Example #1
0
d = dt * (diffusivity * dot(grad(q), grad(p)) - dot(grad(q), u) * p) * dx

a = M + 0.5 * d
L = action(M - 0.5 * d, t)

# Generate code for mass and rhs assembly.

lhs, = compile_form(a, "lhs")
rhs, = compile_form(L, "rhs")

# Set up simulation data structures

valuetype = np.float64

nodes, coords, elements, elem_node = read_triangle(opt['mesh'])

num_nodes = nodes.size

sparsity = op2.Sparsity((nodes, nodes), (elem_node, elem_node), "sparsity")
mat = op2.Mat(sparsity, valuetype, "mat")

tracer_vals = np.zeros(num_nodes, dtype=valuetype)
tracer = op2.Dat(nodes, tracer_vals, valuetype, "tracer")

b_vals = np.zeros(num_nodes, dtype=valuetype)
b = op2.Dat(nodes, b_vals, valuetype, "b")

velocity_vals = np.asarray([1.0, 0.0] * num_nodes, dtype=valuetype)
velocity = op2.Dat(nodes ** 2, velocity_vals, valuetype, "velocity")
Example #2
0
def main(opt):
    # Set up finite element problem

    dt = 0.0001

    T = FiniteElement("Lagrange", "triangle", 1)
    V = VectorElement("Lagrange", "triangle", 1)

    p = TrialFunction(T)
    q = TestFunction(T)
    t = Coefficient(T)
    u = Coefficient(V)
    a = Coefficient(T)

    diffusivity = 0.1

    M = p * q * dx

    adv_rhs = (q * t + dt * dot(grad(q), u) * t) * dx

    d = -dt * diffusivity * dot(grad(q), grad(p)) * dx

    diff = M - 0.5 * d
    diff_rhs = action(M + 0.5 * d, t)

    # Generate code for mass and rhs assembly.

    adv, = compile_form(M, "adv")
    adv_rhs, = compile_form(adv_rhs, "adv_rhs")
    diff, = compile_form(diff, "diff")
    diff_rhs, = compile_form(diff_rhs, "diff_rhs")

    # Set up simulation data structures

    valuetype = np.float64

    nodes, vnodes, coords, elements, elem_node, elem_vnode = read_triangle(opt['mesh'])
    num_nodes = nodes.size

    sparsity = op2.Sparsity((elem_node, elem_node), "sparsity")
    if opt['advection']:
        adv_mat = op2.Mat(sparsity, valuetype, "adv_mat")
        op2.par_loop(adv, elements(3, 3),
                     adv_mat((elem_node[op2.i[0]], elem_node[op2.i[1]]), op2.INC),
                     coords(elem_vnode, op2.READ))
    if opt['diffusion']:
        diff_mat = op2.Mat(sparsity, valuetype, "diff_mat")
        op2.par_loop(diff, elements(3, 3),
                     diff_mat((elem_node[op2.i[0]], elem_node[op2.i[1]]), op2.INC),
                     coords(elem_vnode, op2.READ))

    tracer_vals = np.zeros(num_nodes, dtype=valuetype)
    tracer = op2.Dat(nodes, tracer_vals, valuetype, "tracer")

    b_vals = np.zeros(num_nodes, dtype=valuetype)
    b = op2.Dat(nodes, b_vals, valuetype, "b")

    velocity_vals = np.asarray([1.0, 0.0] * num_nodes, dtype=valuetype)
    velocity = op2.Dat(vnodes, velocity_vals, valuetype, "velocity")

    # Set initial condition

    i_cond_code = """void i_cond(double *c, double *t)
{
  double A   = 0.1; // Normalisation
  double D   = 0.1; // Diffusivity
  double pi  = 3.14159265358979;
  double x   = c[0]-(0.45+%(T)f);
  double y   = c[1]-0.5;
  double r2  = x*x+y*y;

  *t = A*(exp(-r2/(4*D*%(T)f))/(4*pi*D*%(T)f));
}
"""

    T = 0.01

    i_cond = op2.Kernel(i_cond_code % {'T': T}, "i_cond")

    op2.par_loop(i_cond, nodes,
                 coords(op2.IdentityMap, op2.READ),
                 tracer(op2.IdentityMap, op2.WRITE))

    # Assemble and solve
    if opt['visualize']:
        vis_coords = np.asarray([[x, y, 0.0] for x, y in coords.data_ro], dtype=np.float64)
        import viper
        v = viper.Viper(x=viper_shape(tracer.data_ro), coordinates=vis_coords, cells=elem_node.values)

    solver = op2.Solver()

    while T < 0.015:

