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已同步 2025-08-08 07:24:19 +08:00
515 行
25 KiB
Cython
515 行
25 KiB
Cython
# Copyright (C) 2015-2019: The University of Edinburgh
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# Authors: Craig Warren and Antonis Giannopoulos
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#
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# This file is part of gprMax.
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#
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# gprMax is free software: you can redistribute it and/or modify
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# it under the terms of the GNU General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# gprMax is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU General Public License for more details.
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#
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# You should have received a copy of the GNU General Public License
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# along with gprMax. If not, see <http://www.gnu.org/licenses/>.
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import numpy as np
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cimport numpy as np
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from cython.parallel import prange
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from gprMax.config cimport float_or_double
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from gprMax.config cimport real_or_complex
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cdef double mycreal(double complex dc) nogil:
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cdef double complex* dcptr = &dc
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return (<double *>dcptr)[0]
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#########################################################
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# Electric field updates - dispersive materials - Debye #
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#########################################################
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cpdef void update_electric_dispersive_debye_multipole_A(
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int nx,
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int ny,
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int nz,
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int nthreads,
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int maxpoles,
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float_or_double[:, ::1] updatecoeffsE,
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float_or_double[:, ::1] updatecoeffsdispersive,
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np.uint32_t[:, :, :, ::1] ID,
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float_or_double[:, :, :, ::1] Tx,
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float_or_double[:, :, :, ::1] Ty,
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float_or_double[:, :, :, ::1] Tz,
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float_or_double[:, :, ::1] Ex,
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float_or_double[:, :, ::1] Ey,
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float_or_double[:, :, ::1] Ez,
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float_or_double[:, :, ::1] Hx,
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float_or_double[:, :, ::1] Hy,
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float_or_double[:, :, ::1] Hz
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):
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"""This function updates the electric field components when dispersive materials (with multiple poles) are present.
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Args:
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nx, ny, nz (int): Grid size in cells
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nthreads (int): Number of threads to use
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maxpoles (int): Maximum number of poles
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updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
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"""
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cdef Py_ssize_t i, j, k, pole
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cdef int material
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cdef float phi = 0
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# Ex component
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if ny != 1 or nz != 1:
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for i in prange(0, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(1, nz):
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material = ID[0, i, j, k]
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phi = 0
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for pole in range(maxpoles):
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phi = phi + updatecoeffsdispersive[material, pole * 3] * Tx[pole, i, j, k]
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Tx[pole, i, j, k] = updatecoeffsdispersive[material, 1 + (pole * 3)] * Tx[pole, i, j, k] + updatecoeffsdispersive[material, 2 + (pole * 3)] * Ex[i, j, k]
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Ex[i, j, k] = updatecoeffsE[material, 0] * Ex[i, j, k] + updatecoeffsE[material, 2] * (Hz[i, j, k] - Hz[i, j - 1, k]) - updatecoeffsE[material, 3] * (Hy[i, j, k] - Hy[i, j, k - 1]) - updatecoeffsE[material, 4] * phi
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# Ey component
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if nx != 1 or nz != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(0, ny):
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for k in range(1, nz):
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material = ID[1, i, j, k]
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phi = 0
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for pole in range(maxpoles):
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phi = phi + updatecoeffsdispersive[material, pole * 3] * Ty[pole, i, j, k]
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Ty[pole, i, j, k] = updatecoeffsdispersive[material, 1 + (pole * 3)] * Ty[pole, i, j, k] + updatecoeffsdispersive[material, 2 + (pole * 3)] * Ey[i, j, k]
