Resuelve -(Uxx + Uyy)+ U = exp(xy) en 0 < x < 1 y 0 < y < 1 u(x,0) = 0 u(x,1) = 0 u(0,y) = 0 u(1,y) = 0 Solucion: Dominio: (0.000000,0.000000) a (1.000000,1.000000) Nodos de los elementos Elemento 1 ---> Nodos ( 0, 1, 7, 6 ) Elemento 2 ---> Nodos ( 1, 2, 8, 7 ) Elemento 3 ---> Nodos ( 2, 3, 9, 8 ) Elemento 4 ---> Nodos ( 3, 4, 10, 9 ) Elemento 5 ---> Nodos ( 4, 5, 11, 10 ) Elemento 6 ---> Nodos ( 6, 7, 13, 12 ) Elemento 7 ---> Nodos ( 7, 8, 14, 13 ) Elemento 8 ---> Nodos ( 8, 9, 15, 14 ) Elemento 9 ---> Nodos ( 9, 10, 16, 15 ) Elemento 10 ---> Nodos ( 10, 11, 17, 16 ) Elemento 11 ---> Nodos ( 12, 13, 19, 18 ) Elemento 12 ---> Nodos ( 13, 14, 20, 19 ) Elemento 13 ---> Nodos ( 14, 15, 21, 20 ) Elemento 14 ---> Nodos ( 15, 16, 22, 21 ) Elemento 15 ---> Nodos ( 16, 17, 23, 22 ) Elemento 16 ---> Nodos ( 18, 19, 25, 24 ) Elemento 17 ---> Nodos ( 19, 20, 26, 25 ) Elemento 18 ---> Nodos ( 20, 21, 27, 26 ) Elemento 19 ---> Nodos ( 21, 22, 28, 27 ) Elemento 20 ---> Nodos ( 22, 23, 29, 28 ) Elemento 21 ---> Nodos ( 24, 25, 31, 30 ) Elemento 22 ---> Nodos ( 25, 26, 32, 31 ) Elemento 23 ---> Nodos ( 26, 27, 33, 32 ) Elemento 24 ---> Nodos ( 27, 28, 34, 33 ) Elemento 25 ---> Nodos ( 28, 29, 35, 34 ) Nodos Nodo: 0 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +0.0000000000e+00 ) Nodo: 1 ( -1 ) ---> Nodo: ( +2.0000000000e-01 , +0.0000000000e+00 ) Nodo: 2 ( -1 ) ---> Nodo: ( +4.0000000000e-01 , +0.0000000000e+00 ) Nodo: 3 ( -1 ) ---> Nodo: ( +6.0000000000e-01 , +0.0000000000e+00 ) Nodo: 4 ( -1 ) ---> Nodo: ( +8.0000000000e-01 , +0.0000000000e+00 ) Nodo: 5 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +0.0000000000e+00 ) Nodo: 6 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +2.0000000000e-01 ) Nodo: 7 ( 0 ) ---> Nodo: ( +2.0000000000e-01 , +2.0000000000e-01 ) Nodo: 8 ( 1 ) ---> Nodo: ( +4.0000000000e-01 , +2.0000000000e-01 ) Nodo: 9 ( 2 ) ---> Nodo: ( +6.0000000000e-01 , +2.0000000000e-01 ) Nodo: 10 ( 3 ) ---> Nodo: ( +8.0000000000e-01 , +2.0000000000e-01 ) Nodo: 11 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +2.0000000000e-01 ) Nodo: 12 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +4.0000000000e-01 ) Nodo: 13 ( 4 ) ---> Nodo: ( +2.0000000000e-01 , +4.0000000000e-01 ) Nodo: 14 ( 5 ) ---> Nodo: ( +4.0000000000e-01 , +4.0000000000e-01 ) Nodo: 15 ( 6 ) ---> Nodo: ( +6.0000000000e-01 , +4.0000000000e-01 ) Nodo: 16 ( 7 ) ---> Nodo: ( +8.0000000000e-01 , +4.0000000000e-01 ) Nodo: 17 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +4.0000000000e-01 ) Nodo: 18 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +6.0000000000e-01 ) Nodo: 19 ( 8 ) ---> Nodo: ( +2.0000000000e-01 , +6.0000000000e-01 ) Nodo: 20 ( 9 ) ---> Nodo: ( +4.0000000000e-01 , +6.0000000000e-01 ) Nodo: 21 ( 10 ) ---> Nodo: ( +6.0000000000e-01 , +6.0000000000e-01 ) Nodo: 22 ( 11 ) ---> Nodo: ( +8.0000000000e-01 , +6.0000000000e-01 ) Nodo: 23 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +6.0000000000e-01 ) Nodo: 24 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +8.0000000000e-01 ) Nodo: 25 ( 12 ) ---> Nodo: ( +2.0000000000e-01 , +8.0000000000e-01 ) Nodo: 26 ( 13 ) ---> Nodo: ( +4.0000000000e-01 , +8.0000000000e-01 ) Nodo: 27 ( 14 ) ---> Nodo: ( +6.0000000000e-01 , +8.0000000000e-01 ) Nodo: 28 ( 15 ) ---> Nodo: ( +8.0000000000e-01 , +8.0000000000e-01 ) Nodo: 29 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +8.0000000000e-01 ) Nodo: 30 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +1.0000000000e+00 ) Nodo: 31 ( -1 ) ---> Nodo: ( +2.0000000000e-01 , +1.0000000000e+00 ) Nodo: 32 ( -1 ) ---> Nodo: ( +4.0000000000e-01 , +1.0000000000e+00 ) Nodo: 33 ( -1 ) ---> Nodo: ( +6.0000000000e-01 , +1.0000000000e+00 ) Nodo: 34 ( -1 ) ---> Nodo: ( +8.0000000000e-01 , +1.0000000000e+00 ) Nodo: 35 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +1.0000000000e+00 ) Matriz Densa "Matriz Temporal para Generar Matriz de Rigidez" de dimensión: 4 x 4 Número de entradas distintas de cero: 16 Numero máximo de columnas ocupadas: 4 +0.6711111111 -0.1644444444 -0.3322222222 -0.1644444444 -0.1644444444 +0.6711111111 -0.1644444444 -0.3322222222 -0.3322222222 -0.1644444444 +0.6711111111 -0.1644444444 -0.1644444444 -0.3322222222 -0.1644444444 +0.6711111111 Matriz Bandada Compacta "Matriz de carga" de dimensión: 16 x 16 y banda 9 Número de entradas distintas de cero: 100 Numero máximo de columnas ocupadas: 9 +2.6844444444 -0.3288888889 +0.0000000000 +0.0000000000 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3288888889 +2.6844444444 -0.3288888889 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3288888889 +2.6844444444 -0.3288888889 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3288888889 +2.6844444444 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +2.6844444444 -0.3288888889 +0.0000000000 +0.0000000000 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 -0.3288888889 +2.6844444444 -0.3288888889 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 -0.3288888889 +2.6844444444 -0.3288888889 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 +0.0000000000 +0.0000000000 -0.3288888889 +2.6844444444 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +2.6844444444 -0.3288888889 +0.0000000000 +0.0000000000 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 -0.3288888889 +2.6844444444 -0.3288888889 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 -0.3288888889 +2.6844444444 -0.3288888889 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 +0.0000000000 +0.0000000000 -0.3288888889 +2.6844444444 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3288888889 -0.3322222222 +0.0000000000 +0.0000000000 +2.6844444444 -0.3288888889 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 -0.3288888889 +2.6844444444 -0.3288888889 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 -0.3322222222 +0.0000000000 -0.3288888889 +2.6844444444 -0.3288888889 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 -0.3322222222 -0.3288888889 +0.0000000000 +0.0000000000 -0.3288888889 +2.6844444444 Vector "Vector de carga" de dimensión: 16 Vector "Vector Extendido" de dimensión: 20 Vector extendido "Vector de carga global" de dimensión: 36 +1.0044667738e-02 +2.0269810074e-02 +2.0544639336e-02 +2.0825065493e-02 +2.1111225411e-02 +1.0652460777e-02 +2.0269810074e-02 +4.1644534091e-02 +4.3361497323e-02 +4.5161287004e-02 +4.7048315592e-02 +2.4175901234e-02 +2.0544639336e-02 +4.3361497323e-02 +4.6991908591e-02 +5.0939851510e-02 +5.5234190666e-02 +2.9141359901e-02 +2.0825065493e-02 +4.5161287004e-02 +5.0939851510e-02 +5.7473125495e-02 +6.4861604215e-02 +3.5129756393e-02 +2.1111225411e-02 +4.7048315592e-02 +5.5234190666e-02 +6.4861604215e-02 +7.6187391763e-02 +4.2352439707e-02 +1.0652460777e-02 +2.4175901234e-02 +2.9141359901e-02 +3.5129756393e-02 +4.2352439707e-02 +2.3941714504e-02 Método CGM, iteraciones para resolver el sistema lineal 6 Vector "Solución sistema lineal" de dimensión: 16 Vector "Vector Extendido" de dimensión: 20 Vector extendido "Solución" de dimensión: 36 0: +0.0000000000e+00 1: +0.0000000000e+00 2: +0.0000000000e+00 3: +0.0000000000e+00 4: +0.0000000000e+00 5: +0.0000000000e+00 6: +0.0000000000e+00 7: +3.9554662884e-02 8: +5.6023131492e-02 9: +5.7872583412e-02 10: +4.3220688925e-02 11: +0.0000000000e+00 12: +0.0000000000e+00 13: +5.6023131492e-02 14: +8.3329020433e-02 15: +8.7197907551e-02 16: +6.3780413980e-02 17: +0.0000000000e+00 18: +0.0000000000e+00 19: +5.7872583412e-02 20: +8.7197907551e-02 21: +9.3026914651e-02 22: +6.9783609304e-02 23: +0.0000000000e+00 24: +0.0000000000e+00 25: +4.3220688925e-02 26: +6.3780413980e-02 27: +6.9783609304e-02 28: +5.6992663934e-02 29: +0.0000000000e+00 30: +0.0000000000e+00 31: +0.0000000000e+00 32: +0.0000000000e+00 33: +0.0000000000e+00 34: +0.0000000000e+00 35: +0.0000000000e+00 Tiempo Cálculo: 0.000000 Método Jacobi, iteraciones para resolver el sistema lineal 26 Vector "Solución sistema lineal" de dimensión: 16 Vector "Vector Extendido" de dimensión: 20 Vector extendido "Solución" de dimensión: 36 0: +0.0000000000e+00 1: +0.0000000000e+00 2: +0.0000000000e+00 3: +0.0000000000e+00 4: +0.0000000000e+00 5: +0.0000000000e+00 6: +0.0000000000e+00 7: +3.9546561953e-02 8: +5.6011615102e-02 9: +5.7860024364e-02 10: +4.3214641819e-02 11: +0.0000000000e+00 12: +0.0000000000e+00 13: +5.6011615102e-02 14: +8.3312408938e-02 15: +8.7178275375e-02 16: +6.3767204288e-02 17: +0.0000000000e+00 18: +0.0000000000e+00 19: +5.7860024364e-02 20: +8.7178275375e-02 21: +9.3008994235e-02 22: +6.9772092107e-02 23: +0.0000000000e+00 24: +0.0000000000e+00 25: +4.3214641819e-02 26: +6.3767204288e-02 27: +6.9772092107e-02 28: +5.6986153549e-02 29: +0.0000000000e+00 30: +0.0000000000e+00 31: +0.0000000000e+00 32: +0.0000000000e+00 33: +0.0000000000e+00 34: +0.0000000000e+00 35: +0.0000000000e+00 Tiempo Cálculo: 0.000000 Método Gauss-Seidel, iteraciones para resolver el