Add semi-implicit CI test (ECP-WarpX#4565)

* Add semi-implicit CI test

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update CI benchmark values

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Examples/Tests/Implicit/analysis_1d.py

@@ -10,6 +10,7 @@
 # This is a script that analyses the simulation results from
 # the script `inputs_1d`. This simulates a 1D periodic plasma using the implicit solver.
 import os
+import re
 import sys
 
 import numpy as np
@@ -28,7 +29,11 @@
 delta_E = (total_energy - total_energy[0])/total_energy[0]
 max_delta_E = np.abs(delta_E).max()
 
-tolerance_rel = 1.e-14
+if re.match('SemiImplicitPicard_1d', fn):
+    tolerance_rel = 2.5e-5
+elif re.match('ImplicitPicard_1d', fn):
+    # This case should have near machine precision conservation of energy
+    tolerance_rel = 1.e-14
 
 print(f"max change in energy: {max_delta_E}")
 print(f"tolerance: {tolerance_rel}")

Examples/Tests/Implicit/inputs_1d_semiimplicit

@@ -0,0 +1,81 @@
+#################################
+############ CONSTANTS #############
+#################################
+
+my_constants.n0 = 1.e30          # plasma densirty, m^-3
+my_constants.nz = 40             # number of grid cells
+my_constants.Ti = 100.           # ion temperature, eV
+my_constants.Te = 100.           # electron temperature, eV
+my_constants.wpe = q_e*sqrt(n0/(m_e*epsilon0))  # electron plasma frequency, radians/s
+my_constants.de0 = clight/wpe    # skin depth, m
+my_constants.nppcz = 100         # number of particles/cell in z
+my_constants.dt = 0.1/wpe        # time step size, s
+
+#################################
+####### GENERAL PARAMETERS ######
+#################################
+
+max_step = 100
+amr.n_cell = nz
+amr.max_level = 0
+
+geometry.dims = 1
+geometry.prob_lo = 0.0
+geometry.prob_hi = 10.*de0
+boundary.field_lo = periodic
+boundary.field_hi = periodic
+boundary.particle_lo = periodic
+boundary.particle_hi = periodic
+
+#################################
+############ NUMERICS ###########
+#################################
+
+warpx.const_dt = dt
+algo.evolve_scheme = semi_implicit_picard
+algo.max_picard_iterations = 5
+algo.picard_iteration_tolerance = 0.
+algo.current_deposition = esirkepov
+algo.field_gathering = energy-conserving
+algo.particle_shape = 2
+warpx.use_filter = 0
+
+#################################
+############ PLASMA #############
+#################################
+
+particles.species_names = electrons protons
+
+electrons.species_type = electron
+electrons.injection_style = "NUniformPerCell"
+electrons.num_particles_per_cell_each_dim = nppcz
+electrons.profile = constant
+electrons.density = n0
+electrons.momentum_distribution_type = gaussian
+electrons.ux_th = sqrt(Te*q_e/m_e)/clight
+electrons.uy_th = sqrt(Te*q_e/m_e)/clight
+electrons.uz_th = sqrt(Te*q_e/m_e)/clight
+
+protons.species_type = proton
+protons.injection_style = "NUniformPerCell"
+protons.num_particles_per_cell_each_dim = nppcz
+protons.profile = constant
+protons.density = n0
+protons.momentum_distribution_type = gaussian
+protons.ux_th = sqrt(Ti*q_e/m_p)/clight
+protons.uy_th = sqrt(Ti*q_e/m_p)/clight
+protons.uz_th = sqrt(Ti*q_e/m_p)/clight
+
+# Diagnostics
+diagnostics.diags_names = diag1
+diag1.intervals = 100
+diag1.diag_type = Full
+diag1.fields_to_plot = Ex Ey Ez Bx By Bz jx jy jz rho divE
+diag1.electrons.variables = w ux uy uz
+diag1.protons.variables = w ux uy uz
+
+warpx.reduced_diags_names = particle_energy field_energy
+particle_energy.type = ParticleEnergy
+particle_energy.intervals = 1
+field_energy.type = FieldEnergy
+field_energy.intervals = 1

Regression/Checksum/benchmarks_json/SemiImplicitPicard_1d.json

@@ -0,0 +1,29 @@
+{
+  "lev=0": {
+    "Bx": 3559.0541122456157,
+    "By": 1685.942868827529,
+    "Bz": 0.0,
+    "Ex": 796541204346.5195,
+    "Ey": 961740397927.6577,
+    "Ez": 3528140764527.8877,
+    "divE": 2.0829159085076083e+21,
+    "jx": 7.683674095607745e+17,
+    "jy": 1.4132459141738875e+18,
+    "jz": 1.350650739310074e+18,
+    "rho": 18442528652.19583
+  },
+  "protons": {
+    "particle_momentum_x": 5.231109104020749e-19,
+    "particle_momentum_y": 5.367985047933474e-19,
+    "particle_momentum_z": 5.253213505843665e-19,
+    "particle_position_x": 0.00010628272743703473,
+    "particle_weight": 5.314093261582036e+22
+  },
+  "electrons": {
+    "particle_momentum_x": 1.196357181461066e-20,
+    "particle_momentum_y": 1.2271903040162696e-20,
+    "particle_momentum_z": 1.2277743615209627e-20,
+    "particle_position_x": 0.0001064956905491333,
+    "particle_weight": 5.314093261582036e+22
+  }
+}

Regression/WarpX-tests.ini

@@ -4479,3 +4479,20 @@ compileTest = 0
 doVis = 0
 compareParticles = 1
 analysisRoutine = Examples/Tests/Implicit/analysis_1d.py
+
+[SemiImplicitPicard_1d]
+buildDir = .
+inputFile = Examples/Tests/Implicit/inputs_1d_semiimplicit
+runtime_params = warpx.abort_on_warning_threshold=high
+dim = 1
+addToCompileString =
+cmakeSetupOpts = -DWarpX_DIMS=1
+restartTest = 0
+useMPI = 1
+numprocs = 2
+useOMP = 0
+numthreads = 1
+compileTest = 0
+doVis = 0
+compareParticles = 1
+analysisRoutine = Examples/Tests/Implicit/analysis_1d.py