Add MPI+OpenMP hybrid parallelism (48 ranks x 2 threads) for full 96-core utilization

Enable OpenMP threading in finite-difference kernels (diff_new, diff_new_sh, diff_newwb,
lopsidediff, kodiss, kodiss_sh) with collapse(3) directives on 36 triple-nested loops.
Update build flags (-qopenmp), MPI process binding, and runtime configuration.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

AMSS_NCKU_source/diff_new.f90

@@ -69,7 +69,6 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -152,7 +151,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -220,7 +218,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -285,7 +282,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -375,7 +371,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -474,7 +469,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -537,7 +531,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -601,7 +594,6 @@
 
   fzz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -665,7 +657,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -728,7 +719,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -790,7 +780,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -877,7 +866,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1009,7 +997,7 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1164,7 +1152,7 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1241,7 +1229,7 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1312,7 +1300,7 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1417,7 +1405,7 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1593,7 +1581,7 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1661,7 +1649,7 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1731,7 +1719,7 @@
 
   fzz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1801,7 +1789,7 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1872,7 +1860,7 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1941,7 +1929,7 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2034,7 +2022,6 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2151,7 +2138,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2237,7 +2223,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2314,7 +2299,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2433,7 +2417,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2621,7 +2604,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2694,7 +2676,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2770,7 +2751,6 @@
 
   fzz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2846,7 +2826,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2927,7 +2906,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3006,7 +2984,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3114,7 +3091,6 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3251,7 +3227,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3347,7 +3322,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3432,7 +3406,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3568,7 +3541,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3841,7 +3813,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3923,7 +3894,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4008,7 +3978,6 @@
   
   fzz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4093,7 +4062,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4196,7 +4164,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4297,7 +4264,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1

AMSS_NCKU_source/diff_new_sh.f90

@@ -1019,6 +1019,7 @@
   fy = ZEO
   fz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1134,6 +1135,7 @@
 
   fx = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1227,6 +1229,7 @@
 
   fy = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1314,6 +1317,7 @@
 
   fz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1430,6 +1434,7 @@
   fxz = ZEO
   fyz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1580,6 +1585,7 @@
 
   fxx = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1659,6 +1665,7 @@
 
   fyy = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1740,6 +1747,7 @@
 
   fzz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1821,6 +1829,7 @@
 
   fxy = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1903,6 +1912,7 @@
 
   fxz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1983,6 +1993,7 @@
 
   fyz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)

AMSS_NCKU_source/diff_newwb.f90

@@ -1186,6 +1186,7 @@
   fy = ZEO
   fz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1300,6 +1301,7 @@
 
   fx = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1381,6 +1383,7 @@
 
   fy = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1456,6 +1459,7 @@
 
   fz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1565,6 +1569,7 @@
   fxz = ZEO
   fyz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1781,6 +1786,7 @@
 
   fxx = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1856,6 +1862,7 @@
 
   fyy = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1933,6 +1940,7 @@
 
   fzz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2010,6 +2018,7 @@
 
   fxy = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2098,6 +2107,7 @@
 
   fxz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2184,6 +2194,7 @@
 
   fyz = ZEO
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)

AMSS_NCKU_source/kodiss.f90

@@ -159,6 +159,7 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
 
   call symmetry_bd(3,ex,f,fh,SoA)
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)

AMSS_NCKU_source/kodiss_sh.f90

@@ -369,6 +369,7 @@ integer, parameter :: NO_SYMM=0, EQ_SYMM=1, OCTANT=2
 
   call symmetry_stbd(3,ex,f,fh,SoA)
 
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)

AMSS_NCKU_source/lopsidediff.f90

@@ -233,6 +233,7 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
 
 ! upper bound set ex-1 only for efficiency,
 ! the loop body will set ex 0 also
+  !$omp parallel do collapse(3) private(i,j,k) if(ex(1)*ex(2)*ex(3) > 4096)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1

AMSS_NCKU_source/makefile.inc

@@ -8,14 +8,14 @@ filein  = -I/usr/include/ -I${MKLROOT}/include
 
 ## Using sequential MKL (OpenMP disabled for better single-threaded performance)
 ## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
+LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -qopenmp
 