sistema lineal 15 Vector "Solución sistema lineal" de dimensión: 16 Vector "Vector Extendido" de dimensión: 20 Vector extendido "Solución" de dimensión: 36 0: +0.0000000000e+00 1: +0.0000000000e+00 2: +0.0000000000e+00 3: +0.0000000000e+00 4: +0.0000000000e+00 5: +0.0000000000e+00 6: +0.0000000000e+00 7: +3.9547674130e-02 8: +5.6014544241e-02 9: +5.7863953912e-02 10: +4.3217617986e-02 11: +0.0000000000e+00 12: +0.0000000000e+00 13: +5.6016113404e-02 14: +8.3321015658e-02 15: +8.7188058491e-02 16: +6.3773894486e-02 17: +0.0000000000e+00 18: +0.0000000000e+00 19: +5.7866484008e-02 20: +8.7189692658e-02 21: +9.3021266470e-02 22: +6.9780144723e-02 23: +0.0000000000e+00 24: +0.0000000000e+00 25: +4.3219515054e-02 26: +6.3775522948e-02 27: +6.9780794777e-02 28: +5.6991742282e-02 29: +0.0000000000e+00 30: +0.0000000000e+00 31: +0.0000000000e+00 32: +0.0000000000e+00 33: +0.0000000000e+00 34: +0.0000000000e+00 35: +0.0000000000e+00 Tiempo Cálculo: 0.000000 Método Factorización LU para resolver el sistema lineal Vector "Solución sistema lineal" de dimensión: 16 Vector "Vector Extendido" de dimensión: 20 Vector extendido "Solución" de dimensión: 36 0: +0.0000000000e+00 1: +0.0000000000e+00 2: +0.0000000000e+00 3: +0.0000000000e+00 4: +0.0000000000e+00 5: +0.0000000000e+00 6: +0.0000000000e+00 7: +3.9553778283e-02 8: +5.6023291369e-02 9: +5.7871700631e-02 10: +4.3221858149e-02 11: +0.0000000000e+00 12: +0.0000000000e+00 13: +5.6023291369e-02 14: +8.3331301535e-02 15: +8.7197167972e-02 16: +6.3778880555e-02 17: +0.0000000000e+00 18: +0.0000000000e+00 19: +5.7871700631e-02 20: +8.7197167972e-02 21: +9.3027886832e-02 22: +6.9783768374e-02 23: +0.0000000000e+00 24: +0.0000000000e+00 25: +4.3221858149e-02 26: +6.3778880555e-02 27: +6.9783768374e-02 28: +5.6993369879e-02 29: +0.0000000000e+00 30: +0.0000000000e+00 31: +0.0000000000e+00 32: +0.0000000000e+00 33: +0.0000000000e+00 34: +0.0000000000e+00 35: +0.0000000000e+00 Tiempo Cálculo: 0.000000 Método Inversa para resolver el sistema lineal Vector "Solución sistema lineal" de dimensión: 16 Vector "Vector Extendido" de dimensión: 20 Vector extendido "Solución" de dimensión: 36 0: +0.0000000000e+00 1: +0.0000000000e+00 2: +0.0000000000e+00 3: +0.0000000000e+00 4: +0.0000000000e+00 5: +0.0000000000e+00 6: +0.0000000000e+00 7: +3.9553778283e-02 8: +5.6023291369e-02 9: +5.7871700631e-02 10: +4.3221858149e-02 11: +0.0000000000e+00 12: +0.0000000000e+00 13: +5.6023291369e-02 14: +8.3331301535e-02 15: +8.7197167972e-02 16: +6.3778880555e-02 17: +0.0000000000e+00 18: +0.0000000000e+00 19: +5.7871700631e-02 20: +8.7197167972e-02 21: +9.3027886832e-02 22: +6.9783768374e-02 23: +0.0000000000e+00 24: +0.0000000000e+00 25: +4.3221858149e-02 26: +6.3778880555e-02 27: +6.9783768374e-02 28: +5.6993369879e-02 29: +0.0000000000e+00 30: +0.0000000000e+00 31: +0.0000000000e+00 32: +0.0000000000e+00 33: +0.0000000000e+00 34: +0.0000000000e+00 35: +0.0000000000e+00 Tiempo Cálculo: 0.000000