def setUp(self):
self.grid10 = libst.Grid(0, 10, 10)
self.sol10 = libst.Solver(grid=self.grid10, nvar=1,
time_increment=0.2)
self.ce0 = self.sol10.celm(ielm=0)
self.ce9 = self.sol10.celm(ielm=9)
def setUp(self):
self.grid10 = libst.Grid(0, 10, 10)
self.sol10 = libst.Solver(grid=self.grid10, nvar=1,
time_increment=0.2)
self.sol10.so0.ndarray.fill(-1)
self.sol10.so1.ndarray.fill(-2)
def setUp(self):
self.grid = libst.Grid(0, 10, 10)
self.sol1 = libst.Solver(grid=self.grid, nvar=1, time_increment=0.2)
self.sol2 = libst.Solver(grid=self.grid, nvar=1, time_increment=0.2)
self.ce0s1 = self.sol1.celm(ielm=0)
self.ce0s1p = self.sol1.celm(ielm=0)
self.ce1s1 = self.sol1.celm(ielm=1)
self.ce0s1o = self.sol1.celm(ielm=0, odd_plane=True)
self.ce0s2 = self.sol2.celm(ielm=0)
self.se0s1 = self.sol1.selm(ielm=0)
self.se0s1p = self.sol1.selm(ielm=0)
self.se1s1 = self.sol1.selm(ielm=1)
self.se0s1o = self.sol1.selm(ielm=0, odd_plane=True)
self.se0s2 = self.sol2.selm(ielm=0)
def setUp(self):
self.grid10 = libst.Grid(0, 10, 10)
self.sol10 = libst.Solver(grid=self.grid10, nvar=1, time_increment=0.2)
self.ce0 = self.sol10.celm(ielm=0)
self.ce9 = self.sol10.celm(ielm=9)
# Set trivial solution.
self.sol10.so0.ndarray.fill(1)
self.sol10.so1.ndarray.fill(0)
def setUp(self):
xloc = np.array([0, 1, 3, 10])
self.grid3 = libst.Grid(xloc=xloc)
self.sol3 = libst.Solver(grid=self.grid3, nvar=1, time_increment=0.1)
self.ce0 = self.sol3.celm(ielm=0)
self.ce1 = self.sol3.celm(ielm=1)
self.ce2 = self.sol3.celm(ielm=2)
self.se0 = self.sol3.selm(ielm=0)
self.se1 = self.sol3.selm(ielm=1)
self.se2 = self.sol3.selm(ielm=2)
self.se3 = self.sol3.selm(ielm=3)
def setUp(self):
self.dt = 0.2
self.grid10 = libst.Grid(0, 10, 10)
self.sol10 = libst.Solver(grid=self.grid10, nvar=1,
time_increment=self.dt)
self.se0 = self.sol10.selm(0)
self.se9 = self.sol10.selm(9)
self.se10 = self.sol10.selm(10)
# Set trivial solution.
self.sol10.so0.ndarray.fill(1)
self.sol10.so1.ndarray.fill(0)
def draw():
xloc = np.array([-1, 0, 2, 3.5])
grid = libst.Grid(xloc=xloc)
sol = libst.Solver(grid=grid, nvar=1, time_increment=6/4)
dx = (grid.xmax-grid.xmin)/grid.ncelm
dt = dx
hdt = dt / 2
c = libst.PstCanvas(unit='2cm', padding=0.5)
c.set(linewidth='1pt')
c.set(linecolor='black')
# CE grids.
linewidth = '0.5pt'
for se in sol.selms(odd_plane=False):
c.line((se.x, 0), (se.x, dt), linewidth=linewidth)
c.line((sol.selm(0).x, 0), (sol.selm(grid.ncelm).x, 0),
linewidth=linewidth)
c.line((sol.selm(0).x, hdt), (sol.selm(grid.ncelm).x, hdt),
linewidth=linewidth)
c.line((sol.selm(0).x, dt), (sol.selm(grid.ncelm).x, dt),
linewidth=linewidth)
