Rewrite, with the following features:
- Move to jinja2 templates for the opencl code - Combine PML code into the E, H updates for speed - Add Poynting vector calculation code, including precalculation during H update - Use arrays for PML parameters (p0, p1) - Switch to linearized, C-ordered fields (~50% performance boost??) - Added jinja2 and fdfd_tools dependencies
This commit is contained in:
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cd72219d0b
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68
fdtd.py
68
fdtd.py
@ -8,12 +8,17 @@ import sys
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import time
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import numpy
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import h5py
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import lzma
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import dill
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from fdtd.simulation import Simulation
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from masque import Pattern, shapes
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import gridlock
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import pcgen
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import fdfd_tools
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__author__ = 'Jan Petykiewicz'
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def perturbed_l3(a: float, radius: float, **kwargs) -> Pattern:
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@ -75,7 +80,7 @@ def perturbed_l3(a: float, radius: float, **kwargs) -> Pattern:
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def main():
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max_t = 8000 # number of timesteps
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dx = 40 # discretization (nm/cell)
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dx = 25 # discretization (nm/cell)
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pml_thickness = 8 # (number of cells)
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wl = 1550 # Excitation wavelength and fwhm
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@ -114,19 +119,9 @@ def main():
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eps=n_air**2,
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polygons=mask.as_polygons())
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print(grid.shape)
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print('grid shape: {}'.format(grid.shape))
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# #### Create the simulation grid ####
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sim = Simulation(grid.grids)
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# Conducting boundaries and pmls in every direction
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c_args = []
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pml_args = []
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for d in (0, 1, 2):
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for p in (-1, 1):
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c_args += [{'direction': d, 'polarity': p}]
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pml_args += [{'direction': d, 'polarity': p, 'epsilon_eff': n_slab**2}]
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sim.init_conductors(c_args)
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sim.init_cpml(pml_args)
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sim = Simulation(grid.grids, do_poynting=True, pml_thickness=8)
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# Source parameters and function
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w = 2 * numpy.pi * dx / wl
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@ -137,31 +132,44 @@ def main():
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def field_source(i):
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t0 = i * sim.dt - delay
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return numpy.sin(w * t0) * numpy.exp(-alpha * t0**2)
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with open('sources.c', 'w') as f:
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f.write(sim.sources['E'])
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f.write('\n==========================================\n')
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f.write(sim.sources['H'])
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if sim.update_S:
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f.write('\n==========================================\n')
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f.write(sim.sources['S'])
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# #### Run a bunch of iterations ####
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# event = sim.whatever([prev_event]) indicates that sim.whatever should be queued immediately and run
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# once prev_event is finished.
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output_file = h5py.File('simulation_output.h5', 'w')
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start = time.perf_counter()
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for t in range(max_t):
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event = sim.cpml_E([])
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sim.update_E([event]).wait()
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sim.update_E([]).wait()
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sim.E[1][tuple(grid.shape//2)] += field_source(t)
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event = sim.conductor_E([])
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event = sim.cpml_H([event])
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event = sim.update_H([event])
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sim.conductor_H([event]).wait()
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ind = numpy.ravel_multi_index(tuple(grid.shape//2), dims=grid.shape, order='C') + numpy.prod(grid.shape)
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sim.E[ind] += field_source(t)
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e = sim.update_H([])
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if sim.update_S:
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e = sim.update_S([e])
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e.wait()
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print('iteration {}: average {} iterations per sec'.format(t, (t+1)/(time.perf_counter()-start)))
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sys.stdout.flush()
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if t % 100 == 0:
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print('iteration {}: average {} iterations per sec'.format(t, (t+1)/(time.perf_counter()-start)))
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sys.stdout.flush()
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# Save field slices
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if (t % 20 == 0 and (max_t - t < 1000 or t < 1000)) or t == max_t-1:
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print('saving E-field')
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for j, f in enumerate(sim.E):
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a = f.get()
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output_file['/E{}_t{}'.format('xyz'[j], t)] = a[:, :, round(a.shape[2]/2)]
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with lzma.open('saved_simulation', 'wb') as f:
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def unvec(f):
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return fdfd_tools.unvec(f, grid.shape)
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d = {
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'grid': grid,
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'E': unvec(sim.E.get()),
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'H': unvec(sim.H.get()),
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}
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if sim.S is not None:
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d['S'] = unvec(sim.S.get())
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dill.dump(d, f)
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if __name__ == '__main__':
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main()
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72
fdtd/base.py
72
fdtd/base.py
@ -1,72 +0,0 @@
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"""
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Basic code snippets for opencl FDTD
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"""
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from typing import List
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import numpy
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def shape_source(shape: List[int] or numpy.ndarray) -> str:
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"""
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Defines sx, sy, sz C constants specifying the shape of the grid in each of the 3 dimensions.
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:param shape: [sx, sy, sz] values.
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:return: String containing C source.
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"""
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sxyz = """
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// Field sizes
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const int sx = {shape[0]};
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const int sy = {shape[1]};
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const int sz = {shape[2]};
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""".format(shape=shape)
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return sxyz
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# Defines dix, diy, diz constants used for stepping in the x, y, z directions in a linear array
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# (ie, given Ex[i] referring to position (x, y, z), Ex[i+diy] will refer to position (x, y+1, z))
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dixyz_source = """
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// Convert offset in field xyz to linear index offset
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const int dix = sz * sy;
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const int diy = sz;
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const int diz = 1;
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"""
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# Given a linear index i and shape sx, sy, sz, defines x, y, and z as the 3D indices of the current element (i).
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xyz_source = """
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// Convert linear index to field index (xyz)
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const int x = i / (sz * sy);
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const int y = (i - x * sz * sy) / sz;
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const int z = (i - y * sz - x * sz * sy);
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"""
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# Source code for updating the E field; maxes use of dixyz_source.
