def test_1d_scalar_1(): print('============== test_1d_scalar_1 ================') # ... define the weak formulation x = Symbol('x') u = Symbol('u') v = Symbol('v') a = Lambda((x, v, u), Dot(Grad(u), Grad(v)) + u * v) # ... # ... create a finite element space p = 3 ne = 64 print('> Grid :: {ne}'.format(ne=ne)) print('> Degree :: {p}'.format(p=p)) grid = linspace(0., 1., ne + 1) V = SplineSpace(p, grid=grid) # ... # ... kernel_py = compile_kernel('kernel_scalar_1', a, V, backend='python') kernel_f90 = compile_kernel('kernel_scalar_1', a, V, backend='fortran') M_py = assemble_matrix(V, kernel_py) M_f90 = assemble_matrix(V, kernel_f90) # ... assert_identical_coo(M_py, M_f90)
def test_2d_block_3(): print('============== test_2d_block_3 ================') x, y = symbols('x y') u = Symbol('u') v = Symbol('v') epsilon = Constant('epsilon') Laplace = lambda v, u: Dot(Grad(v), Grad(u)) Mass = lambda v, u: v * u u1, u2, p = symbols('u1 u2 p') v1, v2, q = symbols('v1 v2 q') a = Lambda((x, y, v1, v2, q, u1, u2, p), Laplace(v1, u1) - dx(v1) * p + Laplace(v2, u2) - dy(v2) * p + q * (dx(u1) + dy(u2)) + epsilon * Mass(q, p)) print('> input := {0}'.format(a)) # ... create a finite element space p1 = 2 p2 = 2 ne1 = 8 ne2 = 8 print('> Grid :: [{ne1},{ne2}]'.format(ne1=ne1, ne2=ne2)) print('> Degree :: [{p1},{p2}]'.format(p1=p1, p2=p2)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V = TensorFemSpace(V1, V2) V = VectorFemSpace(V, V, V) # ... # ... kernel_py = compile_kernel('kernel_block_3', a, V, d_args={'epsilon': 'double'}, backend='python') kernel_f90 = compile_kernel('kernel_block_3', a, V, d_args={'epsilon': 'double'}, backend='fortran') M_py = assemble_matrix(V, kernel_py, args={'epsilon': 1.e-3}) M_f90 = assemble_matrix(V, kernel_f90, args={'epsilon': 1.e-3}) # ... assert_identical_coo(M_py, M_f90) print('')
def test_3d_scalar_2(): print('============== test_3d_scalar_2 ================') # ... define the weak formulation x, y, z = symbols('x y z') u = Symbol('u') v = Symbol('v') alpha = Constant('alpha') nu = Constant('nu') a = Lambda((x, v, u), alpha * Dot(Grad(u), Grad(v)) + nu * u * v) # ... # ... create a finite element space p1 = 2 p2 = 2 p3 = 2 ne1 = 2 ne2 = 2 ne3 = 2 # ... print('> Grid :: [{},{},{}]'.format(ne1, ne2, ne3)) print('> Degree :: [{},{},{}]'.format(p1, p2, p3)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) grid_3 = linspace(0., 1., ne3 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V3 = SplineSpace(p3, grid=grid_3) V = TensorFemSpace(V1, V2, V3) # ... # ... kernel_py = compile_kernel('kernel_scalar_2', a, V, d_constants={'nu': 0.1}, d_args={'alpha': 'double'}, backend='python') kernel_f90 = compile_kernel('kernel_scalar_2', a, V, d_constants={'nu': 0.1}, d_args={'alpha': 'double'}, backend='fortran') M_py = assemble_matrix(V, kernel_py, args={'alpha': 2.0}) M_f90 = assemble_matrix(V, kernel_f90, args={'alpha': 2.0}) # ... assert_identical_coo(M_py, M_f90)
def test_3d_block_2(): print('============== test_3d_block_2 ================') x, y, z = symbols('x y z') u = IndexedBase('u') v = IndexedBase('v') F = Field('F') a = Lambda((x, y, z, v, u), Dot(Curl(u), Curl(v)) + 0.2 * Dot(u, v) + F * u[0] * v[0]) # ... create a finite element space p1 = 2 p2 = 2 p3 = 2 ne1 = 2 ne2 = 2 ne3 = 2 print('> Grid :: [{},{},{}]'.format(ne1, ne2, ne3)) print('> Degree :: [{},{},{}]'.format(p1, p2, p3)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) grid_3 = linspace(0., 1., ne3 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V3 = SplineSpace(p3, grid=grid_3) W = TensorFemSpace(V1, V2, V3) # ... # ... vector space V = VectorFemSpace(W, W, W) # ... F = Spline(W) F.coeffs._data[:, :, :] = 1. # ... kernel_py = compile_kernel('kernel_block_2', a, V, backend='python') kernel_f90 = compile_kernel('kernel_block_2', a, V, backend='fortran') M_py = assemble_matrix(V, kernel_py, fields={'F': F}) M_f90 = assemble_matrix(V, kernel_f90, fields={'F': F}) # ... assert_identical_coo(M_py, M_f90)
def test_2d_block_2(): print('============== test_2d_block_2 ================') # ... define the weak formulation x, y = symbols('x y') u = IndexedBase('u') v = IndexedBase('v') F = Field('F') a = Lambda( (x, y, v, u), Rot(u) * Rot(v) + Div(u) * Div(v) + 0.2 * Dot(u, v) + F * u[0] * v[0]) # ... # ... create a finite element space p1 = 2 p2 = 2 ne1 = 8 ne2 = 8 print('> Grid :: [{ne1},{ne2}]'.format(ne1=ne1, ne2=ne2)) print('> Degree :: [{p1},{p2}]'.format(p1=p1, p2=p2)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) W = TensorFemSpace(V1, V2) # ... # ... vector space V = VectorFemSpace(W, W) # ... F = Spline(W) F.coeffs._data[:, :] = 1. # ... kernel_py = compile_kernel('kernel_block_2', a, V, backend='python') kernel_f90 = compile_kernel('kernel_block_2', a, V, backend='fortran') M_py = assemble_matrix(V, kernel_py, fields={'F': F}) M_f90 = assemble_matrix(V, kernel_f90, fields={'F': F}) # ... assert_identical_coo(M_py, M_f90)
def test_3d_scalar_4(): print('============== test_3d_scalar_4 ================') # ... define the weak formulation x, y, z = symbols('x y z') u = Symbol('u') v = Symbol('v') F = Field('F') a = Lambda((x, y, z, v, u), Dot(Grad(F * u), Grad(v)) + u * v) # ... # ... create a finite element space p1 = 2 p2 = 2 p3 = 2 ne1 = 2 ne2 = 2 ne3 = 2 # ... print('> Grid :: [{},{},{}]'.format(ne1, ne2, ne3)) print('> Degree :: [{},{},{}]'.format(p1, p2, p3)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) grid_3 = linspace(0., 1., ne3 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V3 = SplineSpace(p3, grid=grid_3) V = TensorFemSpace(V1, V2, V3) # ... F = Spline(V) F.coeffs._data[:, :, :] = 1. # ... kernel_py = compile_kernel('kernel_scalar_4', a, V, backend='python') kernel_f90 = compile_kernel('kernel_scalar_4', a, V, backend='fortran') M_py = assemble_matrix(V, kernel_py, fields={'F': F}) M_f90 = assemble_matrix(V, kernel_f90, fields={'F': F}) # ... assert_identical_coo(M_py, M_f90)
def test_1d_scalar_2(): print('============== test_1d_scalar_2 ================') # ... define the weak formulation x = Symbol('x') u = Symbol('u') v = Symbol('v') alpha = Constant('alpha') nu = Constant('nu') a = Lambda((x, v, u), alpha * Dot(Grad(u), Grad(v)) + nu * u * v) # ... # ... create a finite element space p = 3 ne = 64 print('> Grid :: {ne}'.format(ne=ne)) print('> Degree :: {p}'.format(p=p)) grid = linspace(0., 1., ne + 1) V = SplineSpace(p, grid=grid) # ... # ... kernel_py = compile_kernel('kernel_scalar_2', a, V, d_constants={'nu': 0.1}, d_args={'alpha': 'double'}, backend='python') kernel_f90 = compile_kernel('kernel_scalar_2', a, V, d_constants={'nu': 0.1}, d_args={'alpha': 'double'}, backend='fortran') M_py = assemble_matrix(V, kernel_py, args={'alpha': 2.0}) M_f90 = assemble_matrix(V, kernel_f90, args={'alpha': 2.0}) # ... assert_identical_coo(M_py, M_f90)
