Integrated Green's Function Poisson Solver (ECP-WarpX#4937)

* [WIP]Integrated Green Function Poisson Solver

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* updated inputs

* Modified IGF.cpp file

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* Latest IGF.cpp

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* Fixed the IGF file

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* IGF final

* IGF file final

* Added BL_PROFILE in IGF file

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* Updated IntegratedGreenFunctionSolver

* Check Compilation Flags

* Added Multiplication

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* removed inputs

* Update Source/ablastr/fields/IntegratedGreenFunctionSolver.cpp

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

* change import orders

* fix macros and add timers

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* update checksums and changed ifdefs

* mod GNUmake

* fix GNUmakefile for real

* heffte ctest

* fix test input name

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* Apply suggestions from code review

* Update Source/ablastr/fields/IntegratedGreenFunctionSolver.cpp

* Start refactoring

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* Continue refactoring

* Finish refactoring

* Fix unused variable

* Fix compilation without heFFTe

* Fix bugs without heFFTe

* Remove unneeded ifdef

* Update checksum

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Alfred Haavaan Mishi <ahmishi@login06.chn.perlmutter.nersc.gov>
Co-authored-by: Alfred Haavaan Mishi <ahmishi@login01.chn.perlmutter.nersc.gov>
Co-authored-by: Alfred Haavaan Mishi <ahmishi@login20.chn.perlmutter.nersc.gov>
Co-authored-by: Arianna Formenti <ariannaformenti@lbl.gov>
Co-authored-by: Remi Lehe <remi.lehe@normalesup.org>

Examples/Tests/open_bc_poisson_solver/CMakeLists.txt

@@ -12,3 +12,15 @@ if(WarpX_FFT)
         OFF  # dependency
     )
 endif()
+
+if(WarpX_HEFFTE)
+    add_warpx_test(
+        test_3d_open_bc_poisson_solver_heffte # name
+        3  # dims
+        2  # nprocs
+        inputs_test_3d_open_bc_poisson_solver_heffte  # inputs
+        analysis.py  # analysis
+        diags/diag1000001  # output
+        OFF  # dependency
+    )
+endif()

Examples/Tests/open_bc_poisson_solver/inputs_test_3d_open_bc_poisson_solver_heffte

@@ -0,0 +1 @@
+FILE = inputs_test_3d_open_bc_poisson_solver

GNUmakefile

@@ -38,6 +38,7 @@ USE_OPENPMD = FALSE
 WarpxBinDir = Bin
 
 USE_FFT = FALSE
+USE_HEFFTE = FALSE
 USE_RZ = FALSE
 
 USE_EB = FALSE

Regression/Checksum/benchmarks_json/test_3d_open_bc_poisson_solver.json

@@ -1,20 +1,20 @@
 {
   "lev=0": {
-    "Bx": 100915975.15792876,
-    "By": 157610677.31483692,
-    "Bz": 2.404060922276648e-13,
-    "Ex": 4.725066923361703e+16,
-    "Ey": 3.0253961494347724e+16,
-    "Ez": 3276584.4383433666,
+    "Bx": 100915975.15403552,
+    "By": 157610677.3147734,
+    "Bz": 1.2276713711194638e-13,
+    "Ex": 4.725066923359797e+16,
+    "Ey": 3.025396149317578e+16,
+    "Ez": 3276584.4383433824,
     "rho": 10994013582437.197
   },
   "electron": {
-    "particle_momentum_x": 5.701279599504008e-19,
-    "particle_momentum_y": 3.650453172860547e-19,
+    "particle_momentum_x": 5.701279599509506e-19,
+    "particle_momentum_y": 3.650453172383178e-19,
     "particle_momentum_z": 1.145432768297242e-10,
     "particle_position_x": 17.31408691249785,
-    "particle_position_y": 0.2583691267187801,
+    "particle_position_y": 0.25836912671878015,
     "particle_position_z": 10066.329600000008,
     "particle_weight": 19969036501.910976
   }
-}
+}

Source/ablastr/fields/IntegratedGreenFunctionSolver.H

@@ -7,6 +7,8 @@
 #ifndef ABLASTR_IGF_SOLVER_H
 #define ABLASTR_IGF_SOLVER_H
 
+#include <ablastr/constant.H>
+
 #include <AMReX_BoxArray.H>
 #include <AMReX_GpuQualifiers.H>
 #include <AMReX_MultiFab.H>
@@ -47,6 +49,35 @@ namespace ablastr::fields
         return G;
     }
 
+    /** @brief add
+     *
+     * @param[in] x x-coordinate of given location
+     * @param[in] y y-coordinate of given location
+     * @param[in] z z-coordinate of given location
+     *
+     * @return the sum of integrated Green function G
+     */
+    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
+    amrex::Real
+    SumOfIntegratedPotential (amrex::Real x, amrex::Real y, amrex::Real z, amrex::Real dx, amrex::Real dy, amrex::Real dz)
+    {
+        using namespace amrex::literals;
+
+
+        amrex::Real const G_value = 1._rt/(4._rt*ablastr::constant::math::pi*ablastr::constant::SI::ep0) * (
+            IntegratedPotential( x+0.5_rt*dx, y+0.5_rt*dy, z+0.5_rt*dz )
+          - IntegratedPotential( x-0.5_rt*dx, y+0.5_rt*dy, z+0.5_rt*dz )
+          - IntegratedPotential( x+0.5_rt*dx, y-0.5_rt*dy, z+0.5_rt*dz )
+          + IntegratedPotential( x-0.5_rt*dx, y-0.5_rt*dy, z+0.5_rt*dz )
+          - IntegratedPotential( x+0.5_rt*dx, y+0.5_rt*dy, z-0.5_rt*dz )
+          + IntegratedPotential( x-0.5_rt*dx, y+0.5_rt*dy, z-0.5_rt*dz )
+          + IntegratedPotential( x+0.5_rt*dx, y-0.5_rt*dy, z-0.5_rt*dz )
+          - IntegratedPotential( x-0.5_rt*dx, y-0.5_rt*dy, z-0.5_rt*dz )
+        );
+
+        return G_value;
+    }
+
     /** @brief Compute the electrostatic potential using the Integrated Green Function method
      *         as in http://dx.doi.org/10.1103/PhysRevSTAB.9.044204
      *