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maxwell_E_source = """
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// E update equations
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Ex[i] += dt / epsx[i] * ((Hz[i] - Hz[i-diy]) - (Hy[i] - Hy[i-diz]));
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Ey[i] += dt / epsy[i] * ((Hx[i] - Hx[i-diz]) - (Hz[i] - Hz[i-dix]));
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Ez[i] += dt / epsz[i] * ((Hy[i] - Hy[i-dix]) - (Hx[i] - Hx[i-diy]));
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"""
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# Source code for updating the H field; maxes use of dixyz_source and assumes mu=0
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maxwell_H_source = """
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// H update equations
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Hx[i] -= dt * ((Ez[i+diy] - Ez[i]) - (Ey[i+diz] - Ey[i]));
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Hy[i] -= dt * ((Ex[i+diz] - Ex[i]) - (Ez[i+dix] - Ez[i]));
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Hz[i] -= dt * ((Ey[i+dix] - Ey[i]) - (Ex[i+diy] - Ex[i]));
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"""
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def type_to_C(float_type: numpy.float32 or numpy.float64) -> str:
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"""
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Returns a string corresponding to the C equivalent of a numpy type.
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Only works for float32 and float64.
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:param float_type: numpy.float32 or numpy.float64
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:return: string containing the corresponding C type (eg. 'double')
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"""
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if float_type == numpy.float32:
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arg_type = 'float'
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elif float_type == numpy.float64:
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arg_type = 'double'
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else:
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raise Exception('Unsupported type')
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return arg_type
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185
fdtd/boundary.py
185
fdtd/boundary.py
@ -1,185 +0,0 @@
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from typing import List, Dict
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import numpy
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def conductor(direction: int,
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polarity: int,
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) -> List[str]:
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"""
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Create source code for conducting boundary conditions.
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:param direction: integer in range(3), corresponding to x,y,z.
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:param polarity: -1 or 1, specifying eg. a -x or +x boundary.
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:return: [E_source, H_source] source code for E and H boundary update steps.
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"""
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if direction not in range(3):
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raise Exception('Invalid direction: {}'.format(direction))
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if polarity not in (-1, 1):
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raise Exception('Invalid polarity: {}'.format(polarity))
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r = 'xyz'[direction]
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uv = 'xyz'.replace(r, '')
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if polarity < 0:
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bc_e = """
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if ({r} == 0) {{
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E{r}[i] = 0;
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E{u}[i] = E{u}[i+di{r}];
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E{v}[i] = E{v}[i+di{r}];
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}}
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"""
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bc_h = """
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if ({r} == 0) {{
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H{r}[i] = H{r}[i+di{r}];
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H{u}[i] = 0;
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H{v}[i] = 0;
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}}
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"""
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elif polarity > 0:
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bc_e = """
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if ({r} == s{r} - 1) {{
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E{r}[i] = -E{r}[i-2*di{r}];
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E{u}[i] = +E{u}[i-di{r}];
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E{v}[i] = +E{v}[i-di{r}];
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}} else if ({r} == s{r} - 2) {{
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E{r}[i] = 0;
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}}
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"""
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bc_h = """
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if ({r} == s{r} - 1) {{
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H{r}[i] = +H{r}[i-di{r}];
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H{u}[i] = -H{u}[i-2*di{r}];
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H{v}[i] = -H{v}[i-2*di{r}];
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}} else if ({r} == s{r} - 2) {{
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H{u}[i] = 0;
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H{v}[i] = 0;
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}}
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"""
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else:
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raise Exception()
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replacements = {'r': r, 'u': uv[0], 'v': uv[1]}
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return [s.format(**replacements) for s in (bc_e, bc_h)]
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def cpml(direction: int,
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polarity: int,
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dt: float,
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thickness: int=8,
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epsilon_eff: float=1,
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) -> Dict:
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"""
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Generate source code for complex phase matched layer (cpml) absorbing boundaries.
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These are not full boundary conditions and require a conducting boundary to be added
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in the same direction as the pml.
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:param direction: integer in range(3), corresponding to x, y, z directions.
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:param polarity: -1 or 1, corresponding to eg. -x or +x direction.
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:param dt: timestep used by the simulation
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:param thickness: Number of cells used by the pml (the grid is NOT expanded to add these cells). Default 8.
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:param epsilon_eff: Effective epsilon_r of the pml layer. Default 1.
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:return: Dict with entries 'E', 'H' (update equations for E and H) and 'psi_E', 'psi_H' (lists of str,
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specifying the field names of the cpml fields used in the E and H update steps. Eg.,
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Psi_xn_Ex for the complex Ex component for the x- pml.)
