def test_compute_shape_parametrization_gradient_graetz():
shape_parametrization_expression = [
("x[0]", "x[1]"), # subdomain 1
("mu[0]*(x[0] - 1) + 1", "x[1]") # subdomain 2
]
shape_parametrization_gradient_expression = [compute_shape_parametrization_gradient(expression_on_subdomain) for expression_on_subdomain in shape_parametrization_expression]
# Auxiliary symbolic quantities
x = MatrixSymbol("x", 2, 1)
mu = MatrixSymbol("mu", 1, 1)
# Start checks
assert len(shape_parametrization_gradient_expression) == 2
# Check subdomain 1
assert len(shape_parametrization_gradient_expression[0]) == 2
assert len(shape_parametrization_gradient_expression[0][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[0][X][X], "1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[0][X][Y], "0", x, mu)
assert len(shape_parametrization_gradient_expression[0][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[0][Y][X], "0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[0][Y][Y], "1", x, mu)
# Check subdomain 2
assert len(shape_parametrization_gradient_expression[1]) == 2
assert len(shape_parametrization_gradient_expression[1][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[1][X][X], "mu[0]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[1][X][Y], "0", x, mu)
assert len(shape_parametrization_gradient_expression[1][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[1][Y][X], "0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[1][Y][Y], "1", x, mu)
def test_compute_shape_parametrization_gradient_navier_stokes():
shape_parametrization_expression = [
("x[0]", "x[1]"), # subdomain 1 bottom
("x[0]", "x[1]"), # subdomain 1 top
("x[0]", "0.5*mu[1]*x[1] - 1.0*mu[1] + 2.0"), # subdomain 2 bottom
("x[0]", "0.5*mu[1]*x[1] - 1.0*mu[1] + 2.0") # subdomain 2 top
]
shape_parametrization_gradient_expression = [compute_shape_parametrization_gradient(expression_on_subdomain) for expression_on_subdomain in shape_parametrization_expression]
# Auxiliary symbolic quantities
x = MatrixSymbol("x", 2, 1)
mu = MatrixSymbol("mu", 2, 1)
# Start checks
assert len(shape_parametrization_gradient_expression) == 4
# Check subdomain 1
assert len(shape_parametrization_gradient_expression[0]) == 2
assert len(shape_parametrization_gradient_expression[0][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[0][X][X], "1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[0][X][Y], "0", x, mu)
assert len(shape_parametrization_gradient_expression[0][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[0][Y][X], "0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[0][Y][Y], "1", x, mu)
# Check subdomain 2
assert len(shape_parametrization_gradient_expression[1]) == 2
assert len(shape_parametrization_gradient_expression[1][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[1][X][X], "1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[1][X][Y], "0", x, mu)
assert len(shape_parametrization_gradient_expression[1][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[1][Y][X], "0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[1][Y][Y], "1", x, mu)
# Check subdomain 3
assert len(shape_parametrization_gradient_expression[2]) == 2
assert len(shape_parametrization_gradient_expression[2][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[2][X][X], "1.0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[2][X][Y], "0", x, mu)
assert len(shape_parametrization_gradient_expression[2][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[2][Y][X], "0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[2][Y][Y], "0.5*mu[1]", x, mu)
# Check subdomain 4
assert len(shape_parametrization_gradient_expression[3]) == 2
assert len(shape_parametrization_gradient_expression[3][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[3][X][X], "1.0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[3][X][Y], "0", x, mu)
assert len(shape_parametrization_gradient_expression[3][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[3][Y][X], "0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[3][Y][Y], "0.5*mu[1]", x, mu)
def test_compute_shape_parametrization_gradient_stokes_optimal_dirichlet_boundary_control(
):
shape_parametrization_expression = [
("x[0]", "x[1]"), # subdomain 1
("0.9 - 9.0 * mu[0] + 10.0 * mu[0] * x[0] ", "x[1]"), # subdomain 2
("0.9 - 9.0 * mu[0] + 10.0 * mu[0] * x[0] ", "x[1]"), # subdomain 3
("0.9 - 9.0 * mu[0] + 10.0 * mu[0] * x[0] ", "x[1]"), # subdomain 4
("0.9 - 9.0 * mu[0] + 10.0 * mu[0] * x[0] ", "x[1]"), # subdomain 5
("2.25 * mu[0] + x[0] * (- 1.25 * mu[0] + 1.125) - 0.225 ",
"x[1]"), # subdomain 6
("2.0 * mu[0] + x[0] *(- mu[0] + 1.1) + x[1] * (-mu[0] + 0.1) - 0.2 ",
"x[1]"), # subdomain 7
("2.25 * mu[0] + x[0] * (- 1.25 * mu[0] + 1.125) - 0.225 ",
"x[1]"), # subdomain 8
("mu[0] + x[0] * (- mu[0] + 1.1) + x[1] * (mu[0] - 0.1) - 0.1",
"x[1]"), # subdomain 9
("x[0]", "x[1]"), # subdomain 10
