new_contents: import numpy
  from convergence_lspr import (run_convergence, picklesave, pickleload,
                                report_results, richardson_extrapolation_lspr,
                                mesh_multiple)
  
  def main():
      print('{:-^60}'.format('Running sphere_multiple_lspr test'))
      try:
          test_outputs = pickleload()
      except FileNotFoundError:
          test_outputs = {}
  
      
      problem_folder = 'input_files'
  
      # multiple spheres lspr 
      param = 'sphere_complex.param'
      test_names = 'sphere_multiple_complex'
  
      #In this case we have 1 sphere of radius 10 and 6 of radius 2
      R=10.
      r=2.    
      total_Area = 4*numpy.pi (R*R + 6*r*r)
  
      if test_name not in test_outputs.keys():
         N, avg_density, iterations, expected_rate, Cext_0, Time = run_convergence(
              mesh_multiple, test_name, problem_folder, param, total_Area=total_Area)
         test_outputs[test_name] = {'N': N,
                                    'avg_density': avg_density, 
                                    'iterations': iterations,
                                    'expected_rate': expected_rate,
                                    'Cext_0': Cext_0,
                                    'Time': Time} 
  
  
      # load data for analysis
      N = test_outputs[test_name]['N']
      avg_density = test_outputs[test_name]['avg_density']
      iterations = test_outputs[test_name]['iterations']
      expected_rate = test_outputs[test_name]['expected_rate']
      Cext_0 = test_outputs[test_name]['Cext_0']
      Time = test_outputs[test_name]['Time']
  
      total_time = Time
  
      #Richardson extrapolation on the main sphere:
      rich_extra = richardson_extrapolation_lspr(test_outputs[test_name]['Cext_0'])  
  
      error = abs(Cext_0 - rich_extra) / abs(rich_extra)
  
      test_outputs[test_name]['error'] = error
      test_outputs[test_name]['rich_extra'] = rich_extra
  
      picklesave(test_outputs)
   
      report_results(error,
                         N,
                         expected_rate,
                         iterations,
                         Cext_0,
                         analytical=None,
                         total_time,
                         test_name=test_name,
                         rich_extra=rich_extra,
                         avg_density=avg_density)
  
  
  if __name__ == "__main__":
      main()
  
subject: Add covnergence test for multiple spheres