phononic/band_gaps.py

Description

Acoustic band gaps in a strongly heterogeneous elastic body, detected using homogenization techniques.

A reference periodic cell contains two domains: the stiff matrix Y_m and the soft (but heavy) inclusion Y_c.

source code

"""
Acoustic band gaps in a strongly heterogeneous elastic body, detected using
homogenization techniques.

A reference periodic cell contains two domains: the stiff matrix :math:`Y_m`
and the soft (but heavy) inclusion :math:`Y_c`.
"""
from __future__ import absolute_import
from sfepy import data_dir
from sfepy.base.base import Struct
from sfepy.base.ioutils import InDir
from sfepy.homogenization.coefficients import Coefficients

from examples.phononic.band_gaps_conf import (BandGapsConf, get_pars,
                                              clip, clip_sqrt)

clip, clip_sqrt # Make pyflakes happy...

incwd = InDir(__file__)

filename = data_dir + '/meshes/2d/special/circle_in_square.mesh'

output_dir = incwd('output/band_gaps')

# aluminium, SI units
D_m = get_pars(2, 5.898e10, 2.681e10)
density_m = 2799.0

# epoxy, SI units
D_c = get_pars(2, 1.798e9, 1.48e9)
density_c = 1142.0

mat_pars = Coefficients(D_m=D_m, density_m=density_m,
                        D_c=D_c, density_c=density_c)

region_selects = Struct(matrix='cells of group 1',
                        inclusion='cells of group 2')

corrs_save_names = {'evp' : 'evp', 'corrs_rs' : 'corrs_rs'}

options = {
    'plot_transform_angle' : None,
    'plot_transform_wave' : ('clip_sqrt', (0, 7000)),
    'plot_transform' : ('clip', (-7000, 7000)),

    'fig_name' : 'band_gaps',
    'fig_name_angle' : 'band_gaps_angle',
    'fig_name_wave' : 'band_gaps_wave',
    'fig_suffix' : '.pdf',

    'coefs_filename' : 'coefs.txt',

    'incident_wave_dir' : [1.0, 1.0],

    'plot_options' : {
        'show' : True,
        'legend' : True,
    },
    'plot_labels' : {
        'band_gaps' : {
            'resonance' : r'$\lambda^r$',
            'masked' : r'masked $\lambda^r$',
            'eig_min' : r'min eig($M$)',
            'eig_max' : r'max eig($M$)',
            'x_axis' : r'$\sqrt{\lambda}$, $\omega$',
            'y_axis' : r'eigenvalues of mass matrix $M$',
        },
    },
    'plot_rsc' : {
        'params' : {'axes.labelsize': 'x-large',
                    'font.size': 14,
                    'legend.fontsize': 'large',
                    'legend.loc': 'upper right',
                    'xtick.labelsize': 'large',
                    'ytick.labelsize': 'large',
                    'text.usetex': True},
    },
    'multiprocessing' : False,
    'float_format' : '%.16e',
}

evp_options = {
    'eigensolver' : 'eig.sgscipy',
    'save_eig_vectors' : (12, 0),
    'scale_epsilon' : 1.0,
    'elasticity_contrast' : 1.0,
}

eigenmomenta_options = {
    # eigenmomentum threshold,
    'threshold' : 1e-2,
    # eigenmomentum threshold is relative w.r.t. largest one,
    'threshold_is_relative' : True,
}

band_gaps_options = {
    'eig_range' : (0, 30), # -> freq_range
                           # = sqrt(eigs[slice(*eig_range)][[0, -1]])
    # 'fixed_freq_range' : (0.1, 3e7),
    'freq_margins' : (10, 10), # % of freq_range
    'freq_eps' : 1e-7, # frequency
    'zero_eps' : 1e-12, # zero finding
    'freq_step' : 0.0001, # % of freq_range

    'log_save_name' : 'band_gaps.log',
    'raw_log_save_name' : 'raw_eigensolution.npz',
}

conf = BandGapsConf(filename, 1, region_selects, mat_pars, options,
                    evp_options, eigenmomenta_options, band_gaps_options,
                    corrs_save_names=corrs_save_names, incwd=incwd,
                    output_dir=output_dir)

define = lambda: conf.conf.to_dict()