        # Advection

        if opt['advection']:
            b.zero()
            op2.par_loop(adv_rhs, elements(3),
                         b(elem_node[op2.i[0]], op2.INC),
                         coords(elem_vnode, op2.READ),
                         tracer(elem_node, op2.READ),
                         velocity(elem_vnode, op2.READ))

            solver.solve(adv_mat, tracer, b)

        # Diffusion

        if opt['diffusion']:
            b.zero()
            op2.par_loop(diff_rhs, elements(3),
                         b(elem_node[op2.i[0]], op2.INC),
                         coords(elem_vnode, op2.READ),
                         tracer(elem_node, op2.READ))

            solver.solve(diff_mat, tracer, b)

        if opt['visualize']:
            v.update(viper_shape(tracer.data_ro))

        T = T + dt

    if opt['print_output'] or opt['test_output']:
        analytical_vals = np.zeros(num_nodes, dtype=valuetype)
        analytical = op2.Dat(nodes, analytical_vals, valuetype, "analytical")

        i_cond = op2.Kernel(i_cond_code % {'T': T}, "i_cond")

        op2.par_loop(i_cond, nodes,
                     coords(op2.IdentityMap, op2.READ),
                     analytical(op2.IdentityMap, op2.WRITE))

    # Print error w.r.t. analytical solution
    if opt['print_output']:
        print "Expected - computed  solution: %s" % tracer.data - analytical.data

    if opt['test_output']:
        l2norm = dot(t - a, t - a) * dx
        l2_kernel, = compile_form(l2norm, "error_norm")
        result = op2.Global(1, [0.0])
        op2.par_loop(l2_kernel, elements,
                     result(op2.INC),
                     coords(elem_vnode,op2.READ),
                     tracer(elem_node,op2.READ),
                     analytical(elem_node,op2.READ)
                     )
        with open("adv_diff.%s.out" % os.path.split(opt['mesh'])[-1], "w") as out:
            out.write(str(result.data[0]) + "\n")
Example #3
0
def run(diffusivity, current_time, dt, endtime, **kwargs):
    op2.init(**kwargs)

    # Set up finite element problem

    T = FiniteElement("Lagrange", "triangle", 1)
    V = VectorElement("Lagrange", "triangle", 1)

    p = TrialFunction(T)
    q = TestFunction(T)
    t = Coefficient(T)
    u = Coefficient(V)

    diffusivity = 0.1

    M = p * q * dx

    adv_rhs = (q * t + dt * dot(grad(q), u) * t) * dx

    d = -dt * diffusivity * dot(grad(q), grad(p)) * dx

    diff_matrix = M - 0.5 * d
    diff_rhs = action(M + 0.5 * d, t)

    # Generate code for mass and rhs assembly.

    mass = compile_form(M, "mass")[0]
    adv_rhs = compile_form(adv_rhs, "adv_rhs")[0]
    diff_matrix = compile_form(diff_matrix, "diff_matrix")[0]
    diff_rhs = compile_form(diff_rhs, "diff_rhs")[0]

    # Set up simulation data structures

    valuetype = np.float64

    nodes, coords, elements, elem_node = read_triangle(kwargs['mesh'])
    num_nodes = nodes.size

    sparsity = op2.Sparsity((elem_node, elem_node), 1, "sparsity")
    mat = op2.Mat(sparsity, valuetype, "mat")

    tracer_vals = np.asarray([0.0] * num_nodes, dtype=valuetype)
    tracer = op2.Dat(nodes, 1, tracer_vals, valuetype, "tracer")

    b_vals = np.asarray([0.0] * num_nodes, dtype=valuetype)
    b = op2.Dat(nodes, 1, b_vals, valuetype, "b")

    velocity_vals = np.asarray([1.0, 0.0] * num_nodes, dtype=valuetype)
    velocity = op2.Dat(nodes, 2, velocity_vals, valuetype, "velocity")

    # Set initial condition

    i_cond_code = """
    void i_cond(double *c, double *t)
    {
      double i_t = 0.01; // Initial time
      double A   = 0.1; // Normalisation
      double D   = 0.1; // Diffusivity
      double pi  = 3.141459265358979;
      double x   = c[0]-0.5;
      double y   = c[1]-0.5;
      double r   = sqrt(x*x+y*y);

      if (r<0.25)
        *t = A*(exp((-(r*r))/(4*D*i_t))/(4*pi*D*i_t));
      else
        *t = 0.0;
    }
    """

    i_cond = op2.Kernel(i_cond_code, "i_cond")

    op2.par_loop(i_cond, nodes, coords(op2.IdentityMap, op2.READ),
                 tracer(op2.IdentityMap, op2.WRITE))

    zero_dat_code = """
    void zero_dat(double *dat)
    {
      *dat = 0.0;
    }
    """

    zero_dat = op2.Kernel(zero_dat_code, "zero_dat")