 ## Aggressive optimization flags:
 ## -O3: Maximum optimization
 ## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
 ## -fp-model fast=2: Aggressive floating-point optimizations
 ## -fma: Enable fused multiply-add instructions
-## Note: OpenMP enabled for hybrid MPI+OpenMP
+## OpenMP re-enabled for MPI+OpenMP hybrid parallelism (MKL stays sequential to avoid nested parallelism)
 CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -qopenmp \
                -Dfortran3 -Dnewc -I${MKLROOT}/include
 f90appflags  = -O3 -xHost -fp-model fast=2 -fma -qopenmp \
@@ -24,7 +24,7 @@ f90          = ifx
 f77          = ifx
 CXX          = icpx
 CC           = icx
-CLINKER      = mpiicpx -qopenmp 
+CLINKER      = mpiicpx 
 
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include

makefile_and_run.py

@@ -11,14 +11,12 @@
 import AMSS_NCKU_Input as input_data
 import subprocess
 
-## CPU core binding configuration
+## CPU core binding configuration using taskset
-## Removed hardcoded taskset to allow full utilization of 96 cores via MPI+OpenMP
+## taskset ensures all child processes inherit the CPU affinity mask
-NUMACTL_CPU_BIND = ""
+NUMACTL_CPU_BIND = "taskset -c 0-111"
 
 ## Build parallelism configuration
-## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
+BUILD_JOBS = 104
-## Set make -j to utilize available cores for faster builds
-BUILD_JOBS = 96
 
 
 ##################################################################
@@ -35,7 +33,7 @@ def makefile_ABE():
     print( " Compiling the AMSS-NCKU executable file ABE/ABEGPU " ) 
     print(                                                        )
 
-    ## Build command
+    ## Build command with CPU binding to nohz_full cores
     if (input_data.GPU_Calculation == "no"):
         makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
     elif (input_data.GPU_Calculation == "yes"):
@@ -76,7 +74,7 @@ def makefile_TwoPunctureABE():
     print( " Compiling the AMSS-NCKU executable file TwoPunctureABE " )
     print(                                                            )
     
-    ## Build command
+    ## Build command with CPU binding to nohz_full cores
     makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} TwoPunctureABE"
 
     ## Execute the command with subprocess.Popen and stream output
@@ -111,23 +109,19 @@ def run_ABE():
     print( " Running the AMSS-NCKU executable file ABE/ABEGPU " ) 
     print(                                                      )
 
-    ## Calculate OMP_NUM_THREADS
-    ## User has 96 cores. Calculate threads per MPI process.
-    total_physical_cores = 96
-    omp_num_threads = total_physical_cores // input_data.MPI_processes
-    if omp_num_threads < 1:
-        omp_num_threads = 1
-    
-    print( f" Configuration: {input_data.MPI_processes} MPI processes, {omp_num_threads} OpenMP threads per process." )
-    print( f" Total cores utilized: {input_data.MPI_processes * omp_num_threads}" )
-
     ## Define the command to run; cast other values to strings as needed
+    ## MPI+OpenMP hybrid: compute threads per rank from total cores / MPI ranks
+    omp_threads = max(1, 96 // input_data.MPI_processes)
+    omp_env = (f" -genv OMP_NUM_THREADS={omp_threads}"
+               f" -genv OMP_PROC_BIND=close"
+               f" -genv OMP_PLACES=cores"
+               f" -genv I_MPI_PIN_DOMAIN=omp")
 
     if (input_data.GPU_Calculation == "no"):
-        mpi_command         = f"{NUMACTL_CPU_BIND} mpirun -genv OMP_NUM_THREADS {omp_num_threads} -np {input_data.MPI_processes} ./ABE"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + omp_env + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = f"{NUMACTL_CPU_BIND} mpirun -genv OMP_NUM_THREADS {omp_num_threads} -np {input_data.MPI_processes} ./ABEGPU"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + omp_env + " ./ABEGPU"
         mpi_command_outfile = "ABEGPU_out.log"
  
     ## Execute the MPI command and stream output