Correction of the computation of the energy spectrum (#154)

---------

Co-authored-by: Weiqun Zhang <[email protected]>

Author: QuentinMale

ExampleCodes/FFT/EnergySpectrum/main.cpp

@@ -22,6 +22,8 @@ int main (int argc, char* argv[])
 
         cMultiFab cx, cy, cz;
         {
+            // Note that the complex Hermitian output array Y has (nx/2+1,ny,nz) elements.
+            // Y[nx-i,j,k] = Y[i,j,k]*
             FFT::R2C<Real,FFT::Direction::forward> fft(geom.Domain());
             auto const& [ba, dm] = fft.getSpectralDataLayout();
             cx.define(ba,dm,1,0);
@@ -55,6 +57,12 @@ int main (int argc, char* argv[])
                 Real value = amrex::norm(cxa[b](i,j,k))
                     +        amrex::norm(cya[b](i,j,k))
                     +        amrex::norm(cza[b](i,j,k));
+                // Account for Hermitian symmetry in x-direction
+                // Hermitian symmetry Y[nx-i,j,k] = Y[i,j,k]*
+                if ((i > 0) && (2*i != nx)) {
+                    // Multiply by 2 because we have +ki and -ki
+                    value *= Real(2.0);
+                }
                 HostDevice::Atomic::Add(pke+di, value);
             }
         });