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TeaLeaf is a mini-app that solves the linear heat conduction equation on a spatially decomposed grid using a 5 point stencil with implicit solvers. TeaLeaf solves the equations in two dimensions.

In TeaLeaf temperatures are stored at the cell centres. A conduction coefficient is calculated that is equal to the cell centred density or the reciprocal of the density. This is then averaged to each face of the cell for use in the solution. The solve is carried out using an implicit method due to the severe timestep limitations imposed by the stability criteria of an explicit solution for a parabolic partial differential equation. The implicit method requires the solution of a system of linear equations which form a regular sparse matrix with a well defined structure.

The computation in TeaLeaf has been broken down into "kernels", low level building blocks with minimal complexity. Each kernel loops over the entire grid and updates the relevant mesh variables. Control logic within each kernel is kept to a minimum, allowing maximum optimisation by the compiler. Memory is sacrificed in order to increase performance, and any updates to variables that would introduce dependencies between loop iterations are written into copies of the mesh.

Normally, third party solvers are used to invert the system of linear equations, because of the complexity of state of the art methods. For reference the simplest iterative method, the Jacobi method, has been included in the reference version as the default as well the option to use a Conjugate Gradient (CG), Chebyshev solver and Polynomially Preconditioned CG method. These have the advantage of being matrix free and independent of library dependencies. By deault a pre-conditioner is not invoked, but a simple pre-conditioners are available as an option which just uses diagonal scaling, and block diagonal preconditioning.

The solvers have been written in Fortran with OpenMP and MPI and they have also been ported to OpenCL and CUDA to provide an accelerated capability.

Other versions invoke third party linear solvers and currently include PETSc, Trilinos and Hypre. For each of these version there are instructions on how to download, build and link in the relevant library.

Current Implementations:

  • Fortran with OpenMP and MPI
  • OpenCL
  • Petsc
  • Trilinos
  • Hypre
  • CUDA

TeaLeaf Build Procedure

Dependencies in TeaLeaf have been kept to a minimum to ease the build process across multiple platforms and environments. There is a single makefile for all compilers and adding a new compiler should be straight forward.

In many case just typing make in the required software directory will work. This is the case if the mpif90 and mpicc wrappers are available on the system.

If the MPI compilers have different names then the build process needs to notified of this by defining two environment variables, MPI_COMPILER and C_MPI_COMPILER.

For example on some Intel systems:

make MPI_COMPILER=mpiifort C_MPI_COMPILER=mpiicc

Or on Cray systems:


OpenMP Build

All compilers use different arguments to invoke OpenMP compilation. A simple call to make will invoke the compiler with -O3. This does not usually include OpenMP by default. To build for OpenMP for a specific compiler a further variable must be defined, COMPILER that will then select the correct option for OpenMP compilation.

For example with the Intel compiler:


Which then append the -openmp to the build flags.

Other supported compiler that will be recognised are:-

  • CRAY
  • SUN
  • GNU
  • XL
  • PGI
  • ARM

The default flags for each of these is show below:-

  • INTEL: -O3 -ipo
  • SUN: -fast
  • GNU: -ipo
  • XL: -O5
  • PGI: -O3 -Minline
  • CRAY: -em Note: that by default the Cray compiler with pick the optimum options for performance.

Other Flags

The default compilation with the COMPILER flag set chooses the optimal performing set of flags for the specified compiler, but with no hardware specific options or IEEE compatability.

To produce a version that has IEEE compatiblity a further flag has to be set on the compiler line.


This flag has no effect if the compiler flag is not set because IEEE options are always compiler specific.

For each compiler the flags associated with IEEE are shown below:-

  • INTEL: -fp-model strict –fp-model source –prec-div –prec-sqrt
  • CRAY: -hpflex_mp=intolerant
  • SUN: -fsimple=0 –fns=no
  • GNU: -ffloat-store
  • PGI: -Kieee
  • PATHSCALE: -mieee-fp
  • XL: -qstrict –qfloat=nomaf

Note that the MPI communications have been written to ensure bitwise identical answers independent of core count. However under some compilers this is not true unless the IEEE flags is set to be true. This is certainly true of the Intel and Cray compiler. Even with the IEEE options set, this is not guarantee that different compilers or platforms will produce the same answers. Indeed a Fortran run can give different answers from a C run with the same compiler, same options and same hardware.

Extra options can be added without modifying the makefile by adding two further flags, OPTIONS and C_OPTIONS, one for the Fortran and one for the C options.


A build for a Xeon Phi would just need the -xavx option above replaced by -mmic.

Finally, a DEBUG flag can be set to use debug options for a specific compiler.


These flags are also compiler specific, and so will depend on the COMPILER environment variable.

So on a system without the standard MPI wrappers, for a build that requires OpenMP, IEEE and AVX this would look like so:-

OPTIONS="-xavx" C_OPTIONS="-xavx"

Running the Code

TeaLeaf takes no command line arguments. It expects to find a file called in the directory it is running in.

There are a number of input files that come with the code. To use any of these they simply need to be copied to in the run directory and TeaLeaf invoked. The invocation is system dependent.

For example for a hybrid run:


mpirun -np 8 tea_leaf

Weak and Strong Scaling

Note that with strong scaling, as the task count increases for the same size global problem, the memory use of each task decreases. Eventually, the mesh data starts to fit into the various levels of cache. So even though the communications overhead is increasing, super-scalar leaps in performance can be seen as task count increases. Eventually all cache benefits are gained and the communications