# x-axis.
sep = 0.05
c.line((sol.selm(0).x, -hdt*1.2), (sol.selm(grid.ncelm).x, -hdt*1.2),
linewidth=linewidth)
c.uput(sep, 'l', (grid.xmin-sep,-hdt*1.2), r'$j$')
c.uput(sep, 'r', (grid.xmax+sep,-hdt*1.2), r'$x$')
for se in sol.selms(odd_plane=False):
c.line((se.x, -hdt*1.2-sep), (se.x, -hdt*1.2+sep))
c.uput(sep, 'd', (se.x,-hdt*1.2-sep), r'$%d$'%se.index)
for se in sol.selms(odd_plane=True):
c.line((se.x, -hdt*1.2-sep/2), (se.x, -hdt*1.2+sep/2))
c.uput(sep, 'd', (se.x,-hdt*1.2-sep), r'$\frac{%d}{2}$'%(se.index*2+1))
# t-axis.
x = grid.xmin - dx*0.6
c.line((x, 0), (x, dt), linewidth=linewidth)
c.uput(sep, 'd', (x, 0-sep), r'$n$')
c.uput(sep, 'u', (x, dt+sep), r'$t$')
c.line((x-sep, 0), (x+sep, 0))
c.uput(sep, 'l', (x-sep, 0), r'$0$')
c.line((x-sep/2, hdt), (x+sep/2, hdt))
c.uput(sep, 'l', (x-sep, hdt), r'$\frac{1}{2}$')
c.line((x-sep, dt), (x+sep, dt))
c.uput(sep, 'l', (x-sep, dt), r'$1$')
# SE and solution propagation.
sep = 0.05
sepx = dx*0.1
sept = dt*0.1
for se in sol.selms(odd_plane=False):
c.selm(se, 0,
sep=sep, linestyle='dotted', dotsep='1pt', linecolor='red')
for se in sol.selms(odd_plane=True):
c.selm(se, hdt,
sep=sep, linestyle='dotted', dotsep='1pt', linecolor='blue')
return c
def draw():
xloc = np.array([-1, 0, 2, 3.5])
grid = libst.Grid(xloc=xloc)
sol = libst.Solver(grid=grid, nvar=1, time_increment=1)
dt = sol.dt
hdt = dt / 2
qdt = hdt / 2
odt = qdt / 2
c = libst.PstCanvas(unit='5cm', padding=[0.75, 0.25, 0.7, 0.25])
c.set(linewidth='1pt')
c.set(linecolor='black')
ce = sol.celm(ielm=1, odd_plane=False)
linewidth = '0.5pt'
# SEs.
sexn = ce.selm_xn
c.line((sexn.x, 0), (sexn.x, hdt), linewidth=linewidth, linecolor='red')
c.line((sexn.x, 0), (sexn.xpos, 0), linewidth=linewidth, linecolor='red')
c.dots((sexn.x, 0), dotstyle='o')
c.uput(0.05, 'dl', (sexn.x, 0), r'$x_{j-\frac{1}{2}}$')
c.dots((sexn.xctr, 0), dotstyle='triangle')
c.uput(0.05, 'u', (sexn.xctr, 0), r'$x^s_{j-\frac{1}{2}}$')
sexp = ce.selm_xp
c.line((sexp.x, 0), (sexp.x, hdt), linewidth=linewidth, linecolor='blue')
c.line((sexp.xneg, 0), (sexp.x, 0), linewidth=linewidth, linecolor='blue')
c.dots((sexp.x, 0), dotstyle='o')
c.uput(0.05, 'dr', (sexp.x, 0), r'$x_{j+\frac{1}{2}}$')
c.dots((sexp.xctr, 0), dotstyle='triangle')
c.uput(0.05, 'u', (sexp.xctr, 0), r'$x^s_{j+\frac{1}{2}}$')
c.dots((sexn.xpos, 0), dotstyle='square')
assert sexn.xpos == sexp.xneg
c.uput(0.05, 'u', (sexn.xpos, 0),
r'$x^+_{j-\frac{1}{2}} = x^-_{j+\frac{1}{2}}$')
setp = ce.selm_tp
c.line((setp.xneg, hdt), (setp.x, hdt),
linewidth=linewidth,
linecolor='orange')
c.line((setp.x, hdt), (setp.xpos, hdt),
linewidth=linewidth,
linecolor='orange')
c.dots((setp.x, hdt), dotstyle='o')
c.dots((setp.xctr, setp.hdt), dotstyle='triangle')
c.uput(0.05, 'd', (setp.x, hdt), r'$x_j=x^s_j$')
