coupling-all-direchlet.py

#!/usr/bin/env python3
# Plot the solution of all approaches in one plot
# @author patrickdiehl@lsu.edu
# @author serge.prudhomme@polymtl.ca
# @date 03/02/2021
import numpy as np
import sys 
import matplotlib.pyplot as plt
import matplotlib

pgf_with_latex = {"text.usetex": True, "font.size" : 12, "pgf.preamble" : [r'\usepackage{xfrac}'] }


example = sys.argv[1]

#############################################################################
# Exact solution 
#############################################################################

def exactSolution(x):
    
    if example == "Cubic":
        return (2/3/np.sqrt(3)) * ( 9*x - 9*x*x + 2 * x * x * x )
    elif example == "Quartic":
        return 16/9 * x * x - 32/27 * x * x * x + 16/81 * x * x * x * x
    elif example == "Quadratic":
        return  4/3 * x - 4/9 * x * x
    else:
        print("Error: Either provide Linear, Quadratic, Quartic, or Cubic")
        sys.exit()


markers = ['s','o','x','.']


n = np.power(2,4)
h = 1./n
nodesFull = 3 * n + 1

xFull = np.linspace(0,3.,nodesFull)

uMDCM = np.loadtxt("coupling-"+example.lower()+"-approach-1-direchlet.csv")    
uMSCM = np.loadtxt("coupling-"+example.lower()+"-approach-2-direchlet.csv")    
uVHCM = np.loadtxt("coupling-"+example.lower()+"-vhm-direchlet.csv")    

plt.axvline(x=1,c="#536872")
plt.axvline(x=2,c="#536872")

plt.plot(xFull,exactSolution(xFull),label="Exact solution",c="black")
plt.plot(xFull,uMDCM,label=r"MDCM",c="black",marker=markers[0],markevery=4)
plt.plot(xFull,uMSCM,label=r"MSCM",c="black",marker=markers[1],markevery=4)
plt.plot(xFull,uVHCM,label=r"VHCM",c="black",marker=markers[2],markevery=4)
plt.ylabel("Displacement")
       
plt.title("Example with "+example.lower()+" solution with $\delta=1/8$ and $m=2$")
plt.legend()
plt.grid()
plt.xlabel("$x$")

plt.savefig("coupling-"+example.lower()+"-all-direchlet.pdf",bbox_inches='tight')