("x[0]", "x[1]"), # subdomain 11
("2.25 * mu[0] + x[0] * (- 1.25 * mu[0] + 1.125) - 0.225 ",
"x[1]"), # subdomain 12
("2.25 * mu[0] + x[0] * (- 1.25 * mu[0] + 1.125) - 0.225 ", "x[1]"
) # subdomain 13
]
shape_parametrization_gradient_expression = [
compute_shape_parametrization_gradient(expression_on_subdomain)
for expression_on_subdomain in shape_parametrization_expression
]
# Auxiliary symbolic quantities
x = MatrixSymbol("x", 2, 1)
mu = MatrixSymbol("mu", 1, 1)
# Start checks
assert len(shape_parametrization_gradient_expression) == 13
# Check subdomain 1
assert len(shape_parametrization_gradient_expression[0]) == 2
assert len(shape_parametrization_gradient_expression[0][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[0][X][X],
"1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[0][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[0][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[0][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[0][Y][Y],
"1", x, mu)
# Check subdomain 2
assert len(shape_parametrization_gradient_expression[1]) == 2
assert len(shape_parametrization_gradient_expression[1][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[1][X][X],
"10.0 * mu[0]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[1][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[1][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[1][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[1][Y][Y],
"1", x, mu)
# Check subdomain 3
assert len(shape_parametrization_gradient_expression[2]) == 2
assert len(shape_parametrization_gradient_expression[2][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[2][X][X],
"10.0 * mu[0]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[2][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[2][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[2][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[2][Y][Y],
"1", x, mu)
# Check subdomain 4
assert len(shape_parametrization_gradient_expression[3]) == 2
assert len(shape_parametrization_gradient_expression[3][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[3][X][X],
"10.0 * mu[0]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[3][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[3][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[3][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[3][Y][Y],
"1", x, mu)
# Check subdomain 5
assert len(shape_parametrization_gradient_expression[4]) == 2
assert len(shape_parametrization_gradient_expression[4][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[4][X][X],
"10.0 * mu[0]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[4][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[4][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[4][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[4][Y][Y],
"1", x, mu)
# Check subdomain 6
assert len(shape_parametrization_gradient_expression[5]) == 2
assert len(shape_parametrization_gradient_expression[5][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[5][X][X],
"- 1.25 * mu[0] + 1.125", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[5][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[5][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[5][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[5][Y][Y],
"1", x, mu)
# Check subdomain 7
assert len(shape_parametrization_gradient_expression[6]) == 2
assert len(shape_parametrization_gradient_expression[6][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[6][X][X],
"- mu[0] + 1.1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[6][X][Y],
"- mu[0] + 0.1", x, mu)
assert len(shape_parametrization_gradient_expression[6][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[6][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[6][Y][Y],
"1", x, mu)
# Check subdomain 8
assert len(shape_parametrization_gradient_expression[7]) == 2
assert len(shape_parametrization_gradient_expression[7][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[7][X][X],
"-1.25 * mu[0] + 1.125", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[7][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[7][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[7][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[7][Y][Y],
"1", x, mu)
# Check subdomain 9
assert len(shape_parametrization_gradient_expression[8]) == 2
assert len(shape_parametrization_gradient_expression[8][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[8][X][X],
"- mu[0] + 1.1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[8][X][Y],
"mu[0] - 0.1", x, mu)
assert len(shape_parametrization_gradient_expression[8][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[8][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[8][Y][Y],
"1", x, mu)
# Check subdomain 10
assert len(shape_parametrization_gradient_expression[9]) == 2
