文件
gprMax/gprMax/grid.py

528 行
21 KiB
Python

# Copyright (C) 2015-2023: The University of Edinburgh, United Kingdom
# Authors: Craig Warren, Antonis Giannopoulos, and John Hartley
#
# This file is part of gprMax.
#
# gprMax is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# gprMax is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with gprMax. If not, see <http://www.gnu.org/licenses/>.
import decimal as d
from collections import OrderedDict
import numpy as np
import gprMax.config as config
from .pml import PML
from .utilities.utilities import fft_power, round_value
np.seterr(invalid="raise")
class FDTDGrid:
"""Holds attributes associated with entire grid. A convenient way for
accessing regularly used parameters.
"""
def __init__(self):
self.title = ""
self.name = "main_grid"
self.mem_use = 0
self.nx = 0
self.ny = 0
self.nz = 0
self.dx = 0
self.dy = 0
self.dz = 0
self.dt = 0
self.dt_mod = None # Time step stability factor
self.iteration = 0 # Current iteration number
self.iterations = 0 # Total number of iterations
self.timewindow = 0
# PML parameters - set some defaults to use if not user provided
self.pmls = {}
self.pmls["formulation"] = "HORIPML"
self.pmls["cfs"] = []
self.pmls["slabs"] = []
# Ordered dictionary required so that PMLs are always updated in the
# same order. The order itself does not matter, however, if must be the
# same from model to model otherwise the numerical precision from adding
# the PML corrections will be different.
self.pmls["thickness"] = OrderedDict((key, 10) for key in PML.boundaryIDs)
self.materials = []
self.mixingmodels = []
self.averagevolumeobjects = True
self.fractalvolumes = []
self.geometryviews = []
self.geometryobjectswrite = []
self.waveforms = []
self.voltagesources = []
self.hertziandipoles = []
self.magneticdipoles = []
self.transmissionlines = []
self.rxs = []
self.srcsteps = [0, 0, 0]
self.rxsteps = [0, 0, 0]
self.snapshots = []
self.subgrids = []
def within_bounds(self, p):
if p[0] < 0 or p[0] > self.nx:
raise ValueError("x")
if p[1] < 0 or p[1] > self.ny:
raise ValueError("y")
if p[2] < 0 or p[2] > self.nz:
raise ValueError("z")
def discretise_point(self, p):
x = round_value(float(p[0]) / self.dx)
y = round_value(float(p[1]) / self.dy)
z = round_value(float(p[2]) / self.dz)
return (x, y, z)
def round_to_grid(self, p):
p = self.discretise_point(p)
p_r = (p[0] * self.dx, p[1] * self.dy, p[2] * self.dz)
return p_r
def within_pml(self, p):
if (
p[0] < self.pmls["thickness"]["x0"]
or p[0] > self.nx - self.pmls["thickness"]["xmax"]
or p[1] < self.pmls["thickness"]["y0"]
or p[1] > self.ny - self.pmls["thickness"]["ymax"]
or p[2] < self.pmls["thickness"]["z0"]
or p[2] > self.nz - self.pmls["thickness"]["zmax"]
):
return True
else:
return False
def initialise_geometry_arrays(self):
"""Initialise an array for volumetric material IDs (solid);
boolean arrays for specifying whether materials can have dielectric
smoothing (rigid); and an array for cell edge IDs (ID).
Solid and ID arrays are initialised to free_space (one);
rigid arrays to allow dielectric smoothing (zero).
"""
self.solid = np.ones((self.nx, self.ny, self.nz), dtype=np.uint32)
self.rigidE = np.zeros((12, self.nx, self.ny, self.nz), dtype=np.int8)
self.rigidH = np.zeros((6, self.nx, self.ny, self.nz), dtype=np.int8)
self.ID = np.ones((6, self.nx + 1, self.ny + 1, self.nz + 1), dtype=np.uint32)
self.IDlookup = {"Ex": 0, "Ey": 1, "Ez": 2, "Hx": 3, "Hy": 4, "Hz": 5}
def initialise_field_arrays(self):
"""Initialise arrays for the electric and magnetic field components."""
self.Ex = np.zeros((self.nx + 1, self.ny + 1, self.nz + 1), dtype=config.sim_config.dtypes["float_or_double"])
self.Ey = np.zeros((self.nx + 1, self.ny + 1, self.nz + 1), dtype=config.sim_config.dtypes["float_or_double"])
self.Ez = np.zeros((self.nx + 1, self.ny + 1, self.nz + 1), dtype=config.sim_config.dtypes["float_or_double"])
self.Hx = np.zeros((self.nx + 1, self.ny + 1, self.nz + 1), dtype=config.sim_config.dtypes["float_or_double"])
self.Hy = np.zeros((self.nx + 1, self.ny + 1, self.nz + 1), dtype=config.sim_config.dtypes["float_or_double"])
self.Hz = np.zeros((self.nx + 1, self.ny + 1, self.nz + 1), dtype=config.sim_config.dtypes["float_or_double"])
def initialise_std_update_coeff_arrays(self):
"""Initialise arrays for storing update coefficients."""
self.updatecoeffsE = np.zeros((len(self.materials), 5), dtype=config.sim_config.dtypes["float_or_double"])
self.updatecoeffsH = np.zeros((len(self.materials), 5), dtype=config.sim_config.dtypes["float_or_double"])
def initialise_dispersive_arrays(self):
"""Initialise field arrays when there are dispersive materials present."""
self.Tx = np.zeros(
(config.get_model_config().materials["maxpoles"], self.nx + 1, self.ny + 1, self.nz + 1),
dtype=config.get_model_config().materials["dispersivedtype"],
)
self.Ty = np.zeros(
(config.get_model_config().materials["maxpoles"], self.nx + 1, self.ny + 1, self.nz + 1),
dtype=config.get_model_config().materials["dispersivedtype"],
)
self.Tz = np.zeros(
(config.get_model_config().materials["maxpoles"], self.nx + 1, self.ny + 1, self.nz + 1),
dtype=config.get_model_config().materials["dispersivedtype"],
)
def initialise_dispersive_update_coeff_array(self):
"""Initialise array for storing update coefficients when there are dispersive
materials present.
"""
self.updatecoeffsdispersive = np.zeros(
(len(self.materials), 3 * config.get_model_config().materials["maxpoles"]),
dtype=config.get_model_config().materials["dispersivedtype"],
)
def reset_fields(self):
"""Clear arrays for field components and PMLs."""
# Clear arrays for field components
self.initialise_field_arrays()
if config.get_model_config().materials["maxpoles"] > 0:
self.initialise_dispersive_arrays()
# Clear arrays for fields in PML
for pml in self.pmls["slabs"]:
pml.initialise_field_arrays()
def mem_est_basic(self):
"""Estimates the amount of memory (RAM) required for grid arrays.
Returns:
mem_use: int of memory (bytes).
"""
solidarray = self.nx * self.ny * self.nz * np.dtype(np.uint32).itemsize
# 12 x rigidE array components + 6 x rigidH array components
rigidarrays = (12 + 6) * self.nx * self.ny * self.nz * np.dtype(np.int8).itemsize
# 6 x field arrays + 6 x ID arrays
fieldarrays = (
(6 + 6)
* (self.nx + 1)
* (self.ny + 1)
* (self.nz + 1)
* np.dtype(config.sim_config.dtypes["float_or_double"]).itemsize
)
# PML arrays
pmlarrays = 0
for k, v in self.pmls["thickness"].items():
if v > 0:
if "x" in k:
pmlarrays += (v + 1) * self.ny * (self.nz + 1)
pmlarrays += (v + 1) * (self.ny + 1) * self.nz
pmlarrays += v * self.ny * (self.nz + 1)
pmlarrays += v * (self.ny + 1) * self.nz
elif "y" in k:
pmlarrays += self.nx * (v + 1) * (self.nz + 1)
pmlarrays += (self.nx + 1) * (v + 1) * self.nz
pmlarrays += (self.nx + 1) * v * self.nz
pmlarrays += self.nx * v * (self.nz + 1)
elif "z" in k:
pmlarrays += self.nx * (self.ny + 1) * (v + 1)
pmlarrays += (self.nx + 1) * self.ny * (v + 1)
pmlarrays += (self.nx + 1) * self.ny * v
pmlarrays += self.nx * (self.ny + 1) * v
mem_use = int(fieldarrays + solidarray + rigidarrays + pmlarrays)
return mem_use
def mem_est_dispersive(self):
"""Estimates the amount of memory (RAM) required for dispersive grid arrays.
Returns:
mem_use: int of memory (bytes).
"""
mem_use = int(
3
* config.get_model_config().materials["maxpoles"]
* (self.nx + 1)
* (self.ny + 1)
* (self.nz + 1)
* np.dtype(config.get_model_config().materials["dispersivedtype"]).itemsize
)
return mem_use
def mem_est_fractals(self):
"""Estimates the amount of memory (RAM) required to build any objects
which use the FractalVolume/FractalSurface classes.
Returns:
mem_use: int of memory (bytes).
"""
mem_use = 0
for vol in self.fractalvolumes:
mem_use += vol.nx * vol.ny * vol.nz * vol.dtype.itemsize
for surface in vol.fractalsurfaces:
surfacedims = surface.get_surface_dims()
mem_use += surfacedims[0] * surfacedims[1] * surface.dtype.itemsize
return mem_use
def tmx(self):
"""Add PEC boundaries to invariant direction in 2D TMx mode.
N.B. 2D modes are a single cell slice of 3D grid.
"""
# Ey & Ez components
self.ID[1, 0, :, :] = 0
self.ID[1, 1, :, :] = 0
self.ID[2, 0, :, :] = 0
self.ID[2, 1, :, :] = 0
def tmy(self):
"""Add PEC boundaries to invariant direction in 2D TMy mode.
N.B. 2D modes are a single cell slice of 3D grid.
"""
# Ex & Ez components
self.ID[0, :, 0, :] = 0
self.ID[0, :, 1, :] = 0
self.ID[2, :, 0, :] = 0
self.ID[2, :, 1, :] = 0
def tmz(self):
"""Add PEC boundaries to invariant direction in 2D TMz mode.
N.B. 2D modes are a single cell slice of 3D grid.
"""
# Ex & Ey components
self.ID[0, :, :, 0] = 0
self.ID[0, :, :, 1] = 0
self.ID[1, :, :, 0] = 0
self.ID[1, :, :, 1] = 0
def calculate_dt(self):
"""Calculate time step at the CFL limit."""
if config.get_model_config().mode == "2D TMx":
self.dt = 1 / (config.sim_config.em_consts["c"] * np.sqrt((1 / self.dy**2) + (1 / self.dz**2)))
elif config.get_model_config().mode == "2D TMy":
self.dt = 1 / (config.sim_config.em_consts["c"] * np.sqrt((1 / self.dx**2) + (1 / self.dz**2)))
elif config.get_model_config().mode == "2D TMz":
self.dt = 1 / (config.sim_config.em_consts["c"] * np.sqrt((1 / self.dx**2) + (1 / self.dy**2)))
else:
self.dt = 1 / (
config.sim_config.em_consts["c"] * np.sqrt((1 / self.dx**2) + (1 / self.dy**2) + (1 / self.dz**2))
)
# Round down time step to nearest float with precision one less than
# hardware maximum. Avoids inadvertently exceeding the CFL due to
# binary representation of floating point number.
self.dt = round_value(self.dt, decimalplaces=d.getcontext().prec - 1)
class CUDAGrid(FDTDGrid):
"""Additional grid methods for solving on GPU using CUDA."""
def __init__(self):
super().__init__()
# Threads per block - used for main electric/magnetic field updates
self.tpb = (128, 1, 1)
# Blocks per grid - used for main electric/magnetic field updates
self.bpg = None
def set_blocks_per_grid(self):
"""Set the blocks per grid size used for updating the electric and
magnetic field arrays on a GPU.
"""
self.bpg = (int(np.ceil(((self.nx + 1) * (self.ny + 1) * (self.nz + 1)) / self.tpb[0])), 1, 1)
def htod_geometry_arrays(self, queue=None):
"""Initialise an array for cell edge IDs (ID) on compute device.
Args:
queue: pyopencl queue.
"""
if config.sim_config.general["solver"] == "cuda":
import pycuda.gpuarray as gpuarray
self.ID_dev = gpuarray.to_gpu(self.ID)
elif config.sim_config.general["solver"] == "opencl":
import pyopencl.array as clarray
self.ID_dev = clarray.to_device(queue, self.ID)
def htod_field_arrays(self, queue=None):
"""Initialise field arrays on compute device.
Args:
queue: pyopencl queue.
"""
if config.sim_config.general["solver"] == "cuda":
import pycuda.gpuarray as gpuarray
self.Ex_dev = gpuarray.to_gpu(self.Ex)
self.Ey_dev = gpuarray.to_gpu(self.Ey)
self.Ez_dev = gpuarray.to_gpu(self.Ez)
self.Hx_dev = gpuarray.to_gpu(self.Hx)
self.Hy_dev = gpuarray.to_gpu(self.Hy)
self.Hz_dev = gpuarray.to_gpu(self.Hz)
elif config.sim_config.general["solver"] == "opencl":
import pyopencl.array as clarray
self.Ex_dev = clarray.to_device(queue, self.Ex)
self.Ey_dev = clarray.to_device(queue, self.Ey)
self.Ez_dev = clarray.to_device(queue, self.Ez)
self.Hx_dev = clarray.to_device(queue, self.Hx)
self.Hy_dev = clarray.to_device(queue, self.Hy)
self.Hz_dev = clarray.to_device(queue, self.Hz)
def htod_dispersive_arrays(self, queue=None):
"""Initialise dispersive material coefficient arrays on compute device.
Args:
queue: pyopencl queue.
"""
if config.sim_config.general["solver"] == "cuda":
import pycuda.gpuarray as gpuarray
self.Tx_dev = gpuarray.to_gpu(self.Tx)
self.Ty_dev = gpuarray.to_gpu(self.Ty)
self.Tz_dev = gpuarray.to_gpu(self.Tz)
self.updatecoeffsdispersive_dev = gpuarray.to_gpu(self.updatecoeffsdispersive)
elif config.sim_config.general["solver"] == "opencl":
import pyopencl.array as clarray
self.Tx_dev = clarray.to_device(queue, self.Tx)
self.Ty_dev = clarray.to_device(queue, self.Ty)
self.Tz_dev = clarray.to_device(queue, self.Tz)
self.updatecoeffsdispersive_dev = clarray.to_device(queue, self.updatecoeffsdispersive)
class OpenCLGrid(CUDAGrid):
"""Additional grid methods for solving on compute device using OpenCL."""
def __init__(self):
super().__init__()
def set_blocks_per_grid(self):
pass
def dispersion_analysis(G):
"""Analysis of numerical dispersion (Taflove et al, 2005, p112) -
worse case of maximum frequency and minimum wavelength
Args:
G: FDTDGrid class describing a grid in a model.
Returns:
results: dict of results from dispersion analysis.
"""
# deltavp: physical phase velocity error (percentage)
# N: grid sampling density
# material: material with maximum permittivity
# maxfreq: maximum significant frequency
# error: error message
results = {"deltavp": None, "N": None, "material": None, "maxfreq": [], "error": ""}
# Find maximum significant frequency
if G.waveforms:
for waveform in G.waveforms:
if waveform.type in ["sine", "contsine"]:
results["maxfreq"].append(4 * waveform.freq)
elif waveform.type == "impulse":
results["error"] = "impulse waveform used."
elif waveform.type == "user":
results["error"] = "user waveform detected."
else:
# Time to analyse waveform - 4*pulse_width as using entire
# time window can result in demanding FFT
waveform.calculate_coefficients()
iterations = round_value(4 * waveform.chi / G.dt)
iterations = min(iterations, G.iterations)
waveformvalues = np.zeros(G.iterations)
for iteration in range(G.iterations):
waveformvalues[iteration] = waveform.calculate_value(iteration * G.dt, G.dt)
# Ensure source waveform is not being overly truncated before attempting any FFT
if np.abs(waveformvalues[-1]) < np.abs(np.amax(waveformvalues)) / 100:
# FFT
freqs, power = fft_power(waveformvalues, G.dt)
# Get frequency for max power
freqmaxpower = np.where(np.isclose(power, 0))[0][0]
# Set maximum frequency to a threshold drop from maximum power, ignoring DC value
try:
freqthres = (
np.where(
power[freqmaxpower:] < -config.get_model_config().numdispersion["highestfreqthres"]
)[0][0]
+ freqmaxpower
)
results["maxfreq"].append(freqs[freqthres])
except ValueError:
results["error"] = (
"unable to calculate maximum power "
+ "from waveform, most likely due to "
+ "undersampling."
)
# Ignore case where someone is using a waveform with zero amplitude, i.e. on a receiver
elif waveform.amp == 0:
pass
# If waveform is truncated don't do any further analysis
else:
results["error"] = (
"waveform does not fit within specified " + "time window and is therefore being truncated."
)
else:
results["error"] = "no waveform detected."
if results["maxfreq"]:
results["maxfreq"] = max(results["maxfreq"])
# Find minimum wavelength (material with maximum permittivity)
maxer = 0
matmaxer = ""
for x in G.materials:
if x.se != float("inf"):
er = x.er
# If there are dispersive materials calculate the complex
# relative permittivity at maximum frequency and take the real part
if x.__class__.__name__ == "DispersiveMaterial":
er = x.calculate_er(results["maxfreq"])
er = er.real
if er > maxer:
maxer = er
matmaxer = x.ID
results["material"] = next(x for x in G.materials if x.ID == matmaxer)
# Minimum velocity
minvelocity = config.c / np.sqrt(maxer)
# Minimum wavelength
minwavelength = minvelocity / results["maxfreq"]
# Maximum spatial step
if "3D" in config.get_model_config().mode:
delta = max(G.dx, G.dy, G.dz)
elif "2D" in config.get_model_config().mode:
if G.nx == 1:
delta = max(G.dy, G.dz)
elif G.ny == 1:
delta = max(G.dx, G.dz)
elif G.nz == 1:
delta = max(G.dx, G.dy)
# Courant stability factor
S = (config.c * G.dt) / delta
# Grid sampling density
results["N"] = minwavelength / delta
# Check grid sampling will result in physical wave propagation
if int(np.floor(results["N"])) >= config.get_model_config().numdispersion["mingridsampling"]:
# Numerical phase velocity
vp = np.pi / (results["N"] * np.arcsin((1 / S) * np.sin((np.pi * S) / results["N"])))
# Physical phase velocity error (percentage)
results["deltavp"] = (((vp * config.c) - config.c) / config.c) * 100
# Store rounded down value of grid sampling density
results["N"] = int(np.floor(results["N"]))
return results