : v (N1, N2, N3)"); Uh1 uP1, vN1, wu01, wv01; Uh2 uP2, vN2, wu02, wv02; Uh3 uP3, vN3, wu03, wv03; // Déclaration des fonctions de migration Uh1 NL1; // probabilités de migrations sur \Omega_1 (P_21=P_31=epsilon_1=NL1) Uh2 NL2; // probabilités de migrations sur \Omega_2 (P_12=P_32=epsilon_2=NL2) Uh3 NL3; // probabilités de migrations sur \ Omega_3 (P_13=P_23=epsilon_3=NL3) // ============================================================= // Calcul des probabilités de migration (fonction gaussienne) // ============================================================= // --- Domaine 1 --- for (int i = 0; i < Th1.nv; i++) { real X = Th1(i).x; real Y = Th1(i).y; NL1[][i] = exp(-(( airport1x - X)^2 + ( airport1y - Y)^2)/(radius1*radius1)); } // --- Domaine 2 --- for (int i = 0; i < Th2.nv; i++) { real X = Th2(i).x; real Y = Th2(i).y; NL2[][i] = exp(-(( airport2x - X)^2 + ( airport2y - Y)^2)/(radius2*radius2)); } // --- Domaine 3 --- for (int i = 0; i < Th3.nv; i++) { real X = Th3(i).x; real Y = Th3(i).y; NL3[][i] = exp(-(( airport3x - X)^2 + ( airport3y - Y)^2)/(radius3*radius3)); } // ============================================================= // Visualisation // ============================================================= // Combined view of all domains plot(NL1, NL2, NL3, fill=true, value=false, cmm="Transit zones on all domains", wait=true); // Individual plots for clarity plot(NL1, fill=true, value=true, cmm="Transit zone on Omega1", wait=true); plot(NL2, fill=true, value=true, cmm="Transit zone on Omega2", wait=true); plot(NL3, fill=true, value=true, cmm="Transit zone on Omega3", wait=true); //************************************************************** // ✦ First Diagnostic: Inter-domain Migration Fluxes ✦ // (Computed using nonlocal influence functions NL_i) //************************************************************** // --- Flux entering Omega_1 from Omega_2 and Omega_3 --- real intU12 = int2d(Th2)(mU12 * u20 * NL2); // flux of u from Ω2 → Ω1 real intV12 = int2d(Th2)(mV12 * v20 * NL2); // flux of v from Ω2 → Ω1 real intU13 = int2d(Th3)(mU13 * u30 * NL3); // flux of u from Ω3 → Ω1 real intV13 = int2d(Th3)(mV13 * v30 * NL3); // flux of v from Ω3 → Ω1 // --- Flux entering Omega_2 from Omega_1 and Omega_3 --- real intU21 = int2d(Th1)(mU21 * u10 * NL1); // flux of u from Ω1 → Ω2 real intV21 = int2d(Th1)(mV21 * v10 * NL1); // flux of v from Ω1 → Ω2 real intU23 = int2d(Th3)(mU23 * u30 * NL3); // flux of u from Ω3 → Ω2 real intV23 = int2d(Th3)(mV23 * v30 * NL3); // flux of v from Ω3 → Ω2 // --- Flux entering Omega_3 from Omega_1 and Omega_2 --- real intU31 = int2d(Th1)(mU31 * u10 * NL1); // flux of u from Ω1 → Ω3 real intV31 = int2d(Th1)(mV31 * v10 * NL1); // flux of v from Ω1 → Ω3 real intU32 = int2d(Th2)(mU32 * u20 * NL2); // flux of u from Ω2 → Ω3 real intV32 = int2d(Th2)(mV32 * v20 * NL2); // flux of v from Ω2 → Ω3 //************************************************************** // ✦ Summary Report – Migration Diagnosis ✦ //************************************************************** cout << endl; cout << "============================================================" << endl; cout << " FIRST DIAGNOSTIC OF MIGRATION FLOWS " << endl; cout << "============================================================" << endl; cout << "\n Fluxes entering omega_1:" << endl; cout << " From omega_2 : U12 = " << intU12 << " | V12 = " << intV12 << endl; cout << " From omega_3 : U13 = " << intU13 << " | V13 = " << intV13 << endl; cout << "\n Fluxes entering omega_2:" << endl; cout << " From omega_1 : U21 = " << intU21 << " | V21 = " << intV21 << endl; cout << " From omega_3 : U23 = " << intU23 << " | V23 = " << intV23 << endl; cout << "\n Fluxes entering omega_3:" << endl; cout << " From omega_1 : U31 = " << intU31 << " | V31 = " << intV31 << endl; cout << " From omega_2 : U32 = " << intU32 << " | V32 = " << intV32 << endl; cout << "============================================================" << endl; // --------------------------- // Omega_1 : Proie 1 (u13) // -------------------------- problem Proie1(uP1,wu01) = int2d(Th1)(uP1*wu01) -int2d(Th1)(u10*wu01) +int2d(Th1)(dt/2*du1*dx(uP1)*dx(wu01)+ dt/2*du1*dy(uP1)*dy(wu01)) +int2d(Th1)(-dt/2*NL1*intU12*wu01-dt/2*NL1*intU13*wu01) // flux migratoire entrant +int2d(Th1)(dt/2*mU21*uP1*NL1*wu01+dt/2*mU31*uP1*NL1*wu01); //flux migratoire sortant // --------------------------- // Omega_1 : Predateur 1 (vN1) // --------------------------- problem Predat1(vN1, wv01) = int2d(Th1)( vN1*wv01 ) -int2d(Th1)( v10*wv01 ) +int2d(Th1)( dt/2*dv1*dx(vN1)*dx(wv01) + dt/2*dv1*dy(vN1)*dy(wv01) ) +int2d(Th1)(-dt/2*NL1*intV12*wv01-dt/2*NL1*intV13*wv01) // flux migratoire entrant +int2d(Th1)(dt/2*mV21*vN1*NL1*wv01+dt/2*mV31*vN1*NL1*wv01); //flux migratoire sortant // --------------------------- // Omega_2 : Proie 2 (uP2) // --------------------------- problem Proie2(uP2,wu02) = int2d(Th2)(uP2*wu02) -int2d(Th2)(u20*wu02) +int2d(Th2)(dt/2*du2*dx(uP2)*dx(wu02)+ dt/2*du2*dy(uP2)*dy(wu02)) +int2d(Th2)(-dt/2*NL2*intU21*wu02-dt/2*NL2*intU23*wu02) // flux migratoire entrant +int2d(Th2)(dt/2*mU12*uP2*NL2*wu02+dt/2*mU32*uP2*NL2*wu02); //flux migratoire sortant // --------------------------- // Omega_2 : Predateur 2 (vN2) // --------------------------- problem Predat2(vN2, wv02) = int2d(Th2)( vN2*wv02 ) -int2d(Th2)( v20*wv02 ) +int2d(Th2)( dt/2*dv2*dx(vN2)*dx(wv02) + dt/2*dv2*dy(vN2)*dy(wv02) ) +int2d(Th2)(-dt/2*NL2*intV21*wv02-dt/2*NL2*intV23*wv02) // flux migratoire entrant +int2d(Th2)(dt/2*mV12*vN2*NL2*wv02+dt/2*mV32*vN2*NL2*wv02); //flux migratoire sortant // --------------------------- // Omega_3 : Proie 3 (uP3) // --------------------------- problem Proie3(uP3, wu03) = int2d(Th3)( uP3 * wu03 ) - int2d(Th3)( u30 * wu03 ) + int2d(Th3)( dt/2*du3*dx(uP3)*dx(wu03) + dt/2*du3*dy(uP3)*dy(wu03) ) // flux migratoire entrant depuis Omega1 et Omega2 (pondéré par NL3) + int2d(Th3)( -dt/2 * NL3 * intU31 * wu03 - dt/2 * NL3 * intU32 * wu03 ) // flux migratoire sortant vers Omega1 et Omega2 (m13 et m23) + int2d(Th3)( dt/2 * mU13 * uP3 * NL3 * wu03 + dt/2 * mU23 * uP3 * NL3 * wu03 ); // --------------------------- // Omega_3 : Predateur 3 (vN3) // --------------------------- problem Predat3(vN3, wv03) = int2d(Th3)( vN3 * wv03 ) - int2d(Th3)( v30 * wv03 ) + int2d(Th3)( dt/2*dv3*dx(vN3)*dx(wv03) + dt/2*dv3*dy(vN3)*dy(wv03) ) // flux migratoire entrant depuis Omega1 et Omega2 + int2d(Th3)( -dt/2 * NL3 * intV31 * wv03 - dt/2 * NL3 * intV32 * wv03 ) // flux migratoire sortant vers Omega1 et Omega2 + int2d(Th3)( dt/2 * mV13 * vN3 * NL3 * wv03 + dt/2 * mV23 * vN3 * NL3 * wv03 ); // ---- Résolution des problèmes ---- Proie1; u10 = uP1; Predat1; v10 = vN1; Proie2; u20 = uP2; Predat2; v20 = vN2; Proie3; u30 = uP3; Predat3; v30 = vN3; // ---- Visualisation des proies ---- plot(u10, u20, u30, fill=true, value=true,cmm="Populations de Proies : Omega1 - Omega2 - Omega3",wait=true); // ---- Visualisation des prédateurs ---- plot(v10, v20, v30, fill=true, value=true, cmm="Populations de Predateurs : Omega1 - Omega2 - Omega3",wait=true); int M = 250; // Nombre total d'étapes de temps // Préparation des structures de données pour l'enregistrement des résultats Uh1[int] X(2); Uh2[int] Y(2); Uh3[int] Z(2); cout <<"entrez M le nombre d_iteration"<> M; real t=0; ofstream file1("data_P1N1-pp.csv"); file1.precision(3); file1 << "t,U1_total,V1_total,U_flux_in,V_flux_in,U_flux_out,V_flux_out" << endl; ofstream file2("data_P2N2-pp.csv"); file2.precision(3); file2 << "t,U2_total,V2_total,U_flux_in,V_flux_in,U_flux_out,V_flux_out" << endl; ofstream file3("data_P3N3-pp.csv"); file3.precision(3); file3 << "t,U3_total,V3_total,U_flux_in,V_flux_in,U_flux_out,V_flux_out" << endl; for (int m = 0; m < M; m++) { // --- Flux entering Omega_1 from Omega_2 and Omega_3 --- intU12 = int2d(Th2)(mU12 * u20 * NL2); // flux of u from Ω2 → Ω1 intV12 = int2d(Th2)(mV12 * v20 * NL2); // flux of v from Ω2 → Ω1 intU13 = int2d(Th3)(mU13 * u30 * NL3); // flux of u from Ω3 → Ω1 intV13 = int2d(Th3)(mV13 * v30 * NL3); // flux of v from Ω3 → Ω1 // --- Flux entering Omega_2 from Omega_1 and Omega_3 --- intU21 = int2d(Th1)(mU21 * u10 * NL1); // flux of u from Ω1 → Ω2 intV21 = int2d(Th1)(mV21 * v10 * NL1); // flux of v from Ω1 → Ω2 intU23 = int2d(Th3)(mU23 * u30 * NL3); // flux of u from Ω3 → Ω2 intV23 = int2d(Th3)(mV23 * v30 * NL3); // flux of v from Ω3 → Ω2 // --- Flux entering Omega_3 from Omega_1 and Omega_2 --- intU31 = int2d(Th1)(mU31 * u10 * NL1); // flux of u from Ω1 → Ω3 intV31 = int2d(Th1)(mV31 * v10 * NL1); // flux of v from Ω1 → Ω3 intU32 = int2d(Th2)(mU32 * u20 * NL2); // flux of u from Ω2 → Ω3 intV32 = int2d(Th2)(mV32 * v20 * NL2); // flux of v from Ω2 → Ω3 // ---- Résolution des problèmes ---- Proie1; u10 = uP1; Predat1; v10 = vN1; Proie2; u20 = uP2; Predat2; v20 = vN2; Proie3; u30 = uP3; Predat3; v30 = vN3; real U1total = int2d(Th1)(u10); real V1total = int2d(Th1)(v10); real U2total = int2d(Th2)(u20); real V2total = int2d(Th2)(v20); real U3total = int2d(Th3)(u30); real V3total = int2d(Th3)(v30); // --- Calcul des flux totaux sortants --- real U1fluxout = int2d(Th1)((mU21 + mU31) * u10 * NL1); real V1fluxout = int2d(Th1)((mV21 + mV31) * v10 * NL1); real U2fluxout = int2d(Th2)((mU12 + mU32) * u20 * NL2); real V2fluxout = int2d(Th2)((mV12 + mV32) * v20 * NL2); real U3fluxout = int2d(Th3)((mU13 + mU23) * u30 * NL3); real V3fluxout = int2d(Th3)((mV13 + mV23) * v30 * NL3); //---------------------------------------------------- // --- Enregistrement des données --- file1 << t << "," << U1total << "," << V1total << "," << intU12 + intU13 << "," << intV12 + intV13 << "," << U1fluxout << "," << V1fluxout << endl; file2 << t << "," << U2total << "," << V2total << "," << intU21 + intU23 << "," << intV21 + intV23 << "," << U2fluxout << "," << V2fluxout << endl; file3 << t << "," << U3total << "," << V3total << "," << intU31 + intU32 << "," << intV31 + intV32 << "," << U3fluxout << "," << V3fluxout << endl; // --- Mise à jour du temps --- t=t + dtau; X[0]=uP1+dtau*fu1(uP1,vN1);//u1 X[1]=vN1+dtau*fv1(uP1,vN1);//v1 Y[0]=uP2+dtau*fu2(uP2,vN2);//u2 Y[1]=vN2+dtau*fv2(uP2,vN2);//v2 Z[0]=uP3+dtau*fu3(uP3,vN3);//u3 Z[1]=vN3+dtau*fv3(uP3,vN3);//v3 u10=uP1+dt*fu1(X[0],X[1]); //u1 v10=vN1+dt*fv1(X[0],X[1]); //v1 u20=uP2+dt*fu2(Y[0],Y[1]); //u2 v20=vN2+dt*fv2(Y[0],Y[1]); //v2 u30=uP3+dt*fu3(Z[0],Z[1]); //u3 v30=vN3+dt*fv3(Z[0],Z[1]); //v1 t=t + dt ; // --- Flux entering Omega_1 from Omega_2 and Omega_3 --- intU12 = int2d(Th2)(mU12 * u20 * NL2); // flux of u from Ω2 → Ω1 intV12 = int2d(Th2)(mV12 * v20 * NL2); // flux of v from Ω2 → Ω1 intU13 = int2d(Th3)(mU13 * u30 * NL3); // flux of u from Ω3 → Ω1 intV13 = int2d(Th3)(mV13 * v30 * NL3); // flux of v from Ω3 → Ω1 // --- Flux entering Omega_2 from Omega_1 and Omega_3 --- intU21 = int2d(Th1)(mU21 * u10 * NL1); // flux of u from Ω1 → Ω2 intV21 = int2d(Th1)(mV21 * v10 * NL1); // flux of v from Ω1 → Ω2 intU23 = int2d(Th3)(mU23 * u30 * NL3); // flux of u from Ω3 → Ω2 intV23 = int2d(Th3)(mV23 * v30 * NL3); // flux of v from Ω3 → Ω2 // --- Flux entering Omega_3 from Omega_1 and Omega_2 --- intU31 = int2d(Th1)(mU31 * u10 * NL1); // flux of u from Ω1 → Ω3 intV31 = int2d(Th1)(mV31 * v10 * NL1); // flux of v from Ω1 → Ω3 intU32 = int2d(Th2)(mU32 * u20 * NL2); // flux of u from Ω2 → Ω3 intV32 = int2d(Th2)(mV32 * v20 * NL2); // flux of v from Ω2 → Ω3 // ---- Résolution des problèmes ---- Proie1; u10 = uP1; Predat1; v10 = vN1; Proie2; u20 = uP2; Predat2; v20 = vN2; Proie3; u30 = uP3; Predat3; v30 = vN3; plot(v10, v20, v30, fill=true, value=true,cmm="Populations de Predateurs : Omega1 - Omega2 - Omega3"); //plot(u10, u20, u30, fill=true, value=true,cmm="Populations de Proies : Omega1 - Omega2 - Omega3"); // ---- Calcul des intégrales totales sur chaque domaine ---- real totalU1 = int2d(Th1)(u10); real totalV1 = int2d(Th1)(v10); real totalU2 = int2d(Th2)(u20); real totalV2 = int2d(Th2)(v20); real totalU3 = int2d(Th3)(u30); real totalV3 = int2d(Th3)(v30); // ---- Diagnostic ---- cout << endl; cout << "============================================================" << endl; cout << " DIAGNOSTIC ET SUIVI DES POPULATIONS " << endl; cout << " Temps t = " << t << " " << endl; cout << "============================================================" << endl; cout << "\n Flux entrants sur omega_1 :" << endl; cout << " Depuis omega_2 : U12 = " << intU12 << " | V12 = " << intV12 << endl; cout << " Depuis omega_3 : U13 = " << intU13 << " | V13 = " << intV13 << endl; cout << " Population totale sur omega_1 : U1 = " << totalU1 << " | V1 = " << totalV1 << endl; cout << "\n Flux entrants sur omega_2 :" << endl; cout << " Depuis omega_1 : U21 = " << intU21 << " | V21 = " << intV21 << endl; cout << " Depuis omega_3 : U23 = " << intU23 << " | V23 = " << intV23 << endl; cout << " Population totale sur omega_2 : U2 = " << totalU2 << " | V2 = " << totalV2 << endl; cout << "\n Flux entrants sur omega_3 :" << endl; cout << " Depuis omega_1 : U31 = " << intU31 << " | V31 = " << intV31 << endl; cout << " Depuis omega_2 : U32 = " << intU32 << " | V32 = " << intV32 << endl; cout << " Population totale sur omega_3 : U3 = " << totalU3 << " | V3 = " << totalV3 << endl; cout << "============================================================" << endl; savevtk("Proie-predat-N1/N1_"+m+".vtu",Th1, u10, v10, dataname=" U1 V1"); savevtk("Proie-predat-N2/N2_"+m+".vtu",Th2, u20, v20,dataname=" U2 V2"); savevtk("Proie-predat-N3/N3_"+m+".vtu",Th3, u30, v30,dataname=" U3 V3"); }