# Fluxes.
vlen = hdt / 6
sep = 0.015
# \Delta x^+_{j-\frac{1}{2}}
c.line(((sexn.x + sexn.xpos) / 2, 0), ((sexn.x + sexn.xpos) / 2, -vlen),
arrows='->',
linecolor='red')
c.uput(
0, 'd', ((sexn.x + sexn.xpos) / 2, -vlen),
r'{\color{red}$(\mathbf{h}^*)^n_{j-\frac{1}{2},+}'
r'\cdot(0, -\Delta x^+_{j-\frac{1}{2}})$}')
# \Delta x^-_{j+\frac{1}{2}}
c.line(((sexp.xneg + sexp.x) / 2, 0), ((sexp.xneg + sexp.x) / 2, -vlen),
arrows='->',
linecolor='blue')
c.uput(
0, 'd', ((sexp.xneg + sexp.x) / 2, -vlen),
r'{\color{blue}$(\mathbf{h}^*)^n_{j+\frac{1}{2},-}'
r'\cdot(0, -\Delta x^-_{j+\frac{1}{2}})$}')
# \Delta x_j
c.line((setp.xctr, hdt + sep), (setp.xctr, hdt + 2 * vlen),
arrows='->',
linecolor='orange')
c.uput(
0, 'u', (setp.xctr, hdt + 2 * vlen),
r'{\color{orange}$\mathbf{h}^{n+\frac{1}{2}}_{j}'
r'\cdot(0, \Delta x_j)$}')
# \Delta t^n_{j-\frac{1}{2}}
c.line((sexn.x, qdt), (sexn.x - vlen, qdt), arrows='->', linecolor='red')
c.uput(
0, 'ul', (sexn.x - vlen, qdt),
r'{\color{red}$(\mathbf{h}^*)^{n,+}_{j-\frac{1}{2}}'
r'\cdot(-\frac{\Delta t}{2}, 0)$}')
# \Delta t^n_{j+\frac{1}{2}}
c.line((sexp.x, qdt), (sexp.x + vlen, qdt), arrows='->', linecolor='blue')
c.uput(
0, 'ur', (sexp.x + vlen, qdt),
r'{\color{blue}$(\mathbf{h}^*)^{n,+}_{j+\frac{1}{2}}'
r'\cdot(\frac{\Delta t}{2}, 0)$}')
return c
def _build_solver(resolution):
# Build grid.
xcrd = np.arange(resolution+1) / resolution
xcrd *= 2 * np.pi
grid = libst.Grid(xcrd)
dx = (grid.xmax - grid.xmin) / grid.ncelm
# Build solver.
time_stop = 2*np.pi
cfl_max = 1.0
dt_max = dx * cfl_max
nstep = int(np.ceil(time_stop / dt_max))
dt = time_stop / nstep
svr = libst.Solver(grid=grid, time_increment=dt, nvar=1)
# Customize to linear wave solver.
def xn(se, iv):
displacement = 0.5 * (se.x + se.xneg) - se.xctr
return se.dxneg * (se.get_so0(iv) + displacement * se.get_so1(iv))
svr.kernel.xn_calc = xn
def xp(se, iv):
displacement = 0.5 * (se.x + se.xpos) - se.xctr
return se.dxpos * (se.get_so0(iv) + displacement * se.get_so1(iv))
svr.kernel.xp_calc = xp
def tn(se, iv):
displacement = se.x - se.xctr
ret = se.get_so0(iv) # f(u)
ret += displacement * se.get_so1(iv) # displacement in x; f_u == 1
ret += se.qdt * se.get_so1(iv) # displacement in t
return se.hdt * ret
svr.kernel.tn_calc = tn
def tp(se, iv):
displacement = se.x - se.xctr
ret = se.get_so0(iv) # f(u)
ret += displacement * se.get_so1(iv) # displacement in x; f_u == 1
ret -= se.qdt * se.get_so1(iv) # displacement in t
return se.hdt * ret
svr.kernel.tp_calc = tp
def so0p(se, iv):
ret = se.get_so0(iv)
ret += (se.x-se.xctr) * se.get_so1(iv) # displacement in x
ret -= se.hdt * se.get_so1(iv) # displacement in t
return ret
svr.kernel.so0p_calc = so0p
def cfl(se):
hdx = min(se.dxneg, se.dxpos)
se.set_cfl(se.hdt / hdx)