assert len(shape_parametrization_gradient_expression[9][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[9][X][X],
"1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[9][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[9][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[9][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[9][Y][Y],
"1", x, mu)
# Check subdomain 11
assert len(shape_parametrization_gradient_expression[10]) == 2
assert len(shape_parametrization_gradient_expression[10][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[10][X][X],
"1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[10][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[10][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[10][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[10][Y][Y],
"1", x, mu)
# Check subdomain 12
assert len(shape_parametrization_gradient_expression[11]) == 2
assert len(shape_parametrization_gradient_expression[11][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[11][X][X],
"- 1.25 * mu[0] + 1.125", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[11][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[11][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[11][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[11][Y][Y],
"1", x, mu)
# Check subdomain 13
assert len(shape_parametrization_gradient_expression[12]) == 2
assert len(shape_parametrization_gradient_expression[12][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[12][X][X],
"- 1.25 * mu[0] + 1.125", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[12][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[12][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[12][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[12][Y][Y],
"1", x, mu)
def test_compute_shape_parametrization_gradient_stokes():
shape_parametrization_expression = [
("mu[4] * x[0] + mu[1] - mu[4]",
"mu[4] * tan(mu[5]) * x[0] + mu[0] * x[1] + mu[2] - tan(mu[5]) - mu[0]"
), # subdomain 1
("mu[4] * x[0] + mu[1] - mu[4]",
"mu[4] * tan(mu[5]) * x[0] + mu[0] * x[1] + mu[2] - tan(mu[5]) - mu[0]"
), # subdomain 2
("mu[1] * x[0]",
"mu[3] * x[1] + mu[2] + mu[0] - 2*mu[3]"), # subdomain 3
("mu[1] * x[0]",
"mu[3] * x[1] + mu[2] + mu[0] - 2*mu[3]"), # subdomain 4
("mu[1] * x[0]", "mu[0] * x[1] + mu[2] - mu[0]"), # subdomain 5
("mu[1] * x[0]", "mu[0] * x[1] + mu[2] - mu[0]"), # subdomain 6
("mu[1] * x[0]", "mu[2] * x[1]"), # subdomain 7
("mu[1] * x[0]", "mu[2] * x[1]"), # subdomain 8
]
shape_parametrization_gradient_expression = [
compute_shape_parametrization_gradient(expression_on_subdomain)
for expression_on_subdomain in shape_parametrization_expression
]
# Auxiliary symbolic quantities
x = MatrixSymbol("x", 2, 1)
mu = MatrixSymbol("mu", 6, 1)
# Start checks
assert len(shape_parametrization_gradient_expression) == 8
# Check subdomain 1
assert len(shape_parametrization_gradient_expression[0]) == 2
assert len(shape_parametrization_gradient_expression[0][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[0][X][X],
"mu[4]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[0][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[0][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[0][Y][X],
"mu[4] * tan(mu[5])", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[0][Y][Y],
"mu[0]", x, mu)
# Check subdomain 2
assert len(shape_parametrization_gradient_expression[1]) == 2
assert len(shape_parametrization_gradient_expression[1][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[1][X][X],
"mu[4]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[1][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[1][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[1][Y][X],
"mu[4] * tan(mu[5])", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[1][Y][Y],
"mu[0]", x, mu)
# Check subdomain 3
assert len(shape_parametrization_gradient_expression[2]) == 2
assert len(shape_parametrization_gradient_expression[2][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[2][X][X],
"mu[1]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[2][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[2][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[2][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[2][Y][Y],
"mu[3]", x, mu)
# Check subdomain 4
assert len(shape_parametrization_gradient_expression[3]) == 2
assert len(shape_parametrization_gradient_expression[3][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[3][X][X],
"mu[1]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[3][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[3][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[3][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[3][Y][Y],
"mu[3]", x, mu)
# Check subdomain 5
assert len(shape_parametrization_gradient_expression[4]) == 2
assert len(shape_parametrization_gradient_expression[4][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[4][X][X],
"mu[1]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[4][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[4][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[4][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[4][Y][Y],
"mu[0]", x, mu)
# Check subdomain 6
assert len(shape_parametrization_gradient_expression[5]) == 2
assert len(shape_parametrization_gradient_expression[5][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[5][X][X],
"mu[1]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[5][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[5][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[5][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[5][Y][Y],
"mu[0]", x, mu)
# Check subdomain 7
assert len(shape_parametrization_gradient_expression[6]) == 2
assert len(shape_parametrization_gradient_expression[6][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[6][X][X],
"mu[1]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[6][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[6][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[6][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[6][Y][Y],
"mu[2]", x, mu)
# Check subdomain 8
assert len(shape_parametrization_gradient_expression[7]) == 2
assert len(shape_parametrization_gradient_expression[7][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[7][X][X],
"mu[1]", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[7][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[7][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[7][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[7][Y][Y],
"mu[2]", x, mu)
def test_compute_shape_parametrization_gradient_hole_rotation():
shape_parametrization_expression = [
("- 2 * sqrt(2.0) * cos(mu[0]) + x[0] * (sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2)"
+
"+ x[1] * (- sqrt(2.0) * sin(mu[0]) / 2 - 3 * sqrt(2.0) * cos(mu[0]) / 2 + 2) + 2",
"- 2 * sqrt(2.0) * sin(mu[0]) + x[0] * (sqrt(2.0) * sin(mu[0]) / 2 - sqrt(2.0) * cos(mu[0]) / 2)"
+
"+ x[1] * (- 3 * sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2 + 2) + 2"
), # subdomain 1
("2 * sqrt(2.0) * sin(mu[0]) + x[0] + x[1] * (sqrt(2.0) * sin(mu[0]) - 1) - 2",
"- 2 * sqrt(2.0) * cos(mu[0]) + x[1] * (- sqrt(2.0) * cos(mu[0]) + 2) + 2"
), # subdomain 2
("- 2 * sqrt(2.0) * cos(mu[0]) + x[0] * (sqrt(2.0) * sin(mu[0]) / 2 - 3 * sqrt(2.0) * cos(mu[0]) / 2 + 2)"
+
"+ x[1] * (- sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2) + 2",
"- 2 * sqrt(2.0) * sin(mu[0]) + x[0] * (- 3 * sqrt(2.0) * sin(mu[0]) / 2 - sqrt(2.0) * cos(mu[0]) / 2 + 2)"
+
"+ x[1] * (sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2) + 2"
), # subdomain 3
("- 2 * sqrt(2.0) * sin(mu[0]) + x[0] * (- sqrt(2.0) * sin(mu[0]) + 2) + 2",
"2 * sqrt(2.0) * cos(mu[0]) + x[0] * (sqrt(2.0) * cos(mu[0]) - 1) + x[1] - 2"
), # subdomain 4
("2 * sqrt(2.0) * sin(mu[0]) + x[0]* (- 3 * sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2 + 2)"
+
"+ x[1] * (- sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2) - 2",
"- 2 * sqrt(2.0) * cos(mu[0]) + x[0] * (sqrt(2.0) * sin(mu[0]) / 2 + 3 * sqrt(2.0) * cos(mu[0]) / 2 - 2)"
+
"+ x[1] * (sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2) + 2"
), # subdomain 5
("2 * sqrt(2.0) * cos(mu[0]) + x[0] * (- sqrt(2.0) * cos(mu[0]) + 2) - 2",
"2 * sqrt(2.0) * sin(mu[0]) + x[0] * (- sqrt(2.0) * sin(mu[0]) + 1) + x[1] - 2"
), # subdomain 6
("- 2 * sqrt(2.0) * sin(mu[0]) + x[0] * (sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2)"
+
"+ x[1] * (3 * sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2 - 2) + 2",
"2 * sqrt(2.0) * cos(mu[0]) + x[0] * (sqrt(2.0) * sin(mu[0]) / 2 - sqrt(2.0) * cos(mu[0]) / 2)"
+
"+ x[1] * (sqrt(2.0) * sin(mu[0]) / 2 - 3 * sqrt(2.0) * cos(mu[0]) / 2 + 2) - 2"
), # subdomain 7
("2 * sqrt(2.0) * cos(mu[0]) + x[0] + x[1] * (- sqrt(2.0) * cos(mu[0]) + 1) - 2",
"2 * sqrt(2.0) * sin(mu[0]) + x[1] * (- sqrt(2.0) * sin(mu[0]) + 2) - 2"
) # subdomain 8
]
shape_parametrization_gradient_expression = [
compute_shape_parametrization_gradient(expression_on_subdomain)
for expression_on_subdomain in shape_parametrization_expression
]
# Auxiliary symbolic quantities
x = MatrixSymbol("x", 2, 1)
mu = MatrixSymbol("mu", 1, 1)
# Start checks
assert len(shape_parametrization_gradient_expression) == 8
# Check subdomain 1
assert len(shape_parametrization_gradient_expression[0]) == 2
assert len(shape_parametrization_gradient_expression[0][X]) == 2
assert symbolic_equal(
shape_parametrization_gradient_expression[0][X][X],
"sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2", x, mu)
assert symbolic_equal(
shape_parametrization_gradient_expression[0][X][Y],
"- sqrt(2.0) * sin(mu[0]) / 2 - 3 * sqrt(2.0) * cos(mu[0]) / 2 + 2", x,
mu)
assert len(shape_parametrization_gradient_expression[0][Y]) == 2
assert symbolic_equal(
shape_parametrization_gradient_expression[0][Y][X],
"sqrt(2.0) * sin(mu[0]) / 2 - sqrt(2.0) * cos(mu[0]) / 2", x, mu)
assert symbolic_equal(
shape_parametrization_gradient_expression[0][Y][Y],
"-3 * sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2 + 2", x,
mu)
# Check subdomain 2
assert len(shape_parametrization_gradient_expression[1]) == 2
assert len(shape_parametrization_gradient_expression[1][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[1][X][X],
"1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[1][X][Y],
"sqrt(2.0) * sin(mu[0]) - 1", x, mu)
assert len(shape_parametrization_gradient_expression[1][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[1][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[1][Y][Y],
"- sqrt(2.0) * cos(mu[0]) + 2", x, mu)
# Check subdomain 3
assert len(shape_parametrization_gradient_expression[2]) == 2
assert len(shape_parametrization_gradient_expression[2][X]) == 2
assert symbolic_equal(
shape_parametrization_gradient_expression[2][X][X],
"sqrt(2.0) * sin(mu[0]) / 2 - 3 * sqrt(2.0) * cos(mu[0]) / 2 + 2", x,
mu)
assert symbolic_equal(
shape_parametrization_gradient_expression[2][X][Y],
"- sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2", x, mu)
assert len(shape_parametrization_gradient_expression[2][Y]) == 2
assert symbolic_equal(
shape_parametrization_gradient_expression[2][Y][X],
"- 3 * sqrt(2.0) * sin(mu[0]) / 2 - sqrt(2.0) * cos(mu[0]) / 2 + 2", x,
mu)
assert symbolic_equal(
shape_parametrization_gradient_expression[2][Y][Y],
"sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2", x, mu)
# Check subdomain 4
assert len(shape_parametrization_gradient_expression[3]) == 2
assert len(shape_parametrization_gradient_expression[3][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[3][X][X],
"- sqrt(2.0) * sin(mu[0]) + 2", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[3][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[3][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[3][Y][X],
"sqrt(2.0) * cos(mu[0]) - 1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[3][Y][Y],
"1", x, mu)
# Check subdomain 5
assert len(shape_parametrization_gradient_expression[4]) == 2
assert len(shape_parametrization_gradient_expression[4][X]) == 2
assert symbolic_equal(
shape_parametrization_gradient_expression[4][X][X],
"- 3 * sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2 + 2", x,
mu)
assert symbolic_equal(
shape_parametrization_gradient_expression[4][X][Y],
"- sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2", x, mu)
assert len(shape_parametrization_gradient_expression[4][Y]) == 2
assert symbolic_equal(
shape_parametrization_gradient_expression[4][Y][X],
"sqrt(2.0) * sin(mu[0]) / 2 + 3 * sqrt(2.0) * cos(mu[0]) / 2 - 2", x,
mu)
assert symbolic_equal(
shape_parametrization_gradient_expression[4][Y][Y],
"sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2", x, mu)
# Check subdomain 6
assert len(shape_parametrization_gradient_expression[5]) == 2
assert len(shape_parametrization_gradient_expression[5][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[5][X][X],
"- sqrt(2.0) * cos(mu[0]) + 2", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[5][X][Y],
"0", x, mu)
assert len(shape_parametrization_gradient_expression[5][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[5][Y][X],
"- sqrt(2.0) * sin(mu[0]) + 1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[5][Y][Y],
"1", x, mu)
# Check subdomain 7
assert len(shape_parametrization_gradient_expression[6]) == 2
assert len(shape_parametrization_gradient_expression[6][X]) == 2
assert symbolic_equal(
shape_parametrization_gradient_expression[6][X][X],
"sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2", x, mu)
assert symbolic_equal(
shape_parametrization_gradient_expression[6][X][Y],
"3 * sqrt(2.0) * sin(mu[0]) / 2 + sqrt(2.0) * cos(mu[0]) / 2 - 2", x,
mu)
assert len(shape_parametrization_gradient_expression[6][Y]) == 2
assert symbolic_equal(
shape_parametrization_gradient_expression[6][Y][X],
"sqrt(2.0) * sin(mu[0]) / 2 - sqrt(2.0) * cos(mu[0]) / 2", x, mu)
assert symbolic_equal(
shape_parametrization_gradient_expression[6][Y][Y],
"sqrt(2.0) * sin(mu[0]) / 2 - 3 * sqrt(2.0) * cos(mu[0]) / 2 + 2", x,
mu)
# Check subdomain 8
assert len(shape_parametrization_gradient_expression[7]) == 2
assert len(shape_parametrization_gradient_expression[7][X]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[7][X][X],
"1", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[7][X][Y],
"- sqrt(2.0) * cos(mu[0]) + 1", x, mu)
assert len(shape_parametrization_gradient_expression[7][Y]) == 2
assert symbolic_equal(shape_parametrization_gradient_expression[7][Y][X],
"0", x, mu)
assert symbolic_equal(shape_parametrization_gradient_expression[7][Y][Y],
"- sqrt(2.0) * sin(mu[0]) + 2", x, mu)
