Commit 4671111d authored by Davide Torlo's avatar Davide Torlo
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updated arxiv link

parent de837464
%% Cell type:markdown id: tags:
 
# Relaxation Deferred Correction notebook
 
%% Cell type:markdown id: tags:
 
This notebook is an extension of the original [Relaxation Runge--Kutta Notebook](https://github.com/ketch/RRK_rr) provided by D. Ketcheson and H. Ranocha on the work of H. Ranocha, M. Sayyari, L. Dalcin, M. Parsani and D. I. Ketcheson on [Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations](https://doi.org/10.1137/19M1263480).
 
Here we use the Deferred Correction method as a Runge--Kutta method. The implementation of the Deferred Correction method as a Runge--Kutta method is included in [DeC.py](DeC.py) and explained in details in the work [Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes ](https://arxiv.org/search/?searchtype=author&query=Torlo%2C+D) by R. Abgrall, E. Le Mélédo, P. Öffner and D. Torlo.
Here we use the Deferred Correction method as a Runge--Kutta method. The implementation of the Deferred Correction method as a Runge--Kutta method is included in [DeC.py](DeC.py) and explained in details in the work [Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes ](https://arxiv.org/abs/2106.05005) by R. Abgrall, E. Le Mélédo, P. Öffner and D. Torlo.
 
%% Cell type:markdown id: tags:
 
# Setup
 
Note that this notebook was developed with NodePy version 0.7.
 
%% Cell type:code id: tags:
 
``` python
import numpy as np
import matplotlib.pyplot as plt
from nodepy import rk, stability_function
from DeC import *
 
rk4 = rk.loadRKM('RK44').__num__()
rk4x2 = rk4*rk4
ssp2 = rk.loadRKM('SSP22').__num__()
ssp3 = rk.loadRKM('SSP33').__num__()
ssp104 = rk.loadRKM('SSP104').__num__()
merson4 = rk.loadRKM('Merson43').__num__()
bs5 = rk.loadRKM('BS5').__num__()
 
decEqRKs =[]
decGLBRKs =[]
for order in range(2,10):
A,b,c=compute_RK_from_DeC(order-1,order,"equispaced") # subtimesteps, iterations, nodetype{"equispaced","gaussLobatto"}
decEqRKs.append(rk.ExplicitRungeKuttaMethod(A,b))
decEqRKs[order-2].name="DeC%dEq"%(order)
A,b,c=compute_RK_from_DeC(np.int(np.ceil(order/2.)),order,"gaussLobatto") # subtimesteps, iterations, nodetype{"equispaced","gaussLobatto"}
decGLBRKs.append(rk.ExplicitRungeKuttaMethod(A,b))
decGLBRKs[order-2].name="DeC%dGLB"%(order)
 
dec3 = decEqRKs[1]
 
dec4equi = decEqRKs[2]
 
dec4galo = decGLBRKs[2]
 
 
 
#short_methods = [ssp2, ssp3, rk4, bs5, dec3]
short_methods = [ ssp2, ssp3, rk4, dec3, dec4equi, dec4galo]
#short_methods = [ dec3, dec4equi, dec4galo]
short_method_labels = ["SSPRK(2,2)=DeC(2)","SSPRK(3,3)", "RK(4,4)", "Dec3", "Dec4equi", "Dec4GaLo"]
#short_method_labels = ["Dec3", "Dec4equi", "Dec4GaLo"]
#short_method_labels = ["SSPRK(2,2)=DeC(2)", "SSPRK(3,3)", "RK(4,4)", "Dec3", "Dec4equi"]
import os
if not os.path.isdir('./figures'):
os.mkdir('./figures')
```
 
%% Cell type:code id: tags:
 
``` python
font = {'family' : 'serif',
'weight' : 'normal',
'size' : 25}
 
import matplotlib
matplotlib.rc('font', **font)
```
 
%% Cell type:code id: tags:
 
``` python
# line cycler adapted to colourblind people for only a few 10
from cycler import cycler
colors = ['#E69F00', '#56B4E9', '#009E73', '#0072B2', '#D55E00', '#CC79A7', '#F0E442']
linestyles = ['-', '--', '-.', ':', "-", "--", "-."]
markers = ['o','D','X','s','v']
colourblind_cycler = (cycler(color=colors) +
cycler(linestyle=linestyles))
plt.rc("axes", prop_cycle=colourblind_cycler)
 
plt.rc("text", usetex=True)
plt.rc("text.latex",
preamble=r"\usepackage{newpxtext}\usepackage{newpxmath}\usepackage{commath}\usepackage{mathtools}")
#plt.rc("font", family="serif", size=14.)
#plt.rc("savefig", dpi=200)
plt.rc("legend", fontsize="medium", fancybox=True, framealpha=0.5)
```
 
