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, 6 insertions, 5 deletions

diff --git a/Source/FieldSolver/SpectralSolver/SpectralFieldData.H b/Source/FieldSolver/SpectralSolver/SpectralFieldData.H
index 4ab88f1a3..c7848d731 100644
--- a/Source/FieldSolver/SpectralSolver/SpectralFieldData.H
+++ b/Source/FieldSolver/SpectralSolver/SpectralFieldData.H
@@ -83,18 +83,19 @@ class SpectralFieldIndex
     // Always
     int Ex = -1, Ey = -1, Ez = -1;
     int Bx = -1, By = -1, Bz = -1;
-    int Jx = -1, Jy = -1, Jz = -1;
-    int rho_old = -1, rho_new = -1, divE = -1;
+    int divE = -1;
 
     // Time averaging
     int Ex_avg = -1, Ey_avg = -1, Ez_avg = -1;
     int Bx_avg = -1, By_avg = -1, Bz_avg = -1;
 
-    // J linear in time
+    // J
+    int Jx_old = -1, Jy_old = -1, Jz_old = -1;
+    int Jx_mid = -1, Jy_mid = -1, Jz_mid = -1;
     int Jx_new = -1, Jy_new = -1, Jz_new = -1;
 
-    // rho quadratic in time
-    int rho_mid = -1;
+    // rho
+    int rho_old = -1, rho_mid = -1, rho_new = -1;
 
     // div(E) and div(B) cleaning
     int F = -1, G = -1;