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"""
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if direction not in range(3):
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raise Exception('Invalid direction: {}'.format(direction))
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if polarity not in (-1, 1):
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raise Exception('Invalid polarity: {}'.format(polarity))
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if thickness <= 2:
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raise Exception('It would be wise to have a pml with 4+ cells of thickness')
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if epsilon_eff <= 0:
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raise Exception('epsilon_eff must be positive')
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m = (3.5, 1)
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sigma_max = 0.8 * (m[0] + 1) / numpy.sqrt(epsilon_eff)
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alpha_max = 0 # TODO: Decide what to do about non-zero alpha
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transverse = numpy.delete(range(3), direction)
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r = 'xyz'[direction]
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np = 'nVp'[numpy.sign(polarity)+1]
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uv = ['xyz'[i] for i in transverse]
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xe = numpy.arange(1, thickness+1, dtype=float)[::-1]
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xh = numpy.arange(1, thickness+1, dtype=float)[::-1]
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if polarity > 0:
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xe -= 0.5
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elif polarity < 0:
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xh -= 0.5
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def par(x):
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sigma = ((x / thickness) ** m[0]) * sigma_max
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alpha = ((1 - x / thickness) ** m[1]) * alpha_max
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p0 = numpy.exp(-(sigma + alpha) * dt)
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p1 = sigma / (sigma + alpha) * (p0 - 1)
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return p0, p1
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p0e, p1e = par(xe)
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p0h, p1h = par(xh)
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vals = {'r': r,
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'u': uv[0],
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'v': uv[1],
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'np': np,
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'th': thickness,
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'p0e': ', '.join((str(x) for x in p0e)),
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'p1e': ', '.join((str(x) for x in p1e)),
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'p0h': ', '.join((str(x) for x in p0h)),
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'p1h': ', '.join((str(x) for x in p1h)),
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'se': '-+'[direction % 2],
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'sh': '+-'[direction % 2]}
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if polarity < 0:
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bounds_if = """
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if ( 0 < {r} && {r} < {th} + 1 ) {{
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const int ir = {r} - 1; // index into pml parameters
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const int ip = {v} + {u} * s{v} + ir * s{v} * s{u}; // linear index into Psi
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"""
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elif polarity > 0:
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bounds_if = """
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if ( (s{r} - 1) > {r} && {r} > (s{r} - 1) - ({th} + 1) ) {{
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const int ir = (s{r} - 1) - ({r} + 1); // index into pml parameters
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const int ip = {v} + {u} * s{v} + ir * s{v} * s{u}; // linear index into Psi
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"""
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else:
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raise Exception('Bad polarity (=0)')
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code_e = """
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// pml parameters:
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const float p0[{th}] = {{ {p0e} }};
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const float p1[{th}] = {{ {p1e} }};
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Psi_{r}{np}_E{u}[ip] = p0[ir] * Psi_{r}{np}_E{u}[ip] + p1[ir] * (H{v}[i] - H{v}[i-di{r}]);
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Psi_{r}{np}_E{v}[ip] = p0[ir] * Psi_{r}{np}_E{v}[ip] + p1[ir] * (H{u}[i] - H{u}[i-di{r}]);
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E{u}[i] {se}= dt / eps{u}[i] * Psi_{r}{np}_E{u}[ip];
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E{v}[i] {sh}= dt / eps{v}[i] * Psi_{r}{np}_E{v}[ip];
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}}
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"""
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code_h = """
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// pml parameters:
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const float p0[{th}] = {{ {p0h} }};
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const float p1[{th}] = {{ {p1h} }};
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Psi_{r}{np}_H{u}[ip] = p0[ir] * Psi_{r}{np}_H{u}[ip] + p1[ir] * (E{v}[i+di{r}] - E{v}[i]);
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Psi_{r}{np}_H{v}[ip] = p0[ir] * Psi_{r}{np}_H{v}[ip] + p1[ir] * (E{u}[i+di{r}] - E{u}[i]);
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H{u}[i] {sh}= dt * Psi_{r}{np}_H{u}[ip];
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H{v}[i] {se}= dt * Psi_{r}{np}_H{v}[ip];
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}}
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"""
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pml_data = {
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'E': (bounds_if + code_e).format(**vals),
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'H': (bounds_if + code_h).format(**vals),
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'psi_E': ['Psi_{r}{np}_E{u}'.format(**vals),
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'Psi_{r}{np}_E{v}'.format(**vals)],
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'psi_H': ['Psi_{r}{np}_H{u}'.format(**vals),
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'Psi_{r}{np}_H{v}'.format(**vals)],
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}
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return pml_data
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84
fdtd/kernels/common.cl
Normal file
84
fdtd/kernels/common.cl
Normal file
@ -0,0 +1,84 @@
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{#
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/* Common code for E, H updates
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*
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* Template parameters:
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* ftype type name (e.g. float or double)
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* shape list of 3 ints specifying shape of fields
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*/
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#}
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typedef {{ftype}} ftype;
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/*
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* Field size info
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*/
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const size_t sx = {{shape[0]}};
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const size_t sy = {{shape[1]}};
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const size_t sz = {{shape[2]}};
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const size_t field_size = sx * sy * sz;
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//Since we use i to index into Ex[], Ey[], ... rather than E[], do nothing if
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// i is outside the bounds of Ex[].
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if (i >= field_size) {
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PYOPENCL_ELWISE_CONTINUE;
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}
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/*
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* Array indexing
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*/
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// Given a linear index i and shape (sx, sy, sz), defines x, y, and z
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// as the 3D indices of the current element (i).
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// (ie, converts linear index [i] to field indices (x, y, z)
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const size_t x = i / (sz * sy);
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const size_t y = (i - x * sz * sy) / sz;
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const size_t z = (i - y * sz - x * sz * sy);
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// Calculate linear index offsets corresponding to offsets in 3D
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// (ie, if E[i] <-> E(x, y, z), then E[i + diy] <-> E(x, y + 1, z)
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const size_t dix = sz * sy;
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const size_t diy = sz;
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const size_t diz = 1;
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/*
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* Pointer math
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*/
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//Pointer offsets into the components of a linearized vector-field
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// (eg. Hx = H + XX, where H and Hx are pointers)
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const size_t XX = 0;
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const size_t YY = field_size;
|
||||
const size_t ZZ = field_size * 2;
|
||||
|
||||
//Define pointers to vector components of each field (eg. Hx = H + XX)
|
||||
__global ftype *Ex = E + XX;
|
||||
__global ftype *Ey = E + YY;
|
||||
__global ftype *Ez = E + ZZ;
|
||||
|
||||
__global ftype *Hx = H + XX;
|
||||
__global ftype *Hy = H + YY;
|
||||
__global ftype *Hz = H + ZZ;
|
||||
|
||||
|
||||
/*
|
||||
* Implement periodic boundary conditions
|
||||
*
|
||||
* mx ([m]inus [x]) gives the index offset of the adjacent cell in the minus-x direction.
|
||||
* In the event that we start at x == 0, we actually want to wrap around and grab the cell
|
||||
* x_{-1} == (sx - 1) instead, ie. mx = (sx - 1) * dix .
|
||||
*
|
||||
* px ([p]lus [x]) gives the index offset of the adjacent cell in the plus-x direction.
|
||||
* In the event that we start at x == (sx - 1), we actually want to wrap around and grab
|
||||
* the cell x_{+1} == 0 instead, ie. px = -(sx - 1) * dix .
|
||||
*/
|
||||
{% for r in 'xyz' %}
|
||||
int m{{r}} = -di{{r}};
|
||||
int p{{r}} = +di{{r}};
|
||||
int wrap_{{r}} = (s{{r}} - 1) * di{{r}};
|
||||
if ( {{r}} == 0 ) {
|
||||
m{{r}} = wrap_{{r}};
|
||||
} else if ( {{r}} == s{{r}} - 1 ) {
|
||||
p{{r}} = -wrap_{{r}};
|
||||
}
|
||||
{% endfor %}
|
||||
78
fdtd/kernels/update_e.cl
Normal file
78
fdtd/kernels/update_e.cl
Normal file
@ -0,0 +1,78 @@
|
||||
/*
|
||||
* Update E-field, including any PMLs.