%% Cell type:code id: tags:
 
``` python
# line cycler adapted to colourblind people for all
from cycler import cycler
colors = ['#E69F00', '#56B4E9', '#009E73', '#0072B2', '#D55E00', '#CC79A7', '#F0E442','#F0E442']
linestyles = ['-', '--', '-.', ':', "-", "--", "-.", "--"]
markers = ['o','D','X','s','v', 'p','1','2','3']
colourblind_cycler = (cycler(color=colors) +
cycler(linestyle=linestyles))
plt.rc("axes", prop_cycle=colourblind_cycler)
 
plt.rc("text", usetex=True)
plt.rc("text.latex",
preamble=r"\usepackage{newpxtext}\usepackage{newpxmath}\usepackage{commath}\usepackage{mathtools}")
#plt.rc("font", family="serif", size=14.)
#plt.rc("savefig", dpi=200)
plt.rc("legend", fontsize="medium", fancybox=True, framealpha=0.5)
```
 
%% Cell type:code id: tags:
 
``` python
def RRK(rkm, dt, f, w0=[1.,0], t_final=1., relaxation=True,
rescale_step=True, debug=False, gammatol=0.1, print_gamma=False,
one_step=False, dissip_factor=1.0):
"""
Relaxation Runge-Kutta method implementation.
 
Options:
 
rkm: Base Runge-Kutta method, in Nodepy format
dt: time step size
f: RHS of ODE system
w0: Initial data
t_final: final solution time
relaxation: if True, use relaxation method. Otherwise, use vanilla RK method.
rescale_step: if True, new time step is t_n + \gamma dt
debug: output some additional diagnostics
gammatol: Fail if abs(1-gamma) exceeds this value
 
"""
w = np.array(w0)
t = 0
# We pre-allocate extra space because if rescale_step==True then
# we don't know exactly how many steps we will take.
ww = np.zeros([len(w0),int((t_final-t)/dt*2.5)+10000])
ww[:,0] = w.copy()
tt = [t]
ii = 0
s = len(rkm)
b = rkm.b
y = np.zeros((s,len(w0)))
max_gammam1 = 0.
gams = []
 
while t < t_final:
if t + dt >= t_final:
dt = t_final - t # Hit final time exactly
 
for i in range(s):
y[i,:] = w.copy()
for j in range(i):
y[i,:] += rkm.A[i,j]*dt*f(y[j,:])
 
F = np.array([f(y[i,:]) for i in range(s)])
 
if relaxation:
numer = 2*sum(b[i]*rkm.A[i,j]*np.dot(F[i],F[j]) \
for i in range(s) for j in range(s))
denom = sum(b[i]*b[j]*np.dot(F[i],F[j]) for i in range(s) for j in range(s))
if denom != 0:
gam = numer/denom
else:
gam = 1.
else: # Use standard RK method
gam = 1.
 
if print_gamma:
print(gam)
 
if np.abs(gam-1.) > gammatol:
print(gam)
raise Exception("The time step is probably too large.")
 
w = w + dissip_factor*gam*dt*sum([b[j]*F[j] for j in range(s)])
if (t+dt < t_final) and rescale_step:
t += dissip_factor*gam*dt
else:
t += dt
ii += 1
tt.append(t)
ww[:,ii] = w.copy()
if debug:
gm1 = np.abs(1.-gam)
max_gammam1 = max(max_gammam1,gm1)
gams.append(gam)
 
if one_step:
return w, gam
 
if debug:
print(max_gammam1)
return tt, ww[:, :ii+1], np.array(gams)
else:
return tt, ww[:,:ii+1]
```
 
%% Cell type:markdown id: tags:
 
# Introductory example (Ranocha's problem)
 
%% Cell type:code id: tags:
 
``` python
def f_prob1(u):
E = u[0]**2 + u[1]**2
return np.array([-u[1],u[0]])/E
```
 
