def METHOD_NAME( problem ):
    """Vary size of \Omega1. Saves also the regions into options['output_dir'].
    Input:
      problem: Problem instance
    Return:
      a generator object:
      1. creates new (modified) problem
      2. yields the new (modified) problem and output container
      3. use the output container for some logging
      4. yields None (to signal next iteration to Application)
    """
    from sfepy.discrete import Problem
    from sfepy.solvers.ts import get_print_info
    output.prefix = 'vary_omega1_size:'
    diameters = nm.linspace( 0.1, 0.6, 7 ) + 0.001
    ofn_trunk, output_format = problem.ofn_trunk, problem.output_format
    output_dir = problem.output_dir
    join = os.path.join
    conf = problem.conf
    cf = conf.get_raw( 'functions' )
    n_digit, aux, d_format = get_print_info( len( diameters ) + 1 )
    for ii, diameter in enumerate( diameters ):
        output( 'iteration %d: diameter %3.2f' % (ii, diameter) )
        cf['select_circ'] = (lambda coors, domain=None:
                             select_circ(coors[:,0], coors[:,1], 0, diameter),)
        conf.edit('functions', cf)
        problem = Problem.from_conf(conf)
        problem.save_regions( join( output_dir, ('regions_' + d_format) % ii ),
                              ['Omega_1'] )
        region = problem.domain.regions['Omega_1']
        if not region.has_cells():
            raise ValueError('region %s has no cells!' % region.name)
        ofn_trunk = ofn_trunk + '_' + (d_format % ii)
        problem.setup_output(output_filename_trunk=ofn_trunk,
                             output_dir=output_dir,
                             output_format=output_format)
        out = []
        yield problem, out
        out_problem, state = out[-1]
        filename = join( output_dir,
                         ('log_%s.txt' % d_format) % ii )
        fd = open( filename, 'w' )
        log_item = '$r(\Omega_1)$: %f\n' % diameter
        fd.write( log_item )
        fd.write( 'solution:\n' )
        nm.savetxt(fd, state())
        fd.close()
        yield None