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_ = { 'name' : , 'select' : , ['kind'] : , ['parent'] : , } **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_ = { 'name' : , 'dtype' : , 'shape' : , 'region' : , 'approx_order' : } see :ref:`User's Guide-Fields` for meaning of , , and . **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_ = { 'name' : , 'kind' : , 'field' : , ['order' : ,] ['dual' : ,] ['history' : ,] } where * - 'unknown field', 'test field' or 'parameter field' * - primary variable - order in the global vector of unknowns * - 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_ = { 'name' : , 'order' : , } where * - the integral name - it has to begin with 'i'! * - 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 :ref:`User's Guide-EssentialBC` for details. Dirichlet Boundary Conditions """"""""""""""""""""""""""""" Dirichlet (essential) boundary conditions, long syntax:: ebc_ = { 'name' : , 'region' : , ['times' : ,] 'dofs' : { : [, : , ...]} } **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_ = { 'name' : , 'region' : (, ), ['times' : ,] 'dofs' : { : [, : , ...]}, 'match' : , } **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_ = { 'name' : , 'region' : (, ) | , ['times' : ,] 'dofs' : { : | None[, ...]}, ['dof_map_fun' : | None,] 'kind' : , [] } **Example**:: lcbc_1 = { 'name' : 'rigid', 'region' : 'Y2', 'dofs' : {'u.all' : None}, 'kind' : 'rigid', } Initial Conditions ^^^^^^^^^^^^^^^^^^ Initial conditions, long syntax:: ic_ = { 'name' : , 'region' : , 'dofs' : { : [, : , ...]} } **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': # 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, }