    # Assemble and solve

    have_advection = True
    have_diffusion = True

    def timestep_iteration():
        # Advection

        if have_advection:
            tic('advection')
            tic('assembly')
            mat.zero()

            op2.par_loop(
                mass, elements(3, 3),
                mat((elem_node[op2.i[0]], elem_node[op2.i[1]]), op2.INC),
                coords(elem_node, op2.READ))

            op2.par_loop(zero_dat, nodes, b(op2.IdentityMap, op2.WRITE))

            op2.par_loop(adv_rhs, elements(3), b(elem_node[op2.i[0]], op2.INC),
                         coords(elem_node, op2.READ),
                         tracer(elem_node, op2.READ),
                         velocity(elem_node, op2.READ))
            toc('assembly')
            tic('solve')
            op2.solve(mat, tracer, b)
            toc('solve')
            toc('advection')

        # Diffusion

        if have_diffusion:
            tic('diffusion')
            tic('assembly')
            mat.zero()

            op2.par_loop(
                diff_matrix, elements(3, 3),
                mat((elem_node[op2.i[0]], elem_node[op2.i[1]]), op2.INC),
                coords(elem_node, op2.READ))

            op2.par_loop(zero_dat, nodes, b(op2.IdentityMap, op2.WRITE))

            op2.par_loop(diff_rhs, elements(3), b(elem_node[op2.i[0]],
                                                  op2.INC),
                         coords(elem_node, op2.READ),
                         tracer(elem_node, op2.READ))

            toc('assembly')
            tic('solve')
            op2.solve(mat, tracer, b)
            toc('solve')
            toc('diffusion')

    # Perform 1 iteration to warm up plan cache then reset initial condition
    timestep_iteration()
    op2.par_loop(i_cond, nodes, coords(op2.IdentityMap, op2.READ),
                 tracer(op2.IdentityMap, op2.WRITE))
    reset()

    # Timed iteration
    t1 = clock()
    while current_time < endtime:
        timestep_iteration()
        current_time += dt
    runtime = clock() - t1
    print "/fluidity :: %f" % runtime
    summary('profile_pyop2_%s_%s.csv' %
            (opt['mesh'].split('/')[-1], opt['backend']))
Example #4
0
    abs = abs * (-1.0);

  A[0]+=0.5*abs*0.1 * y[0][0];

  z[0][0]+=0.2*(0.5*abs*0.1*y[0][0]);
  z[1][0]+=0.2*(0.5*abs*0.1*y[0][0]);
  z[2][0]+=0.2*(0.5*abs*0.1*y[0][0]);
  z[3][0]+=0.2*(0.5*abs*0.1*y[0][0]);
  z[4][0]+=0.2*(0.5*abs*0.1*y[0][0]);
  z[5][0]+=0.2*(0.5*abs*0.1*y[0][0]);
}""", "comp_vol")

# Set up simulation data structures
valuetype = np.float64

nodes, coords, elements, elem_node = read_triangle(mesh_name, layers)

# mesh data
mesh2d = np.array([3, 3, 1])
mesh1d = np.array([2, 1])
A = np.array([[0, 1], [0]])

# the array of dof values for each element type
dofs = np.array([[2, 0], [0, 0], [0, 1]])
dofs_coords = np.array([[2, 0], [0, 0], [0, 0]])
dofs_field = np.array([[0, 0], [0, 0], [0, 1]])
dofs_res = np.array([[1, 0], [0, 0], [0, 0]])

# ALL the nodes, edges amd cells of the 2D mesh
nums = np.array([nodes.size, 0, elements.size])
Example #5
0
  if (area < 0)
    area = area * (-1.0);
  A[0]+=0.5*area*0.1 * y[0][0];

  z[0][0]+=0.2*(0.5*area*0.1*y[0][0]);
  z[1][0]+=0.2*(0.5*area*0.1*y[0][0]);
  z[2][0]+=0.2*(0.5*area*0.1*y[0][0]);
  z[3][0]+=0.2*(0.5*area*0.1*y[0][0]);
  z[4][0]+=0.2*(0.5*area*0.1*y[0][0]);
  z[5][0]+=0.2*(0.5*area*0.1*y[0][0]);
}""", "comp_vol")