%% Cell type:code id: tags:
 
``` python
plt.rc("font", size=20)
```
 
%% Cell type:code id: tags:
 
``` python
#Here, I have to run it again on an linux distribution! On my mac is need to much memory
u0 = np.array([1.,0.])
dt = 0.1
t_final = 10.
 
for i, method in enumerate(short_methods):
tt, uu = RRK(method, dt, f_prob1, w0=u0, t_final=t_final,
relaxation=0, debug=False)
plt.semilogy(tt[1:],uu[0,1:]**2+uu[1,1:]**2-1., lw=3, label=short_method_labels[i]);
 
 
plt.xlabel('$t$');
plt.ylabel('$\|u(t)\|^2-\|u(0)\|^2$')
plt.tight_layout()
plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left')
plt.savefig('./figures/problem1_energy_RK.pdf')
plt.show()
```
 
%%%% Output: display_data
 
![](data:image/png;base64,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)
 
%% Cell type:code id: tags:
 
``` python
u0 = np.array([1.,0.])
dt = 0.1
 
for method in short_methods:
tt, uu = RRK(method, dt, f_prob1, w0=u0, t_final=10.,
relaxation=1, debug=False)
plt.plot(tt,uu[0,:]**2+uu[1,:]**2-1.,lw=2.5);
 
 
plt.xlabel('$t$');
plt.ylabel('$\|u(t)\|^2-\|u(0)\|^2$')
plt.tight_layout()
plt.savefig('./figures/problem1_energy_RRK.pdf')
```
 
%%%% Output: display_data
 
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)
 
%% Cell type:code id: tags:
 
``` python
plt.rc("font", size=16)
 
#names = ['SSP(2,2)', 'SSP(3,3)', 'RK(4,4)', 'BS(8,5)', 'dec_3']
dts = np.array([0.9, 0.5, 0.2, 0.1, 0.03, 0.02, 0.011, 0.005])
dts = np.logspace(-2.5,0.,11)
u0 = np.array([1.,0.])
t_final = 10.
 
fig=plt.figure(figsize=(6,6))
ax = plt.subplot(111)
lines = []
 
for j, rkm in enumerate(short_methods):
for relax in (False, True):
sols = []
for dt in dts:
 
tt, uu = RRK(rkm, dt,f_prob1, w0=u0, t_final=t_final, relaxation=relax, rescale_step=True, gammatol=1.0)
sols.append(uu[0,-1])
 
errors = []
ref = np.cos(t_final)
for i in range(len(sols)):
errors.append(abs(ref-sols[i]))
 
if relax:
plt.loglog(dts, errors,linestyle='dashed',color=colors[j],marker=markers[j],label=None);
else:
lines.append(plt.loglog(dts, errors,linestyle='-',color=colors[j],
marker=markers[j],label=short_method_labels[j])[0])
 
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width * 0.8, box.height])
 
# Put a legend to the right of the current axis
ax.legend(lines,short_method_labels,loc='center left', bbox_to_anchor=(1, 0.5))
 
plt.xlabel('$\Delta t$')
plt.ylabel('Error');
plt.ylim([1.e-14, 10]);
 
plt.plot([1e-2,4e-2],[3.e-4, 4**2*3.e-4],'-ok',alpha=0.5)
plt.plot([1e-2,4e-2],[5.e-6, 4**3*5.e-6],'-ok',alpha=0.5)
plt.plot([1e-2,4e-2],[3.e-10, 4**4*3.e-10],'-ok',alpha=0.5)
#plt.plot([1e-2,4.e-2],[5.e-13, 4**5*5.e-13],'-ok',alpha=0.5)
#plt.plot([4e-2,16e-2],[5.e-13, 4**6*5.e-13],'-ok',alpha=0.5)
 
plt.text(1.e-2,3.e-4,'$p=2$',verticalalignment='bottom',horizontalalignment='right')
plt.text(1.e-2,5.e-6,'$p=3$',verticalalignment='top',horizontalalignment='left')
plt.text(3.e-2,6.e-9,'$p=4$',verticalalignment='bottom',horizontalalignment='left')
#plt.text(1.e-2,5.e-13,'$p=5$',verticalalignment='bottom',horizontalalignment='right')
#plt.text(4.e-2,5.e-13,'$p=6$',verticalalignment='top',horizontalalignment='left')
 
plt.tight_layout()
plt.savefig('./figures/prob1_convergence.pdf', bbox_inches="tight")
```
 
%%%% Output: display_data
 
![](data:image/png;base64,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)
 
