added convergence plot script for scalar test problem to make sure order there is exactly equal to number of iterations K

Author: Daniel Ruprecht

examples/fwsw/run_convergence.py

@@ -0,0 +1,73 @@
+from __future__ import print_function
+
+from pySDC import CollocationClasses as collclass
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from examples.fwsw.ProblemClass import swfw_scalar
+from pySDC.datatype_classes.complex_mesh import mesh, rhs_imex_mesh
+from pySDC.sweeper_classes.imex_1st_order import imex_1st_order
+import pySDC.PFASST_stepwise as mp
+from pySDC import Log
+
+
+
+if __name__ == "__main__":
+
+    # set global logger (remove this if you do not want the output at all)
+    logger = Log.setup_custom_logger('root')
+
+    num_procs = 1
+
+    # This comes as read-in for the level class
+    lparams = {}
+    lparams['restol'] = 1E-12
+
+    sparams = {}
+    sparams['maxiter'] = 4
+
+    # This comes as read-in for the problem class
+    pparams = {}
+    pparams['lambda_s'] = np.array([0.1j], dtype='complex')
+    pparams['lambda_f'] = np.array([1.0j], dtype='complex')
+    pparams['u0'] = 1
+
+    # Fill description dictionary for easy hierarchy creation
+    description = {}
+    description['problem_class'] = swfw_scalar
+    description['problem_params'] = pparams
+    description['dtype_u'] = mesh
+    description['dtype_f'] = rhs_imex_mesh
+    description['collocation_class'] = collclass.CollGaussLegendre
+    description['num_nodes'] = [3]
+    description['do_LU'] = False
+    description['sweeper_class'] = imex_1st_order
+    description['level_params'] = lparams
+
+    # quickly generate block of steps
+    MS = mp.generate_steps(num_procs,sparams,description)
+
+    Nsteps_v = np.array([1, 2, 4, 8, 10, 15, 20])
+    Tend = 1.0
+    t0   = 0
+
+    P = MS[0].levels[0].prob
+    uinit = P.u_exact(t0)
+    uex = P.u_exact(Tend)
+    error = np.zeros(np.size(Nsteps_v))
+    convline = np.zeros(np.size(Nsteps_v))
+    
+    for j in range(0,np.size(Nsteps_v)):
+    # setup parameters "in time"
+      dt   = Tend/float(Nsteps_v[j])
+
+      # call main function to get things done...
+      uend,stats = mp.run_pfasst(MS,u0=uinit,t0=t0,dt=dt,Tend=Tend)
+      error[j] = np.abs(uend.values - uex.values)
+      convline[j] = error[j]*(float(Nsteps_v[j])/float(Nsteps_v[j]))**sparams['maxiter']
+
+    plt.figure()
+    plt.loglog(Nsteps_v, error, 'bo', markersize=12)
+    plt.loglog(Nsteps_v, convline, '-', color='k')
+    plt.show()