PSATD: Implement First-Order Equations (#3466)

* Implement First-Order PSATD Equations

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

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

* Fix Unused Parameter Warning

* Fix RZ Build

* Fix Normalization of G to Match PML

* Add CI Test: 3D Uniform Plasma

* Cleaning

* Update 2D CI Checksums

* Update 3D CI Checksums

* Add F,G to CI Checksums of `uniform_plasma_multiJ`

* Allow User to Choose First-Order v. Second-Order

* Add WARPX_ALWAYS_ASSERT_WITH_MESSAGE

* Rename New Class `PsatdAlgorithmFirstOrder`

* Remove Inline Comment

* Update RZ CI Checksums

* Fix inline comment

* Use auxiliary variables to avoid divisions

* Use auxiliary variables to avoid divisions

* Make `nci_psatd_stability` dir and merge inputs

* Move all Galilean tests to `nci_psatd_stability`

* Fix CI

* Fix index for backward FFT of J

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

1 files changed, 13 insertions, 7 deletions

diff --git a/Source/FieldSolver/SpectralSolver/SpectralFieldData.cpp b/Source/FieldSolver/SpectralSolver/SpectralFieldData.cpp
index 56189e0ff..e1db4e5ab 100644
--- a/Source/FieldSolver/SpectralSolver/SpectralFieldData.cpp
+++ b/Source/FieldSolver/SpectralSolver/SpectralFieldData.cpp
@@ -51,10 +51,8 @@ SpectralFieldIndex::SpectralFieldIndex (const bool update_with_rho,
     {
         Ex = c++; Ey = c++; Ez = c++;
         Bx = c++; By = c++; Bz = c++;
-        Jx = c++; Jy = c++; Jz = c++;
 
         // TODO Allocate rho_old and rho_new only when needed
-        rho_old = c++; rho_new = c++;
 
         // Reuse data corresponding to index Bx = 3 to avoid storing extra memory
         divE = 3;
@@ -69,17 +67,25 @@ SpectralFieldIndex::SpectralFieldIndex (const bool update_with_rho,
 
         if (divb_cleaning) G = c++;
 
-        if (J_in_time == JInTime::Linear)
+        if (J_in_time == JInTime::Constant)
         {
-            Jx_new = c++;
-            Jy_new = c++;
-            Jz_new = c++;
+            Jx_mid = c++; Jy_mid = c++; Jz_mid = c++;
+        }
+        else if (J_in_time == JInTime::Linear)
+        {
+            Jx_old = c++; Jy_old = c++; Jz_old = c++;
+            Jx_new = c++; Jy_new = c++; Jz_new = c++;
         }
 
-        if (rho_in_time == RhoInTime::Quadratic)
+        if (rho_in_time == RhoInTime::Constant)
         {
             rho_mid = c++;
         }
+        else if (rho_in_time == RhoInTime::Linear)
+        {
+            rho_old = c++;
+            rho_new = c++;
+        }
 
         if (pml_rz)
         {