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Ey[i, j, k] = updatecoeffsE[material, 0] * Ey[i, j, k] + updatecoeffsE[material, 3] * (Hx[i, j, k] - Hx[i, j, k - 1]) - updatecoeffsE[material, 1] * (Hz[i, j, k] - Hz[i - 1, j, k]) - updatecoeffsE[material, 4] * phi
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# Ez component
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if nx != 1 or ny != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(0, nz):
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material = ID[2, i, j, k]
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phi = 0
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for pole in range(maxpoles):
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phi = phi + updatecoeffsdispersive[material, pole * 3] * Tz[pole, i, j, k]
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Tz[pole, i, j, k] = updatecoeffsdispersive[material, 1 + (pole * 3)] * Tz[pole, i, j, k] + updatecoeffsdispersive[material, 2 + (pole * 3)] * Ez[i, j, k]
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Ez[i, j, k] = updatecoeffsE[material, 0] * Ez[i, j, k] + updatecoeffsE[material, 1] * (Hy[i, j, k] - Hy[i - 1, j, k]) - updatecoeffsE[material, 2] * (Hx[i, j, k] - Hx[i, j - 1, k]) - updatecoeffsE[material, 4] * phi
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cpdef void update_electric_dispersive_debye_multipole_B(
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int nx,
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int ny,
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int nz,
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int nthreads,
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int maxpoles,
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float_or_double[:, ::1] updatecoeffsdispersive,
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np.uint32_t[:, :, :, ::1] ID,
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float_or_double[:, :, :, ::1] Tx,
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float_or_double[:, :, :, ::1] Ty,
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float_or_double[:, :, :, ::1] Tz,
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float_or_double[:, :, ::1] Ex,
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float_or_double[:, :, ::1] Ey,
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float_or_double[:, :, ::1] Ez
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):
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"""This function updates a temporary dispersive material array when disperisive materials (with multiple poles) are present.
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Args:
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nx, ny, nz (int): Grid size in cells
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nthreads (int): Number of threads to use
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maxpoles (int): Maximum number of poles
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updatecoeffs, T, ID, E (memoryviews): Access to update coeffients, temporary, ID and field component arrays
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"""
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cdef Py_ssize_t i, j, k, pole
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cdef int material
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# Ex component
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if ny != 1 or nz != 1:
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for i in prange(0, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(1, nz):
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material = ID[0, i, j, k]
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for pole in range(maxpoles):
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Tx[pole, i, j, k] = Tx[pole, i, j, k] - updatecoeffsdispersive[material, 2 + (pole * 3)] * Ex[i, j, k]
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# Ey component
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if nx != 1 or nz != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(0, ny):
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for k in range(1, nz):
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material = ID[1, i, j, k]
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for pole in range(maxpoles):
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Ty[pole, i, j, k] = Ty[pole, i, j, k] - updatecoeffsdispersive[material, 2 + (pole * 3)] * Ey[i, j, k]
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# Ez component
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if nx != 1 or ny != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(0, nz):
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material = ID[2, i, j, k]
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for pole in range(maxpoles):
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Tz[pole, i, j, k] = Tz[pole, i, j, k] - updatecoeffsdispersive[material, 2 + (pole * 3)] * Ez[i, j, k]
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cpdef void update_electric_dispersive_debye_1pole_A(
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int nx,
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int ny,
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int nz,
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int nthreads,
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int maxpoles,
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float_or_double[:, ::1] updatecoeffsE,
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float_or_double[:, ::1] updatecoeffsdispersive,
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np.uint32_t[:, :, :, ::1] ID,
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float_or_double[:, :, :, ::1] Tx,
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float_or_double[:, :, :, ::1] Ty,
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float_or_double[:, :, :, ::1] Tz,
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float_or_double[:, :, ::1] Ex,
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float_or_double[:, :, ::1] Ey,
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float_or_double[:, :, ::1] Ez,
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float_or_double[:, :, ::1] Hx,
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float_or_double[:, :, ::1] Hy,
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float_or_double[:, :, ::1] Hz
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):
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"""This function updates the electric field components when dispersive materials (with 1 pole) are present.