|
||||
*
|
||||
* Template parameters:
|
||||
* common_header: Rendered contents of common.cl
|
||||
* pmls: [('x', 'n'), ('z', 'p'),...] list of pml axes and polarities
|
||||
* pml_thickness: Number of cells (integer)
|
||||
*
|
||||
* OpenCL args:
|
||||
* E, H, dt, eps, [p{01}e{np}, Psi_{xyz}{np}_E]
|
||||
*/
|
||||
|
||||
{{common_header}}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
__global ftype *epsx = eps + XX;
|
||||
__global ftype *epsy = eps + YY;
|
||||
__global ftype *epsz = eps + ZZ;
|
||||
|
||||
{% if pmls -%}
|
||||
const int pml_thickness = {{pml_thickness}};
|
||||
{%- endif %}
|
||||
|
||||
/*
|
||||
* Precalclate derivatives
|
||||
*/
|
||||
ftype dHxy = Hx[i] - Hx[i + my];
|
||||
ftype dHxz = Hx[i] - Hx[i + mz];
|
||||
|
||||
ftype dHyx = Hy[i] - Hy[i + mx];
|
||||
ftype dHyz = Hy[i] - Hy[i + mz];
|
||||
|
||||
ftype dHzx = Hz[i] - Hz[i + mx];
|
||||
ftype dHzy = Hz[i] - Hz[i + my];
|
||||
|
||||
/*
|
||||
* PML Update
|
||||
*/
|
||||
// PML effects on E
|
||||
ftype pExi = 0;
|
||||
ftype pEyi = 0;
|
||||
ftype pEzi = 0;
|
||||
|
||||
{% for r, p in pmls -%}
|
||||
{%- set u, v = ['x', 'y', 'z'] | reject('equalto', r) -%}
|
||||
{%- set psi = 'Psi_' ~ r ~ p ~ '_E' -%}
|
||||
{%- if r != 'y' -%}
|
||||
{%- set se, sh = '-', '+' -%}
|
||||
{%- else -%}
|
||||
{%- set se, sh = '+', '-' -%}
|
||||
{%- endif -%}
|
||||
|
||||
{%- if p == 'n' %}
|
||||
|
||||
if ( {{r}} < pml_thickness ) {
|
||||
const size_t ir = {{r}}; // index into pml parameters
|
||||
|
||||
{%- elif p == 'p' %}
|
||||
|
||||
if ( s{{r}} > {{r}} && {{r}} >= s{{r}} - pml_thickness ) {
|
||||
const size_t ir = (s{{r}} - 1) - {{r}}; // index into pml parameters
|
||||
|
||||
{%- endif %}
|
||||
const size_t ip = {{v}} + {{u}} * s{{v}} + ir * s{{v}} * s{{u}}; // linear index into Psi
|
||||
{{psi ~ u}}[ip] = p0e{{p}}[ir] * {{psi ~ u}}[ip] + p1e{{p}}[ir] * dH{{v ~ r}};
|
||||
{{psi ~ v}}[ip] = p0e{{p}}[ir] * {{psi ~ v}}[ip] + p1e{{p}}[ir] * dH{{u ~ r}};
|
||||
pE{{u}}i {{se}}= {{psi ~ u}}[ip];
|
||||
pE{{v}}i {{sh}}= {{psi ~ v}}[ip];
|
||||
}
|
||||
{%- endfor %}
|
||||
|
||||
/*
|
||||
* Update E
|
||||
*/
|
||||
Ex[i] += dt / epsx[i] * (dHzy - dHyz + pExi);
|
||||
Ey[i] += dt / epsy[i] * (dHxz - dHzx + pEyi);
|
||||
Ez[i] += dt / epsz[i] * (dHyx - dHxy + pEzi);
|
||||
125
fdtd/kernels/update_h.cl
Normal file
125
fdtd/kernels/update_h.cl
Normal file
@ -0,0 +1,125 @@
|
||||
/*
|
||||
* Update H-field, including any PMLs.
|
||||
* Also precalculate values for poynting vector if necessary.
