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 ) Elemento 26 ---> Nodos ( 30, 31, 37, 36 ) Elemento 27 ---> Nodos ( 31, 32, 38, 37 ) Elemento 28 ---> Nodos ( 32, 33, 39, 38 ) Elemento 29 ---> Nodos ( 33, 34, 40, 39 ) Elemento 30 ---> Nodos ( 34, 35, 41, 40 ) Elemento 31 ---> Nodos ( 36, 37, 43, 42 ) Elemento 32 ---> Nodos ( 37, 38, 44, 43 ) Elemento 33 ---> Nodos ( 38, 39, 45, 44 ) Elemento 34 ---> Nodos ( 39, 40, 46, 45 ) Elemento 35 ---> Nodos ( 40, 41, 47, 46 ) Elemento 36 ---> Nodos ( 42, 43, 49, 48 ) Elemento 37 ---> Nodos ( 43, 44, 50, 49 ) Elemento 38 ---> Nodos ( 44, 45, 51, 50 ) Elemento 39 ---> Nodos ( 45, 46, 52, 51 ) Elemento 40 ---> Nodos ( 46, 47, 53, 52 ) Elemento 41 ---> Nodos ( 48, 49, 55, 54 ) Elemento 42 ---> Nodos ( 49, 50, 56, 55 ) Elemento 43 ---> Nodos ( 50, 51, 57, 56 ) Elemento 44 ---> Nodos ( 51, 52, 58, 57 ) Elemento 45 ---> Nodos ( 52, 53, 59, 58 ) Elemento 46 ---> Nodos ( 54, 55, 61, 60 ) Elemento 47 ---> Nodos ( 55, 56, 62, 61 ) Elemento 48 ---> Nodos ( 56, 57, 63, 62 ) Elemento 49 ---> Nodos ( 57, 58, 64, 63 ) Elemento 50 ---> Nodos ( 58, 59, 65, 64 ) 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 , +1.0000000000e-01 ) Nodo: 7 ( 0 ) ---> Nodo: ( +2.0000000000e-01 , +1.0000000000e-01 ) Nodo: 8 ( 1 ) ---> Nodo: ( +4.0000000000e-01 , +1.0000000000e-01 ) Nodo: 9 ( 2 ) ---> Nodo: ( +6.0000000000e-01 , +1.0000000000e-01 ) Nodo: 10 ( 3 ) ---> Nodo: ( +8.0000000000e-01 , +1.0000000000e-01 ) Nodo: 11 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +1.0000000000e-01 ) Nodo: 12 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +2.0000000000e-01 ) Nodo: 13 ( 4 ) ---> Nodo: ( +2.0000000000e-01 , +2.0000000000e-01 ) Nodo: 14 ( 5 ) ---> Nodo: ( +4.0000000000e-01 , +2.0000000000e-01 ) Nodo: 15 ( 6 ) ---> Nodo: ( +6.0000000000e-01 , +2.0000000000e-01 ) Nodo: 16 ( 7 ) ---> Nodo: ( +8.0000000000e-01 , +2.0000000000e-01 ) Nodo: 17 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +2.0000000000e-01 ) Nodo: 18 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +3.0000000000e-01 ) Nodo: 19 ( 8 ) ---> Nodo: ( +2.0000000000e-01 , +3.0000000000e-01 ) Nodo: 20 ( 9 ) ---> Nodo: ( +4.0000000000e-01 , +3.0000000000e-01 ) Nodo: 21 ( 10 ) ---> Nodo: ( +6.0000000000e-01 , +3.0000000000e-01 ) Nodo: 22 ( 11 ) ---> Nodo: ( +8.0000000000e-01 , +3.0000000000e-01 ) Nodo: 23 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +3.0000000000e-01 ) Nodo: 24 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +4.0000000000e-01 ) Nodo: 25 ( 12 ) ---> Nodo: ( +2.0000000000e-01 , +4.0000000000e-01 ) Nodo: 26 ( 13 ) ---> Nodo: ( +4.0000000000e-01 , +4.0000000000e-01 ) Nodo: 27 ( 14 ) ---> Nodo: ( +6.0000000000e-01 , +4.0000000000e-01 ) Nodo: 28 ( 15 ) ---> Nodo: ( +8.0000000000e-01 , +4.0000000000e-01 ) Nodo: 29 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +4.0000000000e-01 ) Nodo: 30 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +5.0000000000e-01 ) Nodo: 31 ( 16 ) ---> Nodo: ( +2.0000000000e-01 , +5.0000000000e-01 ) Nodo: 32 ( 17 ) ---> Nodo: ( +4.0000000000e-01 , +5.0000000000e-01 ) Nodo: 33 ( 18 ) ---> Nodo: ( +6.0000000000e-01 , +5.0000000000e-01 ) Nodo: 34 ( 19 ) ---> Nodo: ( +8.0000000000e-01 , +5.0000000000e-01 ) Nodo: 35 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +5.0000000000e-01 ) Nodo: 36 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +6.0000000000e-01 ) Nodo: 37 ( 20 ) ---> Nodo: ( +2.0000000000e-01 , +6.0000000000e-01 ) Nodo: 38 ( 21 ) ---> Nodo: ( +4.0000000000e-01 , +6.0000000000e-01 ) Nodo: 39 ( 22 ) ---> Nodo: ( +6.0000000000e-01 , +6.0000000000e-01 ) Nodo: 40 ( 23 ) ---> Nodo: ( +8.0000000000e-01 , +6.0000000000e-01 ) Nodo: 41 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +6.0000000000e-01 ) Nodo: 42 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +7.0000000000e-01 ) Nodo: 43 ( 24 ) ---> Nodo: ( +2.0000000000e-01 , +7.0000000000e-01 ) Nodo: 44 ( 25 ) ---> Nodo: ( +4.0000000000e-01 , +7.0000000000e-01 ) Nodo: 45 ( 26 ) ---> Nodo: ( +6.0000000000e-01 , +7.0000000000e-01 ) Nodo: 46 ( 27 ) ---> Nodo: ( +8.0000000000e-01 , +7.0000000000e-01 ) Nodo: 47 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +7.0000000000e-01 ) Nodo: 48 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +8.0000000000e-01 ) Nodo: 49 ( 28 ) ---> Nodo: ( +2.0000000000e-01 , +8.0000000000e-01 ) Nodo: 50 ( 29 ) ---> Nodo: ( +4.0000000000e-01 , +8.0000000000e-01 ) Nodo: 51 ( 30 ) ---> Nodo: ( +6.0000000000e-01 , +8.0000000000e-01 ) Nodo: 52 ( 31 ) ---> Nodo: ( +8.0000000000e-01 , +8.0000000000e-01 ) Nodo: 53 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +8.0000000000e-01 ) Nodo: 54 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +9.0000000000e-01 ) Nodo: 55 ( 32 ) ---> Nodo: ( +2.0000000000e-01 , +9.0000000000e-01 ) Nodo: 56 ( 33 ) ---> Nodo: ( +4.0000000000e-01 , +9.0000000000e-01 ) Nodo: 57 ( 34 ) ---> Nodo: ( +6.0000000000e-01 , +9.0000000000e-01 ) Nodo: 58 ( 35 ) ---> Nodo: ( +8.0000000000e-01 , +9.0000000000e-01 ) Nodo: 59 ( -1 ) ---> Nodo: ( +1.0000000000e+00 , +9.0000000000e-01 ) Nodo: 60 ( -1 ) ---> Nodo: ( +0.0000000000e+00 , +1.0000000000e+00 ) Nodo: 61 ( -1 ) ---> Nodo: ( +2.0000000000e-01 , +1.0000000000e+00 ) Nodo: 62 ( -1 ) ---> Nodo: ( +4.0000000000e-01 , +1.0000000000e+00 ) Nodo: 63 ( -1 ) ---> Nodo: ( +6.0000000000e-01 , +1.0000000000e+00 ) Nodo: 64 ( -1 ) ---> Nodo: ( +8.0000000000e-01 , +1.0000000000e+00 ) Nodo: 65 ( -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 +0.8355555556 +0.1677777778 -0.4161111111 -0.5822222222 +0.1677777778 +0.8355555556 -0.5822222222 -0.4161111111 -0.4161111111 -0.5822222222 +0.8355555556 +0.1677777778 -0.5822222222 -0.4161111111 +0.1677777778 +0.8355555556 Matriz Bandada Compacta "Matriz de carga" de dimensión: 36 x 36 y banda 9 Número de entradas distintas de cero: 250 Numero máximo de columnas ocupadas: 9 +3.3422222222 +0.3355555556 +0.0000000000 +0.0000000000 -1.1644444444 -0.4161111111 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.0000000000 +0.3355555556 +3.3422222222 +0.3355555556 +0.0000000000 -0.4161111111 -1.1644444444 -0.4161111111 +0.0000000000 +0.0000000000 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+2.0819810048e-02 +2.1671659284e-02 +2.2559866031e-02 +2.3486041086e-02 +1.2061572005e-02 +1.0203093960e-02 +2.1243943066e-02 +2.2559866031e-02 +2.3958898879e-02 +2.5446387749e-02 +1.3242264497e-02 +1.0272144779e-02 +2.1678161264e-02 +2.3486041086e-02 +2.5446387749e-02 +2.7572199539e-02 +1.4538853995e-02 +1.0341895154e-02 +2.2122729052e-02 +2.4451868980e-02 +2.7028028643e-02 +2.9877594504e-02 +1.5962747315e-02 +1.0412353581e-02 +2.2577918271e-02 +2.5459111459e-02 +2.8709890687e-02 +3.2377907892e-02 +1.7526476831e-02 +1.0483528669e-02 +2.3044008414e-02 +2.6509611122e-02 +3.0498440973e-02 +3.5089798144e-02 +1.9243811808e-02 +1.0555429147e-02 +2.3521286852e-02 +2.7605295235e-02 +3.2400571068e-02 +3.8031362204e-02 +2.1129880778e-02 +1.0628063859e-02 +2.4010049068e-02 +2.8748179739e-02 +3.4423625321e-02 +4.1222260975e-02 +2.3201306049e-02 +5.3384288474e-03 +1.2170876700e-02 +1.4767270031e-02 +1.7917943732e-02 +2.1741309219e-02 +1.2341061480e-02 Método CGM, iteraciones para resolver el sistema lineal 14 Vector "Solución sistema lineal" de dimensión: 36 Vector "Vector Extendido" de dimensión: 30 Vector extendido "Solución" de dimensión: 66 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: +2.3317118654e-02 8: +3.1831339288e-02 9: +3.2738508271e-02 10: +2.5114836523e-02 11: +0.0000000000e+00 12: +0.0000000000e+00 13: +3.8796323464e-02 14: +5.5339573403e-02 15: +5.7183482026e-02 16: +4.2465992806e-02 17: +0.0000000000e+00 18: +0.0000000000e+00 19: +4.9065745348e-02 20: +7.1818580979e-02 21: +7.4637651871e-02 22: +5.4705114288e-02 23: +0.0000000000e+00 24: +0.0000000000e+00 25: +5.5317786623e-02 26: +8.2245055502e-02 27: +8.6069724868e-02 28: +6.3016154585e-02 29: +0.0000000000e+00 30: +0.0000000000e+00 31: +5.8022064083e-02 32: +8.7051065576e-02 33: +9.1862506490e-02 34: +6.7793213565e-02 35: +0.0000000000e+00 36: +0.0000000000e+00 37: +5.7158197600e-02 38: +8.6072632050e-02 39: +9.1740477204e-02 40: +6.8837718390e-02 41: +0.0000000000e+00 42: +0.0000000000e+00 43: +5.2281895519e-02 44: +7.8531031361e-02 45: +8.4696732302e-02 46: +6.5322345207e-02 47: +0.0000000000e+00 48: +0.0000000000e+00 49: +4.2460062188e-02 50: +6.3031788196e-02 51: +6.8901938005e-02 52: +5.5521103179e-02 53: +0.0000000000e+00 54: +0.0000000000e+00 55: +2.6047158790e-02 56: +3.7627567798e-02 57: +4.1664613340e-02 58: +3.6073512746e-02 59: +0.0000000000e+00 60: +0.0000000000e+00 61: +0.0000000000e+00 62: +0.0000000000e+00 63: +0.0000000000e+00 64: +0.0000000000e+00 65: +0.0000000000e+00 Tiempo Cálculo: 0.000000 Método Jacobi, iteraciones para resolver el sistema lineal 1001 Vector "Solución sistema lineal" de dimensión: 36 Vector "Vector Extendido" de dimensión: 30 Vector extendido "Solución" de dimensión: 66 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: 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+7.5109381029e+77 53: +0.0000000000e+00 54: +0.0000000000e+00 55: -3.9487338419e+77 56: -6.3891855687e+77 57: -6.3891855687e+77 58: -3.9487338419e+77 59: +0.0000000000e+00 60: +0.0000000000e+00 61: +0.0000000000e+00 62: +0.0000000000e+00 63: +0.0000000000e+00 64: +0.0000000000e+00 65: +0.0000000000e+00 Tiempo Cálculo: 0.000000 Método Gauss-Seidel, iteraciones para resolver el sistema lineal 33 Vector "Solución sistema lineal" de dimensión: 36 Vector "Vector Extendido" de dimensión: 30 Vector extendido "Solución" de dimensión: 66 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: +2.3308504594e-02 8: +3.1818379340e-02 9: +3.2723788939e-02 10: +2.5103034098e-02 11: +0.0000000000e+00 12: +0.0000000000e+00 13: +3.8783089911e-02 14: +5.5317714750e-02 15: +5.7158180519e-02 16: +4.2446580912e-02 17: +0.0000000000e+00 18: +0.0000000000e+00 19: +4.9049805596e-02 20: +7.1790861411e-02 21: 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Cálculo: 0.000000 Método Factorización LU para resolver el sistema lineal Vector "Solución sistema lineal" de dimensión: 36 Vector "Vector Extendido" de dimensión: 30 Vector extendido "Solución" de dimensión: 66 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: +2.3315916949e-02 8: +3.1831557375e-02 9: +3.2738268555e-02 10: +2.5112866863e-02 11: +0.0000000000e+00 12: +0.0000000000e+00 13: +3.8795513497e-02 14: +5.5339801995e-02 15: +5.7182449310e-02 16: +4.2463061283e-02 17: +0.0000000000e+00 18: +0.0000000000e+00 19: +4.9064873067e-02 20: +7.1817649088e-02 21: +7.4636902551e-02 22: +5.4704451337e-02 23: +0.0000000000e+00 24: +0.0000000000e+00 25: +5.5318212110e-02 26: +8.2244537162e-02 27: +8.6068732502e-02 28: +6.3015963174e-02 29: +0.0000000000e+00 30: +0.0000000000e+00 31: +5.8023079276e-02 32: +8.7051544657e-02 33: +9.1861454947e-02 34: +6.7791884515e-02 35: +0.0000000000e+00 36: +0.0000000000e+00 37: +5.7160324011e-02 38: +8.6073291801e-02 39: +9.1739537326e-02 40: +6.8836246666e-02 41: +0.0000000000e+00 42: +0.0000000000e+00 43: +5.2283336173e-02 44: +7.8532270870e-02 45: +8.4697766120e-02 46: +6.5321879656e-02 47: +0.0000000000e+00 48: +0.0000000000e+00 49: +4.2462231604e-02 50: +6.3034786048e-02 51: +6.8903455993e-02 52: +5.5519974752e-02 53: +0.0000000000e+00 54: +0.0000000000e+00 55: +2.6047798734e-02 56: +3.7629839948e-02 57: +4.1666469431e-02 58: +3.6072486343e-02 59: +0.0000000000e+00 60: +0.0000000000e+00 61: +0.0000000000e+00 62: +0.0000000000e+00 63: +0.0000000000e+00 64: +0.0000000000e+00 65: +0.0000000000e+00 Tiempo Cálculo: 0.000000 Método Inversa para resolver el sistema lineal Vector "Solución sistema lineal" de dimensión: 36 Vector "Vector Extendido" de dimensión: 30 Vector extendido "Solución" de dimensión: 66 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: 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+6.8903455993e-02 52: +5.5519974752e-02 53: +0.0000000000e+00 54: +0.0000000000e+00 55: +2.6047798734e-02 56: +3.7629839948e-02 57: +4.1666469431e-02 58: +3.6072486343e-02 59: +0.0000000000e+00 60: +0.0000000000e+00 61: +0.0000000000e+00 62: +0.0000000000e+00 63: +0.0000000000e+00 64: +0.0000000000e+00 65: +0.0000000000e+00 Tiempo Cálculo: 0.000000