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Args:
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nx, ny, nz (int): Grid size in cells
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nthreads (int): Number of threads to use
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maxpoles (int): Maximum number of poles
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updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
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"""
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cdef Py_ssize_t i, j, k
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cdef int material
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cdef float phi = 0
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# Ex component
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if ny != 1 or nz != 1:
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for i in prange(0, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(1, nz):
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material = ID[0, i, j, k]
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phi = updatecoeffsdispersive[material, 0] * Tx[0, i, j, k]
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Tx[0, i, j, k] = updatecoeffsdispersive[material, 1] * Tx[0, i, j, k] + updatecoeffsdispersive[material, 2] * Ex[i, j, k]
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Ex[i, j, k] = updatecoeffsE[material, 0] * Ex[i, j, k] + updatecoeffsE[material, 2] * (Hz[i, j, k] - Hz[i, j - 1, k]) - updatecoeffsE[material, 3] * (Hy[i, j, k] - Hy[i, j, k - 1]) - updatecoeffsE[material, 4] * phi
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# Ey component
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if nx != 1 or nz != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(0, ny):
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for k in range(1, nz):
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material = ID[1, i, j, k]
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phi = updatecoeffsdispersive[material, 0] * Ty[0, i, j, k]
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Ty[0, i, j, k] = updatecoeffsdispersive[material, 1] * Ty[0, i, j, k] + updatecoeffsdispersive[material, 2] * Ey[i, j, k]
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Ey[i, j, k] = updatecoeffsE[material, 0] * Ey[i, j, k] + updatecoeffsE[material, 3] * (Hx[i, j, k] - Hx[i, j, k - 1]) - updatecoeffsE[material, 1] * (Hz[i, j, k] - Hz[i - 1, j, k]) - updatecoeffsE[material, 4] * phi
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# Ez component
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if nx != 1 or ny != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(0, nz):
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material = ID[2, i, j, k]
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phi = updatecoeffsdispersive[material, 0] * Tz[0, i, j, k]
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Tz[0, i, j, k] = updatecoeffsdispersive[material, 1] * Tz[0, i, j, k] + updatecoeffsdispersive[material, 2] * Ez[i, j, k]
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Ez[i, j, k] = updatecoeffsE[material, 0] * Ez[i, j, k] + updatecoeffsE[material, 1] * (Hy[i, j, k] - Hy[i - 1, j, k]) - updatecoeffsE[material, 2] * (Hx[i, j, k] - Hx[i, j - 1, k]) - updatecoeffsE[material, 4] * phi
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cpdef void update_electric_dispersive_debye_1pole_B(
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int nx,
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int ny,
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int nz,
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int nthreads,
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int maxpoles,
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float_or_double[:, ::1] updatecoeffsdispersive,
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np.uint32_t[:, :, :, ::1] ID,
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float_or_double[:, :, :, ::1] Tx,
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float_or_double[:, :, :, ::1] Ty,
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float_or_double[:, :, :, ::1] Tz,
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float_or_double[:, :, ::1] Ex,
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float_or_double[:, :, ::1] Ey,
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float_or_double[:, :, ::1] Ez
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):
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"""This function updates a temporary dispersive material array when disperisive materials (with 1 pole) are present.
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Args:
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nx, ny, nz (int): Grid size in cells
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nthreads (int): Number of threads to use
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maxpoles (int): Maximum number of poles
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updatecoeffs, T, ID, E (memoryviews): Access to update coeffients, temporary, ID and field component arrays
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"""
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cdef Py_ssize_t i, j, k
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cdef int material
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# Ex component
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if ny != 1 or nz != 1:
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for i in prange(0, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(1, nz):
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material = ID[0, i, j, k]
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Tx[0, i, j, k] = Tx[0, i, j, k] - updatecoeffsdispersive[material, 2] * Ex[i, j, k]
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# Ey component
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if nx != 1 or nz != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(0, ny):
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for k in range(1, nz):
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material = ID[1, i, j, k]
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Ty[0, i, j, k] = Ty[0, i, j, k] - updatecoeffsdispersive[material, 2] * Ey[i, j, k]
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# Ez component
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if nx != 1 or ny != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(0, nz):
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material = ID[2, i, j, k]
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Tz[0, i, j, k] = Tz[0, i, j, k] - updatecoeffsdispersive[material, 2] * Ez[i, j, k]
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#################################################################
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# Electric field updates - dispersive materials - Drude, Lorenz #
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#################################################################
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cpdef void update_electric_dispersive_multipole_A(
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int nx,
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int ny,
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int nz,
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int nthreads,
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int maxpoles,
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float_or_double[:, ::1] updatecoeffsE,
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real_or_complex[:, ::1] updatecoeffsdispersive,
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np.uint32_t[:, :, :, ::1] ID,
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real_or_complex[:, :, :, ::1] Tx,
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real_or_complex[:, :, :, ::1] Ty,
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real_or_complex[:, :, :, ::1] Tz,
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float_or_double[:, :, ::1] Ex,
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float_or_double[:, :, ::1] Ey,
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float_or_double[:, :, ::1] Ez,
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float_or_double[:, :, ::1] Hx,
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float_or_double[:, :, ::1] Hy,
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float_or_double[:, :, ::1] Hz
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):
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"""This function updates the electric field components when dispersive materials (with multiple poles) are present.
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Args:
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nx, ny, nz (int): Grid size in cells
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nthreads (int): Number of threads to use
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maxpoles (int): Maximum number of poles
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updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
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"""
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cdef Py_ssize_t i, j, k, pole
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cdef int material
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cdef float phi
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# Ex component
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if ny != 1 or nz != 1:
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for i in prange(0, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(1, nz):
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material = ID[0, i, j, k]
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phi = 0
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for pole in range(maxpoles):
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phi = phi + mycreal(updatecoeffsdispersive[material, pole * 3]) * mycreal(Tx[pole, i, j, k])
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Tx[pole, i, j, k] = updatecoeffsdispersive[material, 1 + (pole * 3)] * Tx[pole, i, j, k] + updatecoeffsdispersive[material, 2 + (pole * 3)] * Ex[i, j, k]
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Ex[i, j, k] = updatecoeffsE[material, 0] * Ex[i, j, k] + updatecoeffsE[material, 2] * (Hz[i, j, k] - Hz[i, j - 1, k]) - updatecoeffsE[material, 3] * (Hy[i, j, k] - Hy[i, j, k - 1]) - updatecoeffsE[material, 4] * phi
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# Ey component
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if nx != 1 or nz != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(0, ny):
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for k in range(1, nz):
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material = ID[1, i, j, k]
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phi = 0
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for pole in range(maxpoles):
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phi = phi + mycreal(updatecoeffsdispersive[material, pole * 3]) * mycreal(Ty[pole, i, j, k])
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Ty[pole, i, j, k] = updatecoeffsdispersive[material, 1 + (pole * 3)] * Ty[pole, i, j, k] + updatecoeffsdispersive[material, 2 + (pole * 3)] * Ey[i, j, k]
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Ey[i, j, k] = updatecoeffsE[material, 0] * Ey[i, j, k] + updatecoeffsE[material, 3] * (Hx[i, j, k] - Hx[i, j, k - 1]) - updatecoeffsE[material, 1] * (Hz[i, j, k] - Hz[i - 1, j, k]) - updatecoeffsE[material, 4] * phi
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# Ez component
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if nx != 1 or ny != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(0, nz):
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material = ID[2, i, j, k]
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phi = 0
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for pole in range(maxpoles):
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phi = phi + mycreal(updatecoeffsdispersive[material, pole * 3]) * mycreal(Tz[pole, i, j, k])
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Tz[pole, i, j, k] = updatecoeffsdispersive[material, 1 + (pole * 3)] * Tz[pole, i, j, k] + updatecoeffsdispersive[material, 2 + (pole * 3)] * Ez[i, j, k]
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Ez[i, j, k] = updatecoeffsE[material, 0] * Ez[i, j, k] + updatecoeffsE[material, 1] * (Hy[i, j, k] - Hy[i - 1, j, k]) - updatecoeffsE[material, 2] * (Hx[i, j, k] - Hx[i, j - 1, k]) - updatecoeffsE[material, 4] * phi
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cpdef void update_electric_dispersive_multipole_B(
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int nx,
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int ny,
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int nz,
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int nthreads,
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int maxpoles,
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real_or_complex[:, ::1] updatecoeffsdispersive,
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np.uint32_t[:, :, :, ::1] ID,
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real_or_complex[:, :, :, ::1] Tx,
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real_or_complex[:, :, :, ::1] Ty,
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real_or_complex[:, :, :, ::1] Tz,
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float_or_double[:, :, ::1] Ex,
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float_or_double[:, :, ::1] Ey,
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float_or_double[:, :, ::1] Ez
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):
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"""This function updates a temporary dispersive material array when disperisive materials (with multiple poles) are present.
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Args:
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nx, ny, nz (int): Grid size in cells
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nthreads (int): Number of threads to use
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maxpoles (int): Maximum number of poles
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updatecoeffs, T, ID, E (memoryviews): Access to update coeffients, temporary, ID and field component arrays
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"""
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cdef Py_ssize_t i, j, k, pole
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cdef int material
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# Ex component
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if ny != 1 or nz != 1:
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for i in prange(0, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(1, nz):
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material = ID[0, i, j, k]
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for pole in range(maxpoles):
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Tx[pole, i, j, k] = Tx[pole, i, j, k] - updatecoeffsdispersive[material, 2 + (pole * 3)] * Ex[i, j, k]
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# Ey component
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if nx != 1 or nz != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(0, ny):
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for k in range(1, nz):
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material = ID[1, i, j, k]
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for pole in range(maxpoles):
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Ty[pole, i, j, k] = Ty[pole, i, j, k] - updatecoeffsdispersive[material, 2 + (pole * 3)] * Ey[i, j, k]
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# Ez component
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if nx != 1 or ny != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(0, nz):
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material = ID[2, i, j, k]
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for pole in range(maxpoles):
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Tz[pole, i, j, k] = Tz[pole, i, j, k] - updatecoeffsdispersive[material, 2 + (pole * 3)] * Ez[i, j, k]
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cpdef void update_electric_dispersive_1pole_A(
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int nx,
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int ny,
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int nz,
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int nthreads,
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int maxpoles,
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float_or_double[:, ::1] updatecoeffsE,
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real_or_complex[:, ::1] updatecoeffsdispersive,
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np.uint32_t[:, :, :, ::1] ID,
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real_or_complex[:, :, :, ::1] Tx,
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real_or_complex[:, :, :, ::1] Ty,
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real_or_complex[:, :, :, ::1] Tz,
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float_or_double[:, :, ::1] Ex,
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float_or_double[:, :, ::1] Ey,
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float_or_double[:, :, ::1] Ez,
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float_or_double[:, :, ::1] Hx,
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float_or_double[:, :, ::1] Hy,
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float_or_double[:, :, ::1] Hz
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):
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"""This function updates the electric field components when dispersive materials (with 1 pole) are present.