|
||||
*
|
||||
* Template parameters:
|
||||
* common_header: Rendered contents of common.cl
|
||||
* pmls: [('x', 'n'), ('z', 'p'),...] list of pml axes and polarities
|
||||
* pml_thickness: Number of cells (integer)
|
||||
* do_poynting: Whether to precalculate poynting vector components (boolean)
|
||||
*
|
||||
* OpenCL args:
|
||||
* E, H, dt, [p{01}h{np}, Psi_{xyz}{np}_H], [oS]
|
||||
*/
|
||||
|
||||
{{common_header}}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
{% if pmls -%}
|
||||
const int pml_thickness = {{pml_thickness}};
|
||||
{%- endif %}
|
||||
|
||||
/*
|
||||
* Precalculate derivatives
|
||||
*/
|
||||
ftype dExy = Ex[i + py] - Ex[i];
|
||||
ftype dExz = Ex[i + pz] - Ex[i];
|
||||
|
||||
ftype dEyx = Ey[i + px] - Ey[i];
|
||||
ftype dEyz = Ey[i + pz] - Ey[i];
|
||||
|
||||
ftype dEzx = Ez[i + px] - Ez[i];
|
||||
ftype dEzy = Ez[i + py] - Ez[i];
|
||||
|
||||
{%- if do_poynting %}
|
||||
|
||||
|
||||
/*
|
||||
* Precalculate averaged E
|
||||
*/
|
||||
ftype aExy = Ex[i + py] + Ex[i];
|
||||
ftype aExz = Ex[i + pz] + Ex[i];
|
||||
|
||||
ftype aEyx = Ey[i + px] + Ey[i];
|
||||
ftype aEyz = Ey[i + pz] + Ey[i];
|
||||
|
||||
ftype aEzx = Ez[i + px] + Ez[i];
|
||||
ftype aEzy = Ez[i + py] + Ez[i];
|
||||
{%- endif %}
|
||||
|
||||
|
||||
/*
|
||||
* PML Update
|
||||
*/
|
||||
// PML contributions to H
|
||||
ftype pHxi = 0;
|
||||
ftype pHyi = 0;
|
||||
ftype pHzi = 0;
|
||||
|
||||
{%- for r, p in pmls -%}
|
||||
{%- set u, v = ['x', 'y', 'z'] | reject('equalto', r) -%}
|
||||
{%- set psi = 'Psi_' ~ r ~ p ~ '_H' -%}
|
||||
{%- if r != 'y' -%}
|
||||
{%- set se, sh = '-', '+' -%}
|
||||
{%- else -%}
|
||||
{%- set se, sh = '+', '-' -%}
|
||||
{%- endif -%}
|
||||
|
||||
{%- if p == 'n' %}
|
||||
|
||||
if ( {{r}} < pml_thickness ) {
|
||||
const size_t ir = {{r}}; // index into pml parameters
|
||||
|
||||
{%- elif p == 'p' %}
|
||||
|
||||
if ( s{{r}} > {{r}} && {{r}} >= s{{r}} - pml_thickness ) {
|
||||
const size_t ir = (s{{r}} - 1) - {{r}}; // index into pml parameters
|
||||
|
||||
{%- endif %}
|
||||
const size_t ip = {{v}} + {{u}} * s{{v}} + ir * s{{v}} * s{{u}}; // linear index into Psi
|
||||
{{psi ~ u}}[ip] = p0h{{p}}[ir] * {{psi ~ u}}[ip] + p1h{{p}}[ir] * dE{{v ~ r}};
|
||||
{{psi ~ v}}[ip] = p0h{{p}}[ir] * {{psi ~ v}}[ip] + p1h{{p}}[ir] * dE{{u ~ r}};
|
||||
pH{{u}}i {{sh}}= {{psi ~ u}}[ip];
|
||||
pH{{v}}i {{se}}= {{psi ~ v}}[ip];
|
||||
}
|
||||
{%- endfor %}
|
||||
|
||||
/*
|
||||
* Update H
|
||||
*/
|
||||
{% if do_poynting -%}
|
||||
// Save old H for averaging
|
||||
ftype Hx_old = Hx[i];
|
||||
ftype Hy_old = Hy[i];
|
||||
ftype Hz_old = Hz[i];
|
||||
{%- endif %}
|
||||
|
||||
// H update equations
|
||||
Hx[i] -= dt * (dEzy - dEyz + pHxi);
|
||||
Hy[i] -= dt * (dExz - dEzx + pHyi);
|
||||
Hz[i] -= dt * (dEyx - dExy + pHzi);
|
||||
|
||||
{% if do_poynting -%}
|
||||
// Average H across timesteps
|
||||
ftype aHxt = Hx[i] + Hx_old;
|
||||
ftype aHyt = Hy[i] + Hy_old;
|
||||
ftype aHzt = Hz[i] + Hz_old;
|
||||
|
||||
/*
|
||||
* Calculate unscaled S components at H locations
|
||||
*/
|
||||
__global ftype *oSxy = oS + 0 * field_size;
|
||||
__global ftype *oSyz = oS + 1 * field_size;
|
||||
__global ftype *oSzx = oS + 2 * field_size;
|
||||
__global ftype *oSxz = oS + 3 * field_size;
|
||||
__global ftype *oSyx = oS + 4 * field_size;
|
||||
__global ftype *oSzy = oS + 5 * field_size;
|
||||
|
||||
oSxy[i] = aEyx * aHzt;
|
||||
oSxz[i] = -aEzx * aHyt;
|
||||
oSyz[i] = aEzy * aHxt;
|
||||
oSyx[i] = -aExy * aHzt;
|
||||
oSzx[i] = aExz * aHyt;
|
||||
oSzy[i] = -aEyz * aHxt;
|
||||
{%- endif -%}
|
||||
36
fdtd/kernels/update_s.cl
Normal file
36
fdtd/kernels/update_s.cl
Normal file
@ -0,0 +1,36 @@
|
||||
/*
|
||||
* Update E-field, including any PMLs.
|
||||
*
|
||||
* Template parameters:
|
||||
* common_header: Rendered contents of common.cl
|
||||
* pmls: [('x', 'n'), ('z', 'p'),...] list of pml axes and polarities
|
||||
* pml_thickness: Number of cells (integer)
|
||||
*
|
||||
* OpenCL args:
|
||||
* E, H, dt, S, oS
|
||||
*/
|
||||
|
||||
{{common_header}}
|
||||
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
|
||||
/*
|
||||
* Calculate S from oS (pre-calculated components)
|
||||
*/
|
||||
__global ftype *Sx = S + XX;
|
||||
__global ftype *Sy = S + YY;
|
||||
__global ftype *Sz = S + ZZ;
|
||||
|
||||
// Use unscaled S components from H locations
|
||||
__global ftype *oSxy = oS + 0 * field_size;
|
||||
__global ftype *oSyz = oS + 1 * field_size;
|
||||
__global ftype *oSzx = oS + 2 * field_size;
|
||||
__global ftype *oSxz = oS + 3 * field_size;
|
||||
__global ftype *oSyx = oS + 4 * field_size;
|
||||
__global ftype *oSzy = oS + 5 * field_size;
|
||||
|
||||
ftype s_factor = dt * 0.125;
|
||||
Sx[i] = (oSxy[i] + oSxz[i] + oSxy[i + my] + oSxz[i + mz]) * s_factor;
|
||||
Sy[i] = (oSyz[i] + oSyx[i] + oSyz[i + mz] + oSyx[i + mx]) * s_factor;
|
||||
Sz[i] = (oSzx[i] + oSzy[i] + oSzx[i + mx] + oSzy[i + my]) * s_factor;
|
||||
@ -3,15 +3,23 @@ Class for constructing and holding the basic FDTD operations and fields
|
||||
"""
|
||||
|
||||
from typing import List, Dict, Callable
|
||||
from collections import OrderedDict
|
||||
import numpy
|
||||
import jinja2
|
||||
import warnings
|
||||
|
||||
import pyopencl
|
||||
import pyopencl.array
|
||||
from pyopencl.elementwise import ElementwiseKernel
|
||||
|
||||
from . import boundary, base
|
||||
from .base import type_to_C
|
||||
from fdfd_tools import vec
|
||||
|
||||
|
||||
__author__ = 'Jan Petykiewicz'
|
||||
|
||||
|
||||
# Create jinja2 env on module load
|
||||
jinja_env = jinja2.Environment(loader=jinja2.PackageLoader(__name__, 'kernels'))
|
||||
|
||||
|
||||
class Simulation(object):
|
||||
@ -20,6 +28,7 @@ class Simulation(object):
|
||||
"""
|
||||
E = None # type: List[pyopencl.array.Array]
|
||||
H = None # type: List[pyopencl.array.Array]
|
||||
S = None # type: List[pyopencl.array.Array]
|
||||
eps = None # type: List[pyopencl.array.Array]
|
||||
dt = None # type: float
|
||||
|
||||
@ -30,24 +39,20 @@ class Simulation(object):
|
||||
|
||||
update_E = None # type: Callable[[],pyopencl.Event]
|
||||
update_H = None # type: Callable[[],pyopencl.Event]
|
||||
|
||||
conductor_E = None # type: Callable[[],pyopencl.Event]
|
||||
conductor_H = None # type: Callable[[],pyopencl.Event]
|
||||
|
||||
cpml_E = None # type: Callable[[],pyopencl.Event]
|
||||
cpml_H = None # type: Callable[[],pyopencl.Event]
|
||||
|
||||
cpml_psi_E = None # type: Dict[str, pyopencl.array.Array]
|
||||
cpml_psi_H = None # type: Dict[str, pyopencl.array.Array]
|
||||
update_S = None # type: Callable[[],pyopencl.Event]
|
||||
sources = None # type: Dict[str, str]
|
||||
|
||||
def __init__(self,
|
||||
epsilon: List[numpy.ndarray],
|
||||
dt: float=.99/numpy.sqrt(3),
|
||||
initial_E: List[numpy.ndarray]=None,
|
||||
initial_H: List[numpy.ndarray]=None,
|
||||
context: pyopencl.Context=None,
|
||||
queue: pyopencl.CommandQueue=None,
|
||||
float_type: numpy.float32 or numpy.float64=numpy.float32):
|
||||
dt: float = .99/numpy.sqrt(3),
|
||||
initial_E: List[numpy.ndarray] = None,
|
||||
initial_H: List[numpy.ndarray] = None,
|
||||
context: pyopencl.Context = None,
|
||||
queue: pyopencl.CommandQueue = None,
|
||||
float_type: numpy.float32 or numpy.float64 = numpy.float32,
|
||||
pml_thickness: int = 10,
|
||||
pmls: List[List[str]] = None,
|
||||
do_poynting: bool = True):
|
||||
"""
|
||||
Initialize the simulation.
|
||||
|
||||
@ -67,7 +72,7 @@ class Simulation(object):
|
||||
Exception('All epsilon grids must have the same shape. Shapes are {}', [e.shape for e in epsilon])
|
||||
|
||||
if context is None:
|
||||
self.context = pyopencl.create_some_context(False)
|
||||
self.context = pyopencl.create_some_context()
|
||||
else:
|
||||
self.context = context
|
||||
|
||||
@ -84,126 +89,149 @@ class Simulation(object):
|
||||
self.dt = dt
|
||||
|
||||
self.arg_type = float_type
|
||||
|
||||
self.eps = [pyopencl.array.to_device(self.queue, e.astype(float_type)) for e in epsilon]
|
||||
self.sources = {}
|
||||
self.eps = pyopencl.array.to_device(self.queue, vec(epsilon).astype(float_type))
|
||||
|
||||
if initial_E is None:
|
||||
self.E = [pyopencl.array.zeros_like(self.eps[0]) for _ in range(3)]
|
||||
self.E = pyopencl.array.zeros_like(self.eps)
|
||||
else:
|
||||
if len(initial_E) != 3:
|
||||
Exception('Initial_E must be a list of length 3')
|
||||
if not all((E.shape == epsilon[0].shape for E in initial_E)):
|
||||
Exception('Initial_E list elements must have same shape as epsilon elements')
|
||||
self.E = [pyopencl.array.to_device(self.queue, E.astype(float_type)) for E in initial_E]
|
||||
self.E = pyopencl.array.to_device(self.queue, vec(E).astype(float_type))
|
||||
|
||||
if initial_H is None:
|
||||
self.H = [pyopencl.array.zeros_like(self.eps[0]) for _ in range(3)]
|
||||
self.H = pyopencl.array.zeros_like(self.eps)
|
||||
else:
|
||||
if len(initial_H) != 3:
|
||||
Exception('Initial_H must be a list of length 3')
|
||||
if not all((H.shape == epsilon[0].shape for H in initial_H)):
|
||||
Exception('Initial_H list elements must have same shape as epsilon elements')
|
||||
self.H = [pyopencl.array.to_device(self.queue, H.astype(float_type)) for H in initial_H]
|
||||
self.H = pyopencl.array.to_device(self.queue, vec(H).astype(float_type))
|
||||
|
||||
if pmls is None:
|
||||
pmls = [[d, p] for d in 'xyz' for p in 'np']
|
||||
|
||||
ctype = type_to_C(self.arg_type)
|
||||
E_args = [ctype + ' *E' + c for c in 'xyz']
|
||||
H_args = [ctype + ' *H' + c for c in 'xyz']
|
||||
eps_args = [ctype + ' *eps' + c for c in 'xyz']
|
||||
dt_arg = [ctype + ' dt']
|
||||
def ptr(arg: str) -> str:
|
||||
return ctype + ' *' + arg
|
||||
|
||||
sxyz = base.shape_source(epsilon[0].shape)
|
||||
E_source = sxyz + base.dixyz_source + base.maxwell_E_source
|
||||
H_source = sxyz + base.dixyz_source + base.maxwell_H_source
|
||||
base_fields = OrderedDict()
|
||||
base_fields[ptr('E')] = self.E
|
||||
base_fields[ptr('H')] = self.H
|
||||
base_fields[ctype + ' dt'] = self.dt
|
||||
|
||||
eps_field = OrderedDict()
|
||||
eps_field[ptr('eps')] = self.eps
|
||||
|
||||
common_source = jinja_env.get_template('common.cl').render(
|
||||
ftype=ctype,
|
||||
shape=epsilon[0].shape,
|
||||
)
|
||||
jinja_args = {
|
||||
'common_header': common_source,
|
||||
'pml_thickness': pml_thickness,
|
||||
'pmls': pmls,
|
||||
'do_poynting': do_poynting,
|
||||
}
|
||||
E_source = jinja_env.get_template('update_e.cl').render(**jinja_args)
|
||||
H_source = jinja_env.get_template('update_h.cl').render(**jinja_args)
|
||||
|
||||
self.sources['E'] = E_source
|
||||
self.sources['H'] = H_source
|
||||
|
||||
if do_poynting:
|
||||
S_source = jinja_env.get_template('update_s.cl').render(**jinja_args)
|
||||
self.sources['S'] = S_source
|
||||
|
||||
self.oS = pyopencl.array.zeros(self.queue, self.E.shape + (2,), dtype=float_type)
|
||||
self.S = pyopencl.array.zeros_like(self.E)
|
||||
S_fields = OrderedDict()
|
||||
S_fields[ptr('oS')] = self.oS
|
||||
S_fields[ptr('S')] = self.S
|
||||
else:
|
||||
S_fields = OrderedDict()
|
||||
|
||||
'''
|
||||
PML
|
||||
'''
|
||||
m = (3.5, 1)
|
||||
sigma_max = 0.8 * (m[0] + 1) / numpy.sqrt(1.0) # TODO: epsilon_eff (not 1.0)
|
||||
alpha_max = 0 # TODO: Decide what to do about non-zero alpha
|
||||
|
||||
def par(x):
|
||||
sigma = ((x / pml_thickness) ** m[0]) * sigma_max
|
||||
alpha = ((1 - x / pml_thickness) ** m[1]) * alpha_max
|
||||
p0 = numpy.exp(-(sigma + alpha) * dt)
|
||||
p1 = sigma / (sigma + alpha) * (p0 - 1)
|
||||
return p0, p1
|
||||
|
||||
xen, xep, xhn, xhp = (numpy.arange(1, pml_thickness + 1, dtype=float_type)[::-1] for _ in range(4))
|
||||
xep -= 0.5
|
||||
xhn -= 0.5
|
||||
|
||||
pml_p_names = [['p' + a + eh + np for np in 'np' for a in '01'] for eh in 'eh']
|
||||
pml_e_fields = OrderedDict()
|
||||
pml_h_fields = OrderedDict()
|
||||
for ne, nh, pe, ph in zip(*pml_p_names, par(xen) + par(xep), par(xhn) + par(xhp)):
|
||||
pml_e_fields[ptr(ne)] = pyopencl.array.to_device(self.queue, pe)
|
||||
pml_h_fields[ptr(nh)] = pyopencl.array.to_device(self.queue, ph)
|
||||
|
||||
for pml in pmls:
|
||||
uv = 'xyz'.replace(pml[0], '')
|
||||
psi_base = 'Psi_' + ''.join(pml) + '_'
|
||||
psi_names = [[psi_base + eh + c for c in uv] for eh in 'EH']
|
||||
|
||||
psi_shape = list(epsilon[0].shape)
|
||||
psi_shape['xyz'.find(pml[0])] = pml_thickness
|
||||
|
||||
for ne, nh in zip(*psi_names):
|
||||
pml_e_fields[ptr(ne)] = pyopencl.array.zeros(self.queue, tuple(psi_shape), dtype=self.arg_type)
|
||||
pml_h_fields[ptr(nh)] = pyopencl.array.zeros(self.queue, tuple(psi_shape), dtype=self.arg_type)
|
||||
|
||||
self.pml_e_fields = pml_e_fields
|
||||
self.pml_h_fields = pml_h_fields
|
||||
|
||||
|
||||
'''
|
||||
Create operations
|
||||
'''
|
||||
E_args = OrderedDict()
|
||||
[E_args.update(d) for d in (base_fields, eps_field, pml_e_fields)]
|
||||
E_update = ElementwiseKernel(self.context, operation=E_source,
|
||||
arguments=', '.join(E_args + H_args + dt_arg + eps_args))
|
||||
arguments=', '.join(E_args.keys()))
|
||||
|
||||
H_args = OrderedDict()
|
||||
[H_args.update(d) for d in (base_fields, pml_h_fields, S_fields)]
|
||||
H_update = ElementwiseKernel(self.context, operation=H_source,
|
||||
arguments=', '.join(E_args + H_args + dt_arg))
|
||||
arguments=', '.join(H_args.keys()))
|
||||
self.update_E = lambda e: E_update(*E_args.values(), wait_for=e)
|
||||
self.update_H = lambda e: H_update(*H_args.values(), wait_for=e)
|
||||
|
||||
self.update_E = lambda e: E_update(*self.E, *self.H, self.dt, *self.eps, wait_for=e)
|
||||
self.update_H = lambda e: H_update(*self.E, *self.H, self.dt, wait_for=e)
|
||||
if do_poynting:
|
||||
S_args = OrderedDict()
|
||||
[S_args.update(d) for d in (base_fields, S_fields)]
|
||||
S_update = ElementwiseKernel(self.context, operation=S_source,
|
||||
arguments=', '.join(S_args.keys()))
|
||||
|
||||
def init_cpml(self, pml_args: List[Dict]):
|
||||
"""
|
||||
Initialize absorbing layers (cpml: complex phase matched layer). PMLs are not actual
|
||||
boundary conditions, so you should add a conducting boundary (.init_conductors()) for
|
||||
all directions in which you add PMLs.