%% Cell type:code id: tags:
 
``` python
plt.rc("font", size=16)
 
names = ['DeC%dGL'%(order) for order in range(2,10)]
dts = np.logspace(-2.5,0.,6)
u0 = np.array([1.,0.])
t_final = 10.
 
fig=plt.figure(figsize=(6,6))
ax = plt.subplot(111)
lines = []
 
for j, rkm in enumerate(decGLBRKs[:5]):
for relax in (False, True):
sols = []
for dt in dts:
 
tt, uu = RRK(rkm, dt,f_prob1, w0=u0, t_final=t_final, relaxation=relax, rescale_step=True, gammatol=1.0)
sols.append(uu[0,-1])
 
errors = []
ref = np.cos(t_final)
for i in range(len(sols)):
errors.append(abs(ref-sols[i]))
 
if relax:
plt.loglog(dts, errors,linestyle='dashed',color=colors[j],marker=markers[j],label=None);
else:
lines.append(plt.loglog(dts, errors,linestyle='-',color=colors[j],
marker=markers[j],label=names[j])[0])
 
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width * 0.8, box.height])
 
# Put a legend to the right of the current axis
ax.legend(lines,names,loc='center left', bbox_to_anchor=(1, 0.5))
 
plt.xlabel('$\Delta t$')
plt.ylabel('Error');
plt.ylim([1.e-14, 10]);
 
plt.plot([1e-2,4e-2],[3.e-4, 4**2*3.e-4],'-ok',alpha=0.5)
plt.plot([1e-2,4e-2],[5.e-6, 4**3*5.e-6],'-ok',alpha=0.5)
plt.plot([1e-2,4e-2],[3.e-10, 4**4*3.e-10],'-ok',alpha=0.5)
plt.plot([1e-2,4.e-2],[5.e-13, 4**5*5.e-13],'-ok',alpha=0.5)
plt.plot([4e-2,16e-2],[5.e-13, 4**6*5.e-13],'-ok',alpha=0.5)
 
plt.text(1.e-2,3.e-4,'$p=2$',verticalalignment='bottom',horizontalalignment='right')
plt.text(1.e-2,5.e-6,'$p=3$',verticalalignment='top',horizontalalignment='left')
plt.text(3.e-2,6.e-9,'$p=4$',verticalalignment='bottom',horizontalalignment='left')
plt.text(1.e-2,5.e-13,'$p=5$',verticalalignment='bottom',horizontalalignment='right')
plt.text(4.e-2,5.e-13,'$p=6$',verticalalignment='top',horizontalalignment='left')
 
plt.tight_layout()
plt.savefig('./figures/prob1_DeCGLconvergence.pdf', bbox_inches="tight")
```
 
%%%% Output: display_data
 
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)
 
%% Cell type:code id: tags:
 
``` python
dt = 0.5
order = 7
tt, uu = RRK(decEqRKs[order-2], dt, f_prob1, w0=u0, t_final=1000.,
relaxation=0, debug=False)
plt.plot(uu[0,:],uu[1,:],color='#56B4E9')
tt, uu = RRK(decEqRKs[order-2], dt, f_prob1, w0=u0, t_final=1000.,
relaxation=1, debug=False)
plt.plot(uu[0,:],uu[1,:],'-k')
plt.plot(uu[0,0],uu[1,0],'ok')
plt.axis('equal');
```
 
%%%% Output: display_data
 
![](data:image/png;base64,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)
 
%% Cell type:code id: tags:
 
``` python
def makeplot(dt):
plt.figure(figsize=(8,8))
#dt = 1.5
unp1g, gam = RRK(dec3, dt, f_prob1, w0=u0, t_final=1000.,
relaxation=1, debug=False,one_step=True,gammatol=1.0)
du = (unp1g-u0)/gam
unp1 = u0+du
plt.plot([u0[0],unp1g[0]],[u0[1],unp1g[1]],'o-',color='#56B4E9')
plt.plot([u0[0],unp1[0]],[u0[1],unp1[1]],color='r')
 
t = np.linspace(0,2*np.pi,1000)
plt.plot(np.cos(t),np.sin(t),'-k',lw=0.5)
plt.plot(np.cos(dt),np.sin(dt),'ok')
plt.plot(np.cos(gam*dt),np.sin(gam*dt),'ob')
unorm = np.sqrt(unp1[0]**2+unp1[1]**2)
plt.plot(unp1[0]/unorm,unp1[1]/unorm,'og')
plt.axis('equal');
 
makeplot(1.5)
```
 
%%%% Output: display_data
 
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)
 
%% Cell type:code id: tags:
 
``` python
from ipywidgets import widgets, interact
 
interact(makeplot,dt=widgets.FloatSlider(min=0.1,max=1.5));
```
 
%%%% Output: display_data
 
 
%% Cell type:markdown id: tags: