fem_bihar2dps_la.adb fourth order biharmonic PDE solve uxxxx(x,y) + 2 uxxyy(x,y) + uyyyy(x,y) = f(x,y) boundary conditions computed using ub(x,y) ub(x,y) = sin(x)*sin(y) high order shape functions used high order Gauss-Legendre integration used 49 Degrees of Freedom xmin= 0.00, xmax= 3.14, ymin= 0.00, ymax= 3.14 nx= 9, ny= 9 x grid and boundary at ymax i= 1, Ua( 0.00000, 3.14159)= 0.00000 i= 2, Ua( 0.39270, 3.14159)= 0.00000 i= 3, Ua( 0.78540, 3.14159)= 0.00000 i= 4, Ua( 1.17810, 3.14159)= 0.00000 i= 5, Ua( 1.57079, 3.14159)= 0.00000 i= 6, Ua( 1.96349, 3.14159)= 0.00000 i= 7, Ua( 2.35619, 3.14159)= 0.00000 i= 8, Ua( 2.74889, 3.14159)= 0.00000 i= 9, Ua( 3.14159, 3.14159)= 0.00000 y grid and boundary at xmax ii= 1, Ua( 3.14159, 0.00000)= 0.00000 ii= 2, Ua( 3.14159, 0.39270)= 0.00000 ii= 3, Ua( 3.14159, 0.78540)= 0.00000 ii= 4, Ua( 3.14159, 1.17810)= 0.00000 ii= 5, Ua( 3.14159, 1.57079)= 0.00000 ii= 6, Ua( 3.14159, 1.96349)= 0.00000 ii= 7, Ua( 3.14159, 2.35619)= 0.00000 ii= 8, Ua( 3.14159, 2.74889)= 0.00000 ii= 9, Ua( 3.14159, 3.14159)= 0.00000 calling gaulegf npx= 9 calling gaulegf npy= 9 xx(1)= 5.00137365826185E-02, xx(2)= 2.57561516766857E-01, wx(1)= 1.27665402866411E-01, wx(2)= 2.83761227578679E-01 yy(1)= 5.00137365826185E-02, yy(2)= 2.57561516766857E-01, wy(1)= 1.27665402866411E-01, wy(2)= 2.83761227578679E-01 galk(xx(2),yy(2))=-7.39278578790617E+03 galf(xx(2),yy(2))= 5.70906847202242E-01 0.002639000= wall time in seconds to initialize compute stiffness matrix k computed, stiffness matrix f computed, forcing function 128.304247000= wall time in seconds to build k and f 0.015373000= wall time in seconds to solve k u = f writing fem_bihar2dps_la_ada.dat finished writing fem_bihar2dps_la_ada.dat check_soln values maxerr= 1.03565069409228E-05, rmserr= 3.17698520554521E-06, avgerr= 2.22742296262008E-06 0.006893000= wall time in seconds to write and check solution ug computed Galerkin, Ua analytic, error ug( 1, 1)= -0.00000, Ua= 0.00000, err= -0.00000 ug( 1, 2)= -0.00000, Ua= 0.00000, err= -0.00000 ug( 1, 3)= -0.00000, Ua= 0.00000, err= -0.00000 ug( 1, 4)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 1, 5)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 1, 6)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 1, 7)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 1, 8)= -0.00000, Ua= 0.00000, err= -0.00000 ug( 1, 9)= -0.00000, Ua= 0.00000, err= -0.00000 ug( 2, 1)= -0.00000, Ua= 0.00000, err= -0.00000 ug( 2, 2)= 0.09245, Ua= 0.14645, err= -0.05399 ug( 2, 3)= 0.18081, Ua= 0.27060, err= -0.08979 ug( 2, 4)= 0.24297, Ua= 0.35355, err= -0.11058 ug( 2, 5)= 0.26525, Ua= 0.38268, err= -0.11744 ug( 2, 6)= 0.24298, Ua= 0.35355, err= -0.11058 ug( 2, 7)= 0.18081, Ua= 0.27060, err= -0.08979 ug( 2, 8)= 0.09245, Ua= 0.14645, err= -0.05399 ug( 2, 9)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 3, 1)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 3, 2)= 0.18081, Ua= 0.27060, err= -0.08979 ug( 3, 3)= 0.35254, Ua= 0.50000, err= -0.14746 ug( 3, 4)= 0.47306, Ua= 0.65328, err= -0.18022 