|
||||
Allows use of self.cpml_E(events) and self.cpml_H(events).
|
||||
All necessary additional fields are created on the opencl device.
|
||||
self.update_S = lambda e: S_update(*S_args.values(), wait_for=e)
|
||||
|
||||
:param pml_args: A list containing dictionaries which are passed to .boundary.cpml(...).
|
||||
The dt argument is set automatically, but the others must be passed in each entry
|
||||
of pml_args.
|
||||
"""
|
||||
sxyz = base.shape_source(self.eps[0].shape)
|
||||
|
||||
# Prepare per-iteration constants for later use
|
||||
pml_E_source = sxyz + base.dixyz_source + base.xyz_source
|
||||
pml_H_source = sxyz + base.dixyz_source + base.xyz_source
|
||||
def type_to_C(float_type) -> str:
|
||||
"""
|
||||
Returns a string corresponding to the C equivalent of a numpy type.
|
||||
Only works for float16, float32, float64.
|
||||
|
||||
psi_E = []
|
||||
psi_H = []
|
||||
psi_E_names = []
|
||||
psi_H_names = []
|
||||
for arg_set in pml_args:
|
||||
pml_data = boundary.cpml(dt=self.dt, **arg_set)
|
||||
|
||||
pml_E_source += pml_data['E']
|
||||
pml_H_source += pml_data['H']
|
||||
|
||||
ti = numpy.delete(range(3), arg_set['direction'])
|
||||
trans = [self.eps[0].shape[i] for i in ti]
|
||||
psi_shape = (8, trans[0], trans[1])
|
||||
|
||||
psi_E += [pyopencl.array.zeros(self.queue, psi_shape, dtype=self.arg_type)
|
||||
for _ in pml_data['psi_E']]
|
||||
psi_H += [pyopencl.array.zeros(self.queue, psi_shape, dtype=self.arg_type)
|
||||
for _ in pml_data['psi_H']]
|
||||
|
||||
psi_E_names += pml_data['psi_E']
|
||||
psi_H_names += pml_data['psi_H']
|
||||
|
||||
ctype = type_to_C(self.arg_type)
|
||||
E_args = [ctype + ' *E' + c for c in 'xyz']
|
||||
H_args = [ctype + ' *H' + c for c in 'xyz']
|
||||
eps_args = [ctype + ' *eps' + c for c in 'xyz']
|
||||
dt_arg = [ctype + ' dt']
|
||||
arglist_E = [ctype + ' *' + psi for psi in psi_E_names]
|
||||
arglist_H = [ctype + ' *' + psi for psi in psi_H_names]
|
||||
pml_E_args = ', '.join(E_args + H_args + dt_arg + eps_args + arglist_E)
|
||||
pml_H_args = ', '.join(E_args + H_args + dt_arg + arglist_H)
|
||||
|
||||
pml_E = ElementwiseKernel(self.context, arguments=pml_E_args, operation=pml_E_source)
|
||||
pml_H = ElementwiseKernel(self.context, arguments=pml_H_args, operation=pml_H_source)
|
||||
|
||||
self.cpml_E = lambda e: pml_E(*self.E, *self.H, self.dt, *self.eps, *psi_E, wait_for=e)
|
||||
self.cpml_H = lambda e: pml_H(*self.E, *self.H, self.dt, *psi_H, wait_for=e)
|
||||
self.cmpl_psi_E = {k: v for k, v in zip(psi_E_names, psi_E)}
|
||||
self.cmpl_psi_H = {k: v for k, v in zip(psi_H_names, psi_H)}
|
||||
|
||||
def init_conductors(self, conductor_args: List[Dict]):
|
||||
"""
|
||||
Initialize reflecting boundary conditions.
|
||||
Allows use of self.conductor_E(events) and self.conductor_H(events).
|
||||
|
||||
:param conductor_args: List of dictionaries with which to call .boundary.conductor(...).
|
||||
"""
|
||||
|
||||
sxyz = base.shape_source(self.eps[0].shape)
|
||||
|
||||
# Prepare per-iteration constants
|
||||
bc_E_source = sxyz + base.dixyz_source + base.xyz_source
|
||||
bc_H_source = sxyz + base.dixyz_source + base.xyz_source
|
||||
for arg_set in conductor_args:
|
||||
[e, h] = boundary.conductor(**arg_set)
|
||||
bc_E_source += e
|
||||
bc_H_source += h
|
||||
|
||||
E_args = [type_to_C(self.arg_type) + ' *E' + c for c in 'xyz']
|
||||
H_args = [type_to_C(self.arg_type) + ' *H' + c for c in 'xyz']
|
||||
bc_E = ElementwiseKernel(self.context, arguments=E_args, operation=bc_E_source)
|
||||
bc_H = ElementwiseKernel(self.context, arguments=H_args, operation=bc_H_source)
|
||||
|
||||
self.conductor_E = lambda e: bc_E(*self.E, wait_for=e)
|
||||
self.conductor_H = lambda e: bc_H(*self.H, wait_for=e)
|
||||
:param float_type: e.g. numpy.float32
|
||||
:return: string containing the corresponding C type (eg. 'double')
|
||||
"""
|
||||
if float_type == numpy.float16:
|
||||
arg_type = 'half'
|
||||
elif float_type == numpy.float32:
|
||||
arg_type = 'float'
|
||||
elif float_type == numpy.float64:
|
||||
arg_type = 'double'
|
||||
else:
|
||||
raise Exception('Unsupported type')
|
||||
return arg_type
|
||||
|
||||
@ -1,6 +1,8 @@
|
||||
numpy
|
||||
h5py
|
||||
pyopencl
|
||||
jinja2
|
||||
-e git+https://mpxd.net/gogs/jan/float_raster.git@release#egg=float_raster
|
||||
-e git+https://mpxd.net/gogs/jan/gridlock.git@release#egg=gridlock
|
||||
-e git+https://mpxd.net/gogs/jan/masque.git@release#egg=masque
|
||||
-e git+https://mpxd.net/gogs/jan/fdfd_tools.git@master#egg=fdfd_tools
|
||||
|
||||
Loading…
Reference in New Issue
Block a user