svr.kernel.cfl_updater = cfl
# Initialize.
svr.set_so0(0, np.sin(xcrd))
svr.set_so1(0, np.cos(xcrd))
svr.setup_march()
return nstep, xcrd, svr
def draw():
grid = libst.Grid(0, 6, 4)
sol = libst.Solver(grid=grid, nvar=1, time_increment=6 / 4)
dx = (grid.xmax - grid.xmin) / grid.ncelm
dt = dx
hdt = dt / 2
c = libst.PstCanvas(unit='2cm', padding=0.5)
c.set(linewidth='1pt')
c.set(linecolor='black')
# CE grids.
linewidth = '0.5pt'
for se in sol.selms(odd_plane=False):
c.line((se.x, 0), (se.x, dt), linewidth=linewidth)
c.line((sol.selm(0).x, 0), (sol.selm(grid.ncelm).x, 0),
linewidth=linewidth)
c.line((sol.selm(0).x, hdt), (sol.selm(grid.ncelm).x, hdt),
linewidth=linewidth)
c.line((sol.selm(0).x, dt), (sol.selm(grid.ncelm).x, dt),
linewidth=linewidth)
for se in sol.selms(odd_plane=False):
c.line((se.x, dt), (se.x, dt * 1.65),
arrows='->',
linewidth=linewidth,
linestyle='dashed')
c.line((sol.selm(0).x, dt * 1.5), (sol.selm(grid.ncelm).x, dt * 1.5),
linewidth=linewidth,
linestyle='dashed')
# x-axis.
sep = 0.05
c.line((sol.selm(0).x, -hdt * 1.2), (sol.selm(grid.ncelm).x, -hdt * 1.2),
linewidth=linewidth)
c.uput(sep, 'l', (grid.xmin - sep, -hdt * 1.2), r'$j$')
c.uput(sep, 'r', (grid.xmax + sep, -hdt * 1.2), r'$x$')
for se in sol.selms(odd_plane=False):
c.line((se.x, -hdt * 1.2 - sep), (se.x, -hdt * 1.2 + sep))
c.uput(sep, 'd', (se.x, -hdt * 1.2 - sep), r'$%d$' % se.index)
for se in sol.selms(odd_plane=True):
c.line((se.x, -hdt * 1.2 - sep / 2), (se.x, -hdt * 1.2 + sep / 2))
c.uput(sep, 'd', (se.x, -hdt * 1.2 - sep),
r'$\frac{%d}{2}$' % (se.index * 2 + 1))
# t-axis.
x = grid.xmin - dx * 0.6
c.line((x, 0), (x, dt), linewidth=linewidth)
c.uput(sep, 'd', (x, 0 - sep), r'$n$')
c.uput(sep, 'u', (x, dt + sep), r'$t$')
c.line((x - sep, 0), (x + sep, 0))
c.uput(sep, 'l', (x - sep, 0), r'$0$')
c.line((x - sep / 2, hdt), (x + sep / 2, hdt))
c.uput(sep, 'l', (x - sep, hdt), r'$\frac{1}{2}$')
c.line((x - sep, dt), (x + sep, dt))
c.uput(sep, 'l', (x - sep, dt), r'$1$')
# SE and solution propagation.
sep = 0.05
sepx = dx * 0.1
sept = dt * 0.1
for se in sol.selms(odd_plane=False):
c.selm(se,
0,
sep=sep,
linestyle='dotted',
dotsep='1pt',
linecolor='red')
if se.index != grid.ncelm: # left to right.
c.line((se.x + sepx, 0 + sept), (se.xpos - sepx, hdt - sept),
arrows='->',
linecolor='red')
if se.index != 0: # right to left.
c.line((se.x - sepx, 0 + sept), (se.xneg + sepx, hdt - sept),
arrows='->',
linecolor='red')
for se in sol.selms(odd_plane=True):
c.selm(se,
hdt,
sep=sep,
linestyle='dotted',
dotsep='1pt',
linecolor='blue')
if se.index != grid.ncelm - 1: # left to right.
c.line((se.x + sepx, hdt + sept), (se.xpos - sepx, dt - sept),
arrows='->',
linecolor='blue')
if se.index != 0: # right to left.
c.line((se.x - sepx, hdt + sept), (se.xneg + sepx, dt - sept),
arrows='->',
linecolor='blue')
for se in sol.selms(odd_plane=False):
c.selm(se,
dt,
sep=sep,
linestyle='dotted',
dotsep='1pt',
linecolor='orange')
return c