def test_3d_scalar_5(): print('============== test_3d_scalar_5 ================') # ... define the weak formulation x, y, z = symbols('x y z') u = Symbol('u') v = Symbol('v') a = Lambda((x, y, z, v, u), dx(dx(u)) * dx(dx(v)) + dy(dy(u)) * dy(dy(v)) + dz(dz(u)) * dz(dz(v)) + Dot(Grad(u), Grad(v)) + u * v) # ... # ... create a finite element space p1 = 2 p2 = 2 p3 = 2 ne1 = 2 ne2 = 2 ne3 = 2 # ... print('> Grid :: [{},{},{}]'.format(ne1, ne2, ne3)) print('> Degree :: [{},{},{}]'.format(p1, p2, p3)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) grid_3 = linspace(0., 1., ne3 + 1) V1 = SplineSpace(p1, grid=grid_1, nderiv=2) V2 = SplineSpace(p2, grid=grid_2, nderiv=2) V3 = SplineSpace(p3, grid=grid_3, nderiv=2) V = TensorFemSpace(V1, V2, V3) # ... # ... kernel_py = compile_kernel('kernel_scalar_5', a, V, backend='python') kernel_f90 = compile_kernel('kernel_scalar_5', a, V, backend='fortran') M_py = assemble_matrix(V, kernel_py) M_f90 = assemble_matrix(V, kernel_f90) # ... assert_identical_coo(M_py, M_f90)
def test_2d_scalar_6(): print('============== test_2d_scalar_6 ================') # ... define the weak formulation x, y = symbols('x y') u = Symbol('u') v = Symbol('v') a = Lambda((x, y, v, u), dx(dx(u)) * dx(dx(v)) + dy(dy(u)) * dy(dy(v)) + Dot(Grad(u), Grad(v)) + u * v) # ... # ... create a finite element space p1 = 2 p2 = 2 ne1 = 8 ne2 = 8 print('> Grid :: [{ne1},{ne2}]'.format(ne1=ne1, ne2=ne2)) print('> Degree :: [{p1},{p2}]'.format(p1=p1, p2=p2)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) V1 = SplineSpace(p1, grid=grid_1, nderiv=2) V2 = SplineSpace(p2, grid=grid_2, nderiv=2) V = TensorFemSpace(V1, V2) # ... # ... kernel_py = compile_kernel('kernel_scalar_6', a, V, backend='python') kernel_f90 = compile_kernel('kernel_scalar_6', a, V, backend='fortran') M_py = assemble_matrix(V, kernel_py) M_f90 = assemble_matrix(V, kernel_f90) # ... assert_identical_coo(M_py, M_f90)
def test_1d_block_1(): print('============== test_1d_block_1 ================') # ... define the weak formulation x = Symbol('x') u0, u1 = symbols('u0 u1') v0, v1 = symbols('v0 v1') a = Lambda((x, v0, v1, u0, u1), dx(u0) * dx(v0) + dx(u1) * v0 + u0 * dx(v1) + u1 * v1) # ... # ... create a finite element space p = 3 ne = 64 print('> Grid :: {ne}'.format(ne=ne)) print('> Degree :: {p}'.format(p=p)) grid = linspace(0., 1., ne + 1) V = SplineSpace(p, grid=grid) # ... # ... Vector fem space V = VectorFemSpace(V, V) # ... # ... kernel_py = compile_kernel('kernel_block_1', a, V, backend='python') kernel_f90 = compile_kernel('kernel_block_1', backend='fortran') M_py = assemble_matrix(V, kernel_py) M_f90 = assemble_matrix(V, kernel_f90) # ... assert_identical_coo(M_py, M_f90)
def test_2d_scalar_4(): print('============== test_2d_scalar_4 ================') # ... define the weak formulation x, y = symbols('x y') u = Symbol('u') v = Symbol('v') b0 = Function('b0') b1 = Function('b1') a = Lambda((x, y, v, u), (b0(x, y) * dx(v) + b1(x, y) * dy(v)) * (b0(x, y) * dx(u) + b1(x, y) * dy(u))) # ... # ... create a finite element space p1 = 2 p2 = 2 ne1 = 8 ne2 = 8 print('> Grid :: [{ne1},{ne2}]'.format(ne1=ne1, ne2=ne2)) print('> Degree :: [{p1},{p2}]'.format(p1=p1, p2=p2)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V = TensorFemSpace(V1, V2) # ... # ... user defined function def b0(x, y): from numpy import sin from scipy import pi r = 1.1659397624413860850012270020670 * (1.0 + 0.1 * sin(2 * pi * y)) return r def b1(x, y): from numpy import sin from scipy import pi r = 1.0 * (1.0 + 0.1 * sin(2 * pi * y)) return r # ... # ... create an interactive pyccel context from pyccel.epyccel import ContextPyccel context = ContextPyccel(name='context_4') context.insert_function(b0, ['double', 'double'], kind='function', results=['double']) context.insert_function(b1, ['double', 'double'], kind='function', results=['double']) context.compile() # ... # ... kernel_py = compile_kernel('kernel_scalar_4', a, V, context=context, verbose=True, backend='python') kernel_f90 = compile_kernel('kernel_scalar_4', a, V, context=context, verbose=True, backend='fortran') # ... # ... M_py = assemble_matrix(V, kernel_py) M_f90 = assemble_matrix(V, kernel_f90) # ... assert_identical_coo(M_py, M_f90)
def test_2d_scalar_3(): print('============== test_2d_scalar_3 ================') # ... define the weak formulation x, y = symbols('x y') u = Symbol('u') v = Symbol('v') b = Function('b') a = Lambda((x, y, v, u), Dot(Grad(u), Grad(v)) + b(x, y) * u * v) # ... # ... create a finite element space p1 = 2 p2 = 2 ne1 = 8 ne2 = 8 print('> Grid :: [{ne1},{ne2}]'.format(ne1=ne1, ne2=ne2)) print('> Degree :: [{p1},{p2}]'.format(p1=p1, p2=p2)) grid_1 = linspace(0., 1., ne1 + 1) grid_2 = linspace(0., 1., ne2 + 1) V1 = SplineSpace(p1, grid=grid_1) V2 = SplineSpace(p2, grid=grid_2) V = TensorFemSpace(V1, V2) # ... # ... user defined function def b(x, y): r = 1. + x * (1. - x) + y * (1. - y) return r # ... # ... create an interactive pyccel context from pyccel.epyccel import ContextPyccel context = ContextPyccel(name='context_3') context.insert_function(b, ['double', 'double'], kind='function', results=['double']) context.compile() # ... # ... kernel_py = compile_kernel('kernel_scalar_3', a, V, context=context, verbose=True, backend='python') kernel_f90 = compile_kernel('kernel_scalar_3', a, V, context=context, verbose=True, backend='fortran') # ... # ... M_py = assemble_matrix(V, kernel_py) M_f90 = assemble_matrix(V, kernel_f90) # ... assert_identical_coo(M_py, M_f90)
def test_1d_scalar_3(): print('============== test_1d_scalar_3 ================') x = Symbol('x') u = Symbol('u') v = Symbol('v') b = Function('b') a = Lambda((x, v, u), Dot(Grad(u), Grad(v)) + b(x) * u * v) print('> input := {0}'.format(a)) # ... create a finite element space p = 3 ne = 64 print('> Grid :: {ne}'.format(ne=ne)) print('> Degree :: {p}'.format(p=p)) grid = linspace(0., 1., ne + 1) V = SplineSpace(p, grid=grid) # ... # ... user defined function def b(s): r = 1. + s * (1. - s) return r # ... # ... create an interactive pyccel context from pyccel.epyccel import ContextPyccel context = ContextPyccel(name='context_3') context.insert_function(b, ['double'], kind='function', results=['double']) context.compile() # ... # ... kernel_py = compile_kernel('kernel_scalar_3', a, V, context=context, verbose=True, backend='python') kernel_f90 = compile_kernel('kernel_scalar_3', a, V, context=context, verbose=True, backend='fortran') # ... # ... M_py = assemble_matrix(V, kernel_py) M_f90 = assemble_matrix(V, kernel_f90) # ... assert_identical_coo(M_py, M_f90) print('')