def test_fmm():
for dims in [2, 3]:
for kernel in [0, 5]:
sources = np.random.randn(4000, dims)
dipvec = np.random.randn(4000, dims)
fmm_part("pg", iprec=1, kernel=kernel, sources=sources,
dip_charge=1, dipvec=dipvec,
debug=True)
targ_def = (slice(-3, 3, 20j),)
targets = np.mgrid[targ_def*dims]
targets = targets.reshape(dims, -1)
fmm_part("PG", iprec=1, kernel=kernel,
sources=sources, mop_charge=1, target=targets.T,
debug=True)
def main():
sources = np.random.randn(40, 2)
targets = np.mgrid[-7:7:400j, -7:7:400j]
pot_shape = targets.shape[1:]
targets = targets.reshape(2, -1)
pot, grad = fmm_part("PG",
iprec=2,
kernel=HelmholtzKernel(5),
sources=sources,
mop_charge=1,
target=targets.T)
pot = pot.reshape(pot_shape)
try:
import matplotlib.pyplot as pt
except ImportError:
print("matplotlib not installed, not plotting")
else:
pt.imshow(pot.real)
outfile = "helmholtz-potential.png"
pt.savefig(outfile)
print("wrote '%s'" % outfile)
def cauchy_fmm(density):
# This splits the Cauchy kernel into the sum of two directional source
# derivatives of the Laplace kernel. See Section 7.5 of Kress, Linear
# Integral Equations.
dn_part = pyfmmlib.fmm_part("P",
iprec=5,
kernel=pyfmmlib.LaplaceKernel(),
sources=sources,
target=targets,
dip_charge=weight * density,
dipvec=normals)
dt_part = pyfmmlib.fmm_part("P",
iprec=5,
kernel=pyfmmlib.LaplaceKernel(),
sources=sources,
target=targets,
dip_charge=weight * density,
dipvec=tangents)
return dn_part - 1j * dt_part
def test_fmm():
for dims in [2, 3]:
for kernel in [0, 5]:
sources = np.random.randn(4000, dims)
dipvec = np.random.randn(4000, dims)
fmm_part("pg",
iprec=1,
kernel=kernel,
sources=sources,
dip_charge=1,
dipvec=dipvec,
debug=True)
targ_def = (slice(-3, 3, 20j), )
targets = np.mgrid[targ_def * dims]
targets = targets.reshape(dims, -1)
fmm_part("PG",
iprec=1,
kernel=kernel,
sources=sources,
mop_charge=1,
target=targets.T,
debug=True)
from __future__ import division
from pyfmmlib import fmm_part, HelmholtzKernel
import numpy as np
import matplotlib.pyplot as pt
sources = np.random.randn(40, 2)
targets = np.mgrid[-7:7:400j, -7:7:400j]
pot_shape = targets.shape[1:]
targets = targets.reshape(2, -1)
pot, grad = fmm_part("PG", iprec=2, kernel=HelmholtzKernel(5),
sources=sources, mop_charge=1, target=targets.T)
pot = pot.reshape(pot_shape)
pt.imshow(pot.real)
pt.show()
def solve_phi(Swimmers, P, i, outerCorr=0):
"""Solves the boundary integral equation using a Kutta condition and the
Fast Multipole Method.
Args:
Swimmers: List of Swimmer objects being simulated.
RHO: Fluid density.
DEL_T: Time step length.
i: Time step number.
"""
for Swim in Swimmers:
if (outerCorr <= 1):
# mu_past used in differencing for pressure
Swim.Body.mu_past[1:4, :] = Swim.Body.mu_past[0:3, :]
Swim.Body.mu_past[0, :] = Swim.Body.mu
(sigma_all, mu_w_all, a_b, a_e, b_e) = influence_matrices(Swimmers, i)
for SwimI in Swimmers:
a_e[:, SwimI.i_b] = -b_e[:, SwimI.i_e]
a_e[:, SwimI.i_b + SwimI.Body.N - 1] = b_e[:, SwimI.i_e]
a = a_b + a_e
# Prepare FMM inputs
b_places = np.vstack(
(Swimmers[0].Body.AF.x_mid[0, :], Swimmers[0].Body.AF.z_mid[0, :]))
target = np.vstack((Swimmers[0].Body.AF.x_col, Swimmers[0].Body.AF.z_col))
lpanel = panel_vectors(Swimmers[0].Body.AF.x, Swimmers[0].Body.AF.z)[-1]
if (i > 0):
w_places = np.vstack(
(0.5 * (Swimmers[0].Wake.x[1:i + 1] + Swimmers[0].Wake.x[:i]),
0.5 * (Swimmers[0].Wake.z[1:i + 1] + Swimmers[0].Wake.z[:i])))
(nx, nz, lwpanel) = panel_vectors(Swimmers[0].Wake.x[:i + 1],
Swimmers[0].Wake.z[:i + 1])[2:]
n_w = np.vstack((nx, nz))
# Get right-hand side
b_body = np.real(
fmm_part("P",
iprec=5,
kernel=0,
sources=b_places.T,
target=target.T,
mop_charge=sigma_all * lpanel)) / 2. / np.pi
if i == 0:
b = -b_body
else:
b_wake = np.real(
fmm_part("P",
iprec=5,
kernel=0,
sources=w_places.T,
target=target.T,
dipvec=n_w.T,
dip_charge=mu_w_all * lwpanel)) / 2. / np.pi
b = -b_body - b_wake
# Solve for bodies' doublet strengths using explicit Kutta
mu_b_all = np.linalg.solve(a, b)
for Swim in Swimmers:
Swim.Body.pressure(P, i)
Swim.mu_guess = np.empty(2) # [0] is current guess, [1] is previous
Swim.delta_p = np.empty(2) # [0] is current delta_p, [1] is previous
Swim.Body.mu[:] = mu_b_all[Swim.i_b:Swim.i_b + Swim.Body.N]
Swim.mu_guess[0] = Swim.Body.mu[-1] - Swim.Body.mu[0]
Swim.Edge.mu = Swim.mu_guess[0]
Swim.Edge.gamma[0] = -Swim.Edge.mu
Swim.Edge.gamma[1] = Swim.Edge.mu
# Get gamma of body panels for use in wake rollup
Swim.Body.gamma[0] = -Swim.Body.mu[0]
Swim.Body.gamma[1:-1] = Swim.Body.mu[:-1] - Swim.Body.mu[1:]
Swim.Body.gamma[-1] = Swim.Body.mu[-1]
def wake_rollup(Swimmers, DEL_T, i, P):
"""Performs wake rollup on the swimmers' wake panels.
