Add a tutorial that computes energy spectrum

ExampleCodes/FFT/EnergySpectrum/GNUmakefile

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+AMREX_HOME ?= ../../../../amrex
+
+DEBUG = FALSE
+DIM = 3
+COMP = gcc
+USE_MPI = TRUE
+USE_CUDA = FALSE
+USE_HIP = FALSE
+USE_FFT = TRUE
+
+BL_NO_FORT = TRUE
+
+include $(AMREX_HOME)/Tools/GNUMake/Make.defs
+include $(AMREX_HOME)/Src/Base/Make.package
+include $(AMREX_HOME)/Src/FFT/Make.package
+include Make.package
+
+
+include $(AMREX_HOME)/Tools/GNUMake/Make.rules

ExampleCodes/FFT/EnergySpectrum/Make.package

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+CEXE_sources += main.cpp

ExampleCodes/FFT/EnergySpectrum/README

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+This tutorial provides an example of computing the kinetic energy spectrum
+of velocity.
+
+To run this tutorial, one can generate the input data first with the incflo
+code (https://github.com/AMReX-Fluids/incflo).
+
+    $ cd ../../../../
+    $ git clone https://github.com/AMReX-Fluids/AMReX-Hydro.git
+    $ git clone https://github.com/AMReX-Fluids/incflo.git
+    $ cd incflo/test_no_eb_3d
+    $ make -j
+    $ mpiexec -n 4 ./incflo3d.gnu.MPI.ex benchmark.taylor_green_vortices stop_time=0.1 amr.max_level=0 amr.n_cell="64 64 64" geometry.prob_hi="1.0 1.0 1.0"
+    $ # Assuming plt00030 is the plotfile you want to use.
+    $ cp -r plt00030 ../../amrex-tutorials/ExampleCodes/FFT/EnergySpectrum/plot
+    $ cd ../../amrex-tutorials/ExampleCodes/FFT/EnergySpectrum
+

ExampleCodes/FFT/EnergySpectrum/main.cpp

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+#include <AMReX.H>
+#include <AMReX_FFT.H>
+#include <AMReX_PlotFileUtil.H>
+
+using namespace amrex;
+
+int main (int argc, char* argv[])
+{
+    amrex::Initialize(argc, argv);
+    {
+        Geometry geom;
+        MultiFab vx, vy, vz;
+        {
+            PlotFileData plot("plot");
+            geom.define(plot.probDomain(0),
+                        RealBox(plot.probLo(), plot.probHi()),
+                        plot.coordSys(), {1,1,1});
+            vx = plot.get(0, "velx");
+            vy = plot.get(0, "vely");
+            vz = plot.get(0, "velz");
+        }
+
+        cMultiFab cx, cy, cz;
+        {
+            FFT::R2C<Real,FFT::Direction::forward> fft(geom.Domain());
+            auto const& [ba, dm] = fft.getSpectralDataLayout();
+            cx.define(ba,dm,1,0);
+            cy.define(ba,dm,1,0);
+            cz.define(ba,dm,1,0);
+            fft.forward(vx, cx);
+            fft.forward(vy, cy);
+            fft.forward(vz, cz);
+        }
+
+        // For simplicity, we assume the domain is a cube, and we are not
+        // going to worry about scaling.
+
+        int nx = geom.Domain().length(0);
+        int ny = geom.Domain().length(1);
+        int nz = geom.Domain().length(2);
+        int nk = nx;
+        Gpu::DeviceVector<Real> ke(nk,Real(0.0));
+        Real* pke = ke.data();
+        auto const& cxa = cx.const_arrays();
+        auto const& cya = cy.const_arrays();
+        auto const& cza = cz.const_arrays();
+        ParallelFor(cx, [=] AMREX_GPU_DEVICE (int b, int i, int j, int k)
+        {
+            int ki = i;
+            int kj = (j <= ny/2) ? j : ny-j;
+            int kk = (k <= nz/2) ? k : nz-k;
+            Real d = std::sqrt(Real(ki*ki+kj*kj+kk*kk));
+            int di = int(std::round(d));
+            if (di < nk) {
+                Real value = amrex::norm(cxa[b](i,j,k))
+                    +        amrex::norm(cya[b](i,j,k))
+                    +        amrex::norm(cza[b](i,j,k));
+                HostDevice::Atomic::Add(pke+di, value);
+            }
+        });
+
+#ifdef AMREX_USE_GPU
+        Gpu::HostVector<Real> ke_h(ke.size());
+        Gpu::copyAsync(Gpu::deviceToHost, ke.begin(), ke.end(), ke_h.begin());
+        Gpu::streamSynchronize();
+        Real* pke_h = ke_h.data();
+#else
+        Real* pke_h = pke;
+#endif
+
+        ParallelDescriptor::ReduceRealSum(pke_h, nk);
+
+        if (ParallelDescriptor::IOProcessor()) {
+            std::ofstream ofs("spectrum.txt");
+            for (int i = 0; i < nk; ++i) {
+                ofs << i << " " << pke_h[i] << "\n";
+            }
+        }
+    }
+    amrex::Finalize();
+}