Staircased embedded boundaries in the YEE solver (#1881)

* Added staircased embedded boundaris to the YEE solver

* adding spherical resonating cavity test

* adding functions for fields initialization

* style adjustments

* fixing tabs

* fixed name of analysis script

* fixed name of analysis script

* fixed a few wrong preprocessor directives

* workaround for missing boost

* Revert "workaround for missing boost"

This reverts commit 601f9eb2ec6f8c2100304379b2bea1c6cf9d1851.

* another workaround for missing boost

* getting rid of boost by depending on c++17

* Removed a few unused variables

* adding USE_EB to addToCompileString for EB testing

* removed tabs

* fixing the inputs name for EB sphere test

* shortened the test

* zero padding the names of the images

* adjusted two for loops

* removed some unused variables

* improving the fields initialization

* removed the sphere test and implemented the cube test

* fixed edges lengths computation and added comments

* Fixed the case of all_regular geometries

* fixing a bug that was breaking some tests

* adding test folder

* fixed the default values for the EB cube test

* simplified the analysis script

* fixed cubic resonator default results

* inputting the plot file name from command line

* fixing the diag name

* Fixed a bug in edges initialization

Co-authored-by: Remi Lehe <remi.lehe@normalesup.org>

* Adding comments to the staircased yee solver (thanks Remi)

Co-authored-by: Remi Lehe <remi.lehe@normalesup.org>

* fixed the cube resonator test

* removed an unused import

Co-authored-by: Remi Lehe <remi.lehe@normalesup.org>

1 files changed, 86 insertions, 0 deletions

diff --git a/Examples/Modules/embedded_boundary_cube/analysis_fields.py b/Examples/Modules/embedded_boundary_cube/analysis_fields.py
new file mode 100644
index 000000000..58dad1bb7
--- /dev/null
+++ b/Examples/Modules/embedded_boundary_cube/analysis_fields.py
@@ -0,0 +1,86 @@
+#! /usr/bin/env python
+
+import yt
+import os, sys
+from scipy.constants import mu_0, pi, c
+import numpy as np
+sys.path.insert(1, '../../../../warpx/Regression/Checksum/')
+import checksumAPI
+
+# This is a script that analyses the simulation results from
+# the script `inputs_3d`. This simulates a TMmnp mode in a PEC cubic resonator.
+# The magnetic field in the simulation is given (in theory) by:
+# $$ B_x = \frac{-2\mu}{h^2}\, k_x k_z \sin(k_x x)\cos(k_y y)\cos(k_z z)\cos( \omega_p t)$$
+# $$ B_y = \frac{-2\mu}{h^2}\, k_y k_z \cos(k_x x)\sin(k_y y)\cos(k_z z)\cos( \omega_p t)$$
+# $$ B_z = \cos(k_x x)\cos(k_y y)\sin(k_z z)\sin( \omega_p t)$$
+# with
+# $$ h^2 = k_x^2 + k_y^2 + k_z^2$$
+# $$ k_x = \frac{m\pi}{L}$$
+# $$ k_y = \frac{n\pi}{L}$$
+# $$ k_z = \frac{p\pi}{L}$$
+
+hi = [0.8, 0.8, 0.8]
+lo = [-0.8, -0.8, -0.8]
+ncells = [48, 48, 48]
+dx = (hi[0] - lo[0])/ncells[0]
+dy = (hi[1] - lo[1])/ncells[1]
+dz = (hi[2] - lo[2])/ncells[2]
+m = 0
+n = 1
+p = 1
+Lx = 1
+Ly = 1
+Lz = 1
+h_2 = (m * pi / Lx) ** 2 + (n * pi / Ly) ** 2 + (p * pi / Lz) ** 2
+t = 1.3342563807926085e-08
+
+# Compute the analytic solution
+Bx_th = np.zeros(ncells)
+By_th = np.zeros(ncells)
+Bz_th = np.zeros(ncells)
+for i in range(ncells[0]):
+    for j in range(ncells[1]):
+        for k in range(ncells[2]):
+            x = i*dx + lo[0]
+            y = (j+0.5)*dy + lo[1]
+            z = k*dz + lo[2]
+
+            By_th[i, j, k] = -2/h_2*mu_0*(n * pi/Ly)*(p * pi/Lz) * (np.cos(m * pi/Lx * (x - Lx/2)) *
+                                                                    np.sin(n * pi/Ly * (y - Ly/2)) *
+                                                                    np.cos(p * pi/Lz * (z - Lz/2)) *
+                                                                    (-Lx/2 <= x < Lx/2) *
+                                                                    (-Ly/2 <= y < Ly/2) *
+                                                                    (-Lz/2 <= z < Lz/2) *
+                                                                    np.cos(np.sqrt(2) *
+                                                                    np.pi / Lx * c * t))
+
+            x = i*dx + lo[0]
+            y = j*dy + lo[1]
+            z = (k+0.5)*dz + lo[2]
+            Bz_th[i, j, k] = mu_0*(np.cos(m * pi/Lx * (x - Lx/2)) *
+                                   np.cos(n * pi/Ly * (y - Ly/2)) *
+                                   np.sin(p * pi/Lz * (z - Lz/2)) *
+                                   (-Lx/2 <= x < Lx/2) *
+                                   (-Ly/2 <= y < Ly/2) *
+                                   (-Lz/2 <= z < Lz/2) *
+                                   np.cos(np.sqrt(2) * np.pi / Lx * c * t))
+
+# Open the right plot file
+filename = sys.argv[1]
+ds = yt.load(filename)
+data = ds.covering_grid(level=0, left_edge=ds.domain_left_edge, dims=ds.domain_dimensions)
+
+rel_tol_err = 1e-1
+
+# Compute relative l^2 error on By
+By_sim = data['By'].to_ndarray()
+rel_err_y = np.sqrt( np.sum(np.square(By_sim - By_th)) / np.sum(np.square(By_th)))
+assert(rel_err_y < rel_tol_err)
+# Compute relative l^2 error on Bz
+Bz_sim = data['Bz'].to_ndarray()
+rel_err_z = np.sqrt( np.sum(np.square(Bz_sim - Bz_th)) / np.sum(np.square(Bz_th)))
+assert(rel_err_z < rel_tol_err)
+
+test_name = os.path.split(os.getcwd())[1]
+
+checksumAPI.evaluate_checksum(test_name, filename)