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Args:
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nx, ny, nz (int): Grid size in cells
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nthreads (int): Number of threads to use
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maxpoles (int): Maximum number of poles
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updatecoeffs, T, ID, E, H (memoryviews): Access to update coeffients, temporary, ID and field component arrays
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"""
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cdef Py_ssize_t i, j, k
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cdef int material
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cdef float phi = 0
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# Ex component
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if ny != 1 or nz != 1:
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for i in prange(0, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(1, nz):
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material = ID[0, i, j, k]
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phi = mycreal(updatecoeffsdispersive[material, 0]) * mycreal(Tx[0, i, j, k])
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Tx[0, i, j, k] = updatecoeffsdispersive[material, 1] * Tx[0, i, j, k] + updatecoeffsdispersive[material, 2] * Ex[i, j, k]
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Ex[i, j, k] = updatecoeffsE[material, 0] * Ex[i, j, k] + updatecoeffsE[material, 2] * (Hz[i, j, k] - Hz[i, j - 1, k]) - updatecoeffsE[material, 3] * (Hy[i, j, k] - Hy[i, j, k - 1]) - updatecoeffsE[material, 4] * phi
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# Ey component
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if nx != 1 or nz != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(0, ny):
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for k in range(1, nz):
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material = ID[1, i, j, k]
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phi = mycreal(updatecoeffsdispersive[material, 0]) * mycreal(Ty[0, i, j, k])
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Ty[0, i, j, k] = updatecoeffsdispersive[material, 1] * Ty[0, i, j, k] + updatecoeffsdispersive[material, 2] * Ey[i, j, k]
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Ey[i, j, k] = updatecoeffsE[material, 0] * Ey[i, j, k] + updatecoeffsE[material, 3] * (Hx[i, j, k] - Hx[i, j, k - 1]) - updatecoeffsE[material, 1] * (Hz[i, j, k] - Hz[i - 1, j, k]) - updatecoeffsE[material, 4] * phi
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# Ez component
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if nx != 1 or ny != 1:
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(0, nz):
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material = ID[2, i, j, k]
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phi = mycreal(updatecoeffsdispersive[material, 0]) * mycreal(Tz[0, i, j, k])
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Tz[0, i, j, k] = updatecoeffsdispersive[material, 1] * Tz[0, i, j, k] + updatecoeffsdispersive[material, 2] * Ez[i, j, k]
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Ez[i, j, k] = updatecoeffsE[material, 0] * Ez[i, j, k] + updatecoeffsE[material, 1] * (Hy[i, j, k] - Hy[i - 1, j, k]) - updatecoeffsE[material, 2] * (Hx[i, j, k] - Hx[i, j - 1, k]) - updatecoeffsE[material, 4] * phi
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cpdef void update_electric_dispersive_1pole_B(
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int nx,
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int ny,
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int nz,
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int nthreads,
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int maxpoles,
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real_or_complex[:, ::1] updatecoeffsdispersive,
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np.uint32_t[:, :, :, ::1] ID,
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real_or_complex[:, :, :, ::1] Tx,
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real_or_complex[:, :, :, ::1] Ty,
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real_or_complex[:, :, :, ::1] Tz,
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float_or_double[:, :, ::1] Ex,
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float_or_double[:, :, ::1] Ey,
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float_or_double[:, :, ::1] Ez
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):
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"""This function updates a temporary dispersive material array when disperisive materials (with 1 pole) are present.
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|
|
|
Args:
|
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nx, ny, nz (int): Grid size in cells
|
|
nthreads (int): Number of threads to use
|
|
maxpoles (int): Maximum number of poles
|
|
updatecoeffs, T, ID, E (memoryviews): Access to update coeffients, temporary, ID and field component arrays
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"""
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cdef Py_ssize_t i, j, k
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cdef int material
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# Ex component
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if ny != 1 or nz != 1:
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for i in prange(0, nx, nogil=True, schedule='static', num_threads=nthreads):
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for j in range(1, ny):
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for k in range(1, nz):
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material = ID[0, i, j, k]
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Tx[0, i, j, k] = Tx[0, i, j, k] - updatecoeffsdispersive[material, 2] * Ex[i, j, k]
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# Ey component
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if nx != 1 or nz != 1:
|
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
|
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for j in range(0, ny):
|
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for k in range(1, nz):
|
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material = ID[1, i, j, k]
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Ty[0, i, j, k] = Ty[0, i, j, k] - updatecoeffsdispersive[material, 2] * Ey[i, j, k]
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|
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# Ez component
|
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if nx != 1 or ny != 1:
|
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for i in prange(1, nx, nogil=True, schedule='static', num_threads=nthreads):
|
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for j in range(1, ny):
|
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for k in range(0, nz):
|
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material = ID[2, i, j, k]
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Tz[0, i, j, k] = Tz[0, i, j, k] - updatecoeffsdispersive[material, 2] * Ez[i, j, k]
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