# Set up simulation data structures
valuetype = np.float64

nodes, coords, elements, elem_node = read_triangle(mesh_name, layers)

# mesh data
mesh2d = np.array([3, 3, 1])
mesh1d = np.array([2, 1])
A = np.array([[0, 1], [0]])

# the array of dof values for each element type
dofs = np.array([[2, 0], [0, 0], [0, 1]])
dofs_coords = np.array([[2, 0], [0, 0], [0, 0]])
dofs_field = np.array([[0, 0], [0, 0], [0, 1]])
dofs_res = np.array([[1, 0], [0, 0], [0, 0]])

# ALL the nodes, edges amd cells of the 2D mesh
nums = np.array([nodes.size, 0, elements.size])
Example #6
0
d = dt * (diffusivity * dot(grad(q), grad(p)) - dot(grad(q), u) * p) * dx

a = M + 0.5 * d
L = action(M - 0.5 * d, t)

# Generate code for mass and rhs assembly.

lhs, = compile_form(a, "lhs")
rhs, = compile_form(L, "rhs")

# Set up simulation data structures

valuetype = np.float64

nodes, vnodes, coords, elements, elem_node, elem_vnode = read_triangle(opt["mesh"])
num_nodes = nodes.size

sparsity = op2.Sparsity((elem_node, elem_node), "sparsity")
mat = op2.Mat(sparsity, valuetype, "mat")

tracer_vals = np.zeros(num_nodes, dtype=valuetype)
tracer = op2.Dat(nodes, tracer_vals, valuetype, "tracer")

b_vals = np.zeros(num_nodes, dtype=valuetype)
b = op2.Dat(nodes, b_vals, valuetype, "b")

velocity_vals = np.asarray([1.0, 0.0] * num_nodes, dtype=valuetype)
velocity = op2.Dat(vnodes, velocity_vals, valuetype, "velocity")

# Set initial condition
Example #7
0
def run(diffusivity, current_time, dt, endtime, **kwargs):
    op2.init(**kwargs)

    # Set up finite element problem

    T = FiniteElement("Lagrange", "triangle", 1)
    V = VectorElement("Lagrange", "triangle", 1)

    p = TrialFunction(T)
    q = TestFunction(T)
    t = Coefficient(T)
    u = Coefficient(V)

    diffusivity = 0.1

    M = p * q * dx

    adv_rhs = (q * t + dt * dot(grad(q), u) * t) * dx

    d = -dt * diffusivity * dot(grad(q), grad(p)) * dx

    diff_matrix = M - 0.5 * d
    diff_rhs = action(M + 0.5 * d, t)

    # Generate code for mass and rhs assembly.

    mass = compile_form(M, "mass")[0]
    adv_rhs = compile_form(adv_rhs, "adv_rhs")[0]
    diff_matrix = compile_form(diff_matrix, "diff_matrix")[0]
    diff_rhs = compile_form(diff_rhs, "diff_rhs")[0]

    # Set up simulation data structures

    valuetype = np.float64

    nodes, coords, elements, elem_node = read_triangle(kwargs["mesh"])
    num_nodes = nodes.size

    sparsity = op2.Sparsity((elem_node, elem_node), 1, "sparsity")
    mat = op2.Mat(sparsity, valuetype, "mat")

    tracer_vals = np.asarray([0.0] * num_nodes, dtype=valuetype)
    tracer = op2.Dat(nodes, 1, tracer_vals, valuetype, "tracer")

    b_vals = np.asarray([0.0] * num_nodes, dtype=valuetype)
    b = op2.Dat(nodes, 1, b_vals, valuetype, "b")

    velocity_vals = np.asarray([1.0, 0.0] * num_nodes, dtype=valuetype)
    velocity = op2.Dat(nodes, 2, velocity_vals, valuetype, "velocity")

    # Set initial condition

    i_cond_code = """
    void i_cond(double *c, double *t)
    {
      double i_t = 0.01; // Initial time
      double A   = 0.1; // Normalisation
      double D   = 0.1; // Diffusivity
      double pi  = 3.141459265358979;
      double x   = c[0]-0.5;
      double y   = c[1]-0.5;
      double r   = sqrt(x*x+y*y);

      if (r<0.25)
        *t = A*(exp((-(r*r))/(4*D*i_t))/(4*pi*D*i_t));
      else
        *t = 0.0;
    }
    """

    i_cond = op2.Kernel(i_cond_code, "i_cond")

    op2.par_loop(i_cond, nodes, coords(op2.IdentityMap, op2.READ), tracer(op2.IdentityMap, op2.WRITE))

    zero_dat_code = """
    void zero_dat(double *dat)
    {
      *dat = 0.0;
    }
    """

    zero_dat = op2.Kernel(zero_dat_code, "zero_dat")