ug( 3, 5)= 0.51620, Ua= 0.70711, err= -0.19091 ug( 3, 6)= 0.47306, Ua= 0.65328, err= -0.18022 ug( 3, 7)= 0.35254, Ua= 0.50000, err= -0.14746 ug( 3, 8)= 0.18081, Ua= 0.27060, err= -0.08979 ug( 3, 9)= 0.00000, Ua= 0.00000, err= -0.00000 ug( 4, 1)= -0.00000, Ua= 0.00000, err= -0.00000 ug( 4, 2)= 0.24297, Ua= 0.35355, err= -0.11058 ug( 4, 3)= 0.47306, Ua= 0.65328, err= -0.18022 ug( 4, 4)= 0.63434, Ua= 0.85355, err= -0.21921 ug( 4, 5)= 0.69205, Ua= 0.92388, err= -0.23183 ug( 4, 6)= 0.63434, Ua= 0.85355, err= -0.21921 ug( 4, 7)= 0.47306, Ua= 0.65328, err= -0.18022 ug( 4, 8)= 0.24298, Ua= 0.35356, err= -0.11058 ug( 4, 9)= 0.00000, Ua= 0.00000, err= -0.00000 ug( 5, 1)= -0.00000, Ua= 0.00000, err= -0.00000 ug( 5, 2)= 0.26525, Ua= 0.38268, err= -0.11744 ug( 5, 3)= 0.51620, Ua= 0.70711, err= -0.19091 ug( 5, 4)= 0.69205, Ua= 0.92388, err= -0.23183 ug( 5, 5)= 0.75496, Ua= 1.00000, err= -0.24504 ug( 5, 6)= 0.69205, Ua= 0.92388, err= -0.23183 ug( 5, 7)= 0.51620, Ua= 0.70711, err= -0.19091 ug( 5, 8)= 0.26525, Ua= 0.38269, err= -0.11744 ug( 5, 9)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 6, 1)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 6, 2)= 0.24298, Ua= 0.35355, err= -0.11058 ug( 6, 3)= 0.47306, Ua= 0.65328, err= -0.18022 ug( 6, 4)= 0.63434, Ua= 0.85355, err= -0.21921 ug( 6, 5)= 0.69205, Ua= 0.92388, err= -0.23183 ug( 6, 6)= 0.63434, Ua= 0.85355, err= -0.21921 ug( 6, 7)= 0.47306, Ua= 0.65328, err= -0.18022 ug( 6, 8)= 0.24298, Ua= 0.35356, err= -0.11058 ug( 6, 9)= 0.00000, Ua= 0.00000, err= -0.00000 ug( 7, 1)= -0.00000, Ua= 0.00000, err= -0.00000 ug( 7, 2)= 0.18081, Ua= 0.27060, err= -0.08979 ug( 7, 3)= 0.35254, Ua= 0.50000, err= -0.14746 ug( 7, 4)= 0.47306, Ua= 0.65328, err= -0.18022 ug( 7, 5)= 0.51620, Ua= 0.70711, err= -0.19091 ug( 7, 6)= 0.47306, Ua= 0.65328, err= -0.18022 ug( 7, 7)= 0.35254, Ua= 0.50000, err= -0.14746 ug( 7, 8)= 0.18081, Ua= 0.27060, err= -0.08979 ug( 7, 9)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 8, 1)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 8, 2)= 0.09245, Ua= 0.14645, err= -0.05399 ug( 8, 3)= 0.18081, Ua= 0.27060, err= -0.08979 ug( 8, 4)= 0.24298, Ua= 0.35356, err= -0.11058 ug( 8, 5)= 0.26525, Ua= 0.38269, err= -0.11744 ug( 8, 6)= 0.24298, Ua= 0.35356, err= -0.11058 ug( 8, 7)= 0.18081, Ua= 0.27060, err= -0.08979 ug( 8, 8)= 0.09245, Ua= 0.14645, err= -0.05399 ug( 8, 9)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 9, 1)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 9, 2)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 9, 3)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 9, 4)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 9, 5)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 9, 6)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 9, 7)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 9, 8)= 0.00000, Ua= 0.00000, err= 0.00000 ug( 9, 9)= 0.00000, Ua= 0.00000, err= 0.00000 maxerr= 2.45042819647431E-01, avgerr= 8.80627413122178E-02 128.333308000= total wall time in seconds end fem_bihar2dps_la.adb