surface_term_16LGL_points.sagews

xi_LGL_16 = [-0.99999999998420,
          -0.96956804630032,
          -0.89920053307202,
          -0.79200829187099,
          -0.65238870288019,
          -0.48605942188742,
          -0.29983046890075,
          -0.10132627352195,
           0.10132627352195,
           0.29983046890076,
           0.48605942188718,
           0.65238870288226,
           0.79200829186255,
           0.89920053309205,
           0.96956804627192,
           0.99999999999918]

eta_LGL_16 = [-0.99999999998420,
          -0.96956804630032,
          -0.89920053307202,
          -0.79200829187099,
          -0.65238870288019,
          -0.48605942188742,
          -0.29983046890075,
          -0.10132627352195,
           0.10132627352195,
           0.29983046890076,
           0.48605942188718,
           0.65238870288226,
           0.79200829186255,
           0.89920053309205,
           0.96956804627192,
           0.99999999999918]



var('xi, eta, x, y')

(xi, eta, x, y)

xi_poly = []
for i in range(16):
    L = [1]
    for j in range(16):
        if (i != j):
            L[0] *= (xi - xi_LGL_16[j])/(xi_LGL_16[i] - xi_LGL_16[j])
    xi_poly.append(L)

eta_poly = []
for i in range(16):
    L = [1]
    for j in range(16):
        if (i != j):
            L[0] *= (eta - eta_LGL_16[j])/(eta_LGL_16[i] - eta_LGL_16[j])
    eta_poly.append(L)

F_xi = e ** (- (xi ** 2 ) / (0.6 ** 2))

for p in range(16):
    for q in range(16):
        first_boundary = integrate(eta_poly[q][0] * xi_poly[p][0](-1) * F_xi(xi=-1), eta, -1, 1)
        third_boundary = integrate(eta_poly[q][0] * xi_poly[p][0](1) * F_xi(xi=1), eta, -1, 1)
        print(first_boundary + third_boundary)

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