    # Assemble and solve

    have_advection = True
    have_diffusion = True

    def timestep_iteration():
        # Advection

        if have_advection:
            tic("advection")
            tic("assembly")
            mat.zero()

            op2.par_loop(
                mass,
                elements(3, 3),
                mat((elem_node[op2.i[0]], elem_node[op2.i[1]]), op2.INC),
                coords(elem_node, op2.READ),
            )

            op2.par_loop(zero_dat, nodes, b(op2.IdentityMap, op2.WRITE))

            op2.par_loop(
                adv_rhs,
                elements(3),
                b(elem_node[op2.i[0]], op2.INC),
                coords(elem_node, op2.READ),
                tracer(elem_node, op2.READ),
                velocity(elem_node, op2.READ),
            )
            toc("assembly")
            tic("solve")
            op2.solve(mat, tracer, b)
            toc("solve")
            toc("advection")

        # Diffusion

        if have_diffusion:
            tic("diffusion")
            tic("assembly")
            mat.zero()

            op2.par_loop(
                diff_matrix,
                elements(3, 3),
                mat((elem_node[op2.i[0]], elem_node[op2.i[1]]), op2.INC),
                coords(elem_node, op2.READ),
            )

            op2.par_loop(zero_dat, nodes, b(op2.IdentityMap, op2.WRITE))

            op2.par_loop(
                diff_rhs,
                elements(3),
                b(elem_node[op2.i[0]], op2.INC),
                coords(elem_node, op2.READ),
                tracer(elem_node, op2.READ),
            )

            toc("assembly")
            tic("solve")
            op2.solve(mat, tracer, b)
            toc("solve")
            toc("diffusion")

    # Perform 1 iteration to warm up plan cache then reset initial condition
    timestep_iteration()
    op2.par_loop(i_cond, nodes, coords(op2.IdentityMap, op2.READ), tracer(op2.IdentityMap, op2.WRITE))
    reset()

    # Timed iteration
    t1 = clock()
    while current_time < endtime:
        timestep_iteration()
        current_time += dt
    runtime = clock() - t1
    print "/fluidity :: %f" % runtime
    summary("profile_pyop2_%s_%s.csv" % (opt["mesh"].split("/")[-1], opt["backend"]))
Example #8
0
def main(opt):
    # Set up finite element identity problem

    E = FiniteElement("Lagrange", "triangle", 1)

    v = TestFunction(E)
    u = TrialFunction(E)
    f = Coefficient(E)

    a = v * u * dx
    L = v * f * dx

    # Generate code for mass and rhs assembly.

    mass, = compile_form(a, "mass")
    rhs, = compile_form(L, "rhs")

    # Set up simulation data structures

    valuetype = np.float64

    nodes, coords, elements, elem_node = read_triangle(opt['mesh'])

    sparsity = op2.Sparsity((nodes, nodes), (elem_node, elem_node), "sparsity")
    mat = op2.Mat(sparsity, valuetype, "mat")

    b = op2.Dat(nodes, np.zeros(nodes.size, dtype=valuetype), valuetype, "b")
    x = op2.Dat(nodes, np.zeros(nodes.size, dtype=valuetype), valuetype, "x")

    # Set up initial condition

    f_vals = np.array([2 * X + 4 * Y for X, Y in coords.data], dtype=valuetype)
    f = op2.Dat(nodes, f_vals, valuetype, "f")

    # Assemble and solve

    op2.par_loop(mass, elements,
                 mat(op2.INC, (elem_node[op2.i[0]], elem_node[op2.i[1]])),
                 coords(op2.READ, elem_node, flatten=True))

    op2.par_loop(rhs, elements,
                 b(op2.INC, elem_node[op2.i[0]]),
                 coords(op2.READ, elem_node, flatten=True),
                 f(op2.READ, elem_node))

    solver = op2.Solver()
    solver.solve(mat, x, b)

    # Print solution (if necessary)
    if opt['print_output']:
        print "Expected solution: %s" % f.data
        print "Computed solution: %s" % x.data

    # Save output (if necessary)
    if opt['return_output']:
        return f.data, x.data
    if opt['save_output']:
        from cPickle import dump, HIGHEST_PROTOCOL
        import gzip
        out = gzip.open("mass2d_triangle.out.gz", "wb")
        dump((f.data, x.data, b.data, mat.array), out, HIGHEST_PROTOCOL)
        out.close()