Args:
Swimmers: List of Swimmer objects being simulated.
DEL_T: Time step length.
i: Time step number.
"""
if (P['SW_ROLLUP']):
# Wake panels initialize when i==1
if i == 0:
pass
else:
NT = i # Number of targets (wake panel points that are rolling up)
for SwimT in Swimmers:
SwimT.Wake.vx = np.zeros(NT)
SwimT.Wake.vz = np.zeros(NT)
wake_x_midT = 0.5 * (SwimT.Wake.x[1:i + 1] + SwimT.Wake.x[:i])
wake_z_midT = 0.5 * (SwimT.Wake.z[1:i + 1] + SwimT.Wake.z[:i])
target = np.vstack((wake_x_midT, wake_z_midT))
for SwimI in Swimmers:
wake_x_midI = 0.5 * (SwimI.Wake.x[1:i + 1] +
SwimI.Wake.x[:i])
wake_z_midI = 0.5 * (SwimI.Wake.z[1:i + 1] +
SwimI.Wake.z[:i])
edge_x_mid = 0.5 * (SwimI.Edge.x[1] + SwimI.Edge.x[0])
edge_z_mid = 0.5 * (SwimI.Edge.z[1] + SwimI.Edge.z[0])
ed_places = np.vstack((edge_x_mid, edge_z_mid))
bd_places = np.vstack(
(SwimT.Body.AF.x_col, SwimT.Body.AF.z_col))
bs_places = np.vstack(
(SwimT.Body.AF.x_mid[0, :], SwimT.Body.AF.z_mid[0, :]))
wd_places = np.vstack((wake_x_midI, wake_z_midI))
(nx_b, nz_b,
lbpanel) = panel_vectors(SwimI.Body.AF.x,
SwimI.Body.AF.z)[2:]
(nx_e, nz_e,
lepanel) = panel_vectors(SwimI.Edge.x, SwimI.Edge.z)[2:]
(nx_w, nz_w,
lwpanel) = panel_vectors(SwimI.Wake.x[:i + 1],
SwimI.Wake.z[:i + 1])[2:]
n_b = np.vstack((nx_b, nz_b))
n_e = np.vstack((nx_e, nz_e))
n_w = np.vstack((nx_w, nz_w))
# Body source influence on wake velocity
u_bs = np.real(
fmm_part(
"G",
iprec=5,
kernel=0,
sources=bs_places.T,
target=target.T,
mop_charge=SwimI.Body.sigma * lbpanel)) / np.pi
SwimT.Wake.vx += 2. * u_bs[:, 0]
SwimT.Wake.vz += -2. * u_bs[:, 1]
# Body doublet influence on wake velocity
u_bd = np.real(
fmm_part("G",
iprec=5,
kernel=0,
sources=bd_places.T,
target=target.T,
dipvec=n_b.T,
dip_charge=SwimI.Body.mu * lbpanel)) / np.pi
SwimT.Wake.vx += 2. * u_bd[:, 0]
SwimT.Wake.vz += -2. * u_bd[:, 1]
# TE panel influence on wake velocity
u_te = np.real(
fmm_part("G",
iprec=5,
kernel=0,
sources=ed_places.T,
target=target.T,
dipvec=n_e.T,
dip_charge=SwimI.Edge.mu * lepanel)) / np.pi
SwimT.Wake.vx += 2. * u_te[:, 0]
SwimT.Wake.vz += -2. * u_te[:, 1]
# Wake double influence on wake velocity
u_w = np.real(
fmm_part("G",
iprec=5,
kernel=0,
sources=wd_places.T,
target=target.T,
dipvec=n_w.T,
dip_charge=SwimI.Wake.mu[1:i + 1] *
lwpanel)) / np.pi
u_w = np.nan_to_num(u_w)
SwimT.Wake.vx += 2. * u_w[:, 0]
SwimT.Wake.vz += -2. * u_w[:, 1]
for Swim in Swimmers:
# Modify wake with the total induced velocity
Swim.Wake.x[1:i + 1] += Swim.Wake.vx * DEL_T
Swim.Wake.z[1:i + 1] += Swim.Wake.vz * DEL_T
