Problem Description File - Long Syntax¶

Historically, the keywords exist in two flavors:

long syntax is the original one - it is longer to type, but the individual fields are named
short syntax was added later to offer brevity.

Region Definition Syntax¶

Region, long syntax:

region_<number> = {
    'name' : <name>,
    'select' : <selection>,
    ['kind'] : <region kind>,
    ['parent'] : <parent region>,
}

Example definitions:

region_0 = {
    'name' : 'Omega',
    'select' : 'all',
}
region_21 = {
    'name' : 'Right',
    'select' : 'vertices in (x > 0.99)',
    'kind' : 'facet',
}
region_31 = {
    'name' : 'Gamma1',
    'select' : """(cells of group 1 *v cells of group 2)
                  +v r.Right""",
    'kind' : 'facet',
    'parent' : 'Omega',
}

Fields¶

Fields, long syntax:

field_<number> = {
     'name' : <name>,
     'dtype' : <data_type>,
     'shape' : <shape>,
     'region' : <region_name>,
     'approx_order' : <approx_order>,
     ['space' : <space>,]
     ['poly_space_basis' : <poly_space_basis>,]
 }

see Fields for meaning of <data_type>, <shape>, <region_name>, <approx_order>, <space> and <>poly_space_basis>.

Example: scalar P1 elements in 2D on a region Omega:

field_1 = {
    'name' : 'temperature',
    'dtype' : 'real',
    'shape' : 'scalar',
    'region' : 'Omega',
    'approx_order' : 1
}

Variables¶

Variables, long syntax:

variables_<number> = {
    'name' : <name>,
    'kind' : <kind>,
    'field' : <field_name>,
    ['order' : <order>,]
    ['dual' : <variable_name>,]
    ['history' : <history>,]
}

where

<kind> - ‘unknown field’, ‘test field’ or ‘parameter field’
<order> - primary variable - order in the global vector of unknowns
<history> - number of time steps to remember prior to current step

Example:

variable_1 = {
    'name' : 't',
    'kind' : 'unknown field',
    'field' : 'temperature',
    'order' : 0, # order in the global vector of unknowns
    'history' : 1,
}

variable_2 = {
    'name' : 's',
    'kind' : 'test field',
    'field' : 'temperature',
    'dual' : 't',
}

Integrals¶

Integrals, long syntax:

integral_<number> = {
    'name' : <name>,
    'order' : <order>,
}

where

<name> - the integral name - it has to begin with ‘i’!
<order> - the order of polynomials to integrate, or ‘custom’ for integrals with explicitly given values and weights

Example:

integral_1 = {
    'name' : 'i1',
    'order' : 2,
}

import numpy as nm
N = 2
integral_2 = {
    'name' : 'i2',
    'order' : 'custom',
    'vals'    : zip(nm.linspace( 1e-10, 0.5, N ),
                    nm.linspace( 1e-10, 0.5, N )),
    'weights' : [1./N] * N,
}

Essential Boundary Conditions and Constraints¶

See Essential Boundary Conditions and Constraints for details.

Dirichlet Boundary Conditions¶

Dirichlet (essential) boundary conditions, long syntax:

ebc_<number> = {
    'name' : <name>,
    'region' : <region_name>,
    ['times' : <times_specification>,]
    'dofs' : {<dof_specification> : <value>[,
              <dof_specification> : <value>, ...]}
}

Example:

ebc_1 = {
    'name' : 'ZeroSurface',
    'region' : 'Surface',
    'times' : [(0.5, 1.0), (2.3, 5)],
    'dofs' : {'u.all' : 0.0, 'phi.all' : 0.0},
}

Periodic Boundary Conditions¶

Periodic boundary conditions, long syntax:

epbc_<number> = {
    'name' : <name>,
    'region' : (<region1_name>, <region2_name>),
    ['times' : <times_specification>,]
    'dofs' : {<dof_specification> : <dof_specification>[,
              <dof_specification> : <dof_specification>, ...]},
    'match' : <match_function_name>,
}

Example:

epbc_1 = {
    'name' : 'up1',
    'region' : ('Left', 'Right'),
    'dofs' : {'u.all' : 'u.all', 'p.0' : 'p.0'},
    'match' : 'match_y_line',
}

Linear Combination Boundary Conditions¶

Linear combination boundary conditions, long syntax:

lcbc_<number> = {
    'name' : <name>,
    'region' : (<region1_name>, <region2_name>) | <region1_name>,
    ['times' : <times_specification>,]
    'dofs' : {<dof_specification> : <dof_specification> | None[, ...]},
    ['dof_map_fun' : <dof_map_function_name> | None,]
    'kind' : <lcbc_kind>,
    [<kind_specific_options>]
}

Example:

lcbc_1 = {
    'name' : 'rigid',
    'region' : 'Y2',
    'dofs' : {'u.all' : None},
    'kind' : 'rigid',
}

Initial Conditions¶

Initial conditions, long syntax:

ic_<number> = {
    'name' : <name>,
    'region' : <region_name>,
    'dofs' : {<dof_specification> : <value>[,
              <dof_specification> : <value>, ...]}
}

Example:

ic_1 = {
    'name' : 'ic',
    'region' : 'Omega',
    'dofs' : {'T.0' : 5.0},
}

Materials¶

Example:

material_10 = {
    'name' : 'm',
    'values' : {
        # This gets tiled to all physical QPs (constant function)
        'val' : [0.0, -1.0, 0.0],
        # This does not - '.' denotes a special value, e.g. a flag.
        '.val0' : [0.0, 0.1, 0.0],
    },
}

material_3 = {
  'name' : 'm2',
  'function' : 'get_pars',
}

def get_pars(ts, coors, mode=None, **kwargs):
    out = {}
    if mode == 'qp':
        # <array of shape (coors.shape[0], n_row, n_col)>
        out['val'] = nm.ones((coors.shape[0], 1, 1), dtype=nm.float64)
    else: # special mode
        out['val0'] = True

    return out

Configuring Solvers¶

Linear solver:

solver_0 = {
    'name' : 'ls',
    'kind' : 'ls.scipy_direct',
}

Nonlinear solver:

solver_1 = {
    'name' : 'newton',
    'kind' : 'nls.newton',

    'i_max'      : 1,
    'eps_a'      : 1e-10,
    'eps_r'      : 1.0,
    'macheps'   : 1e-16,
    'lin_red'    : 1e-2, # Linear system error < (eps_a * lin_red).
    'ls_red'     : 0.1,
    'ls_red_warp' : 0.001,
    'ls_on'      : 1.1,
    'ls_min'     : 1e-5,
    'check'     : 0,
    'delta'     : 1e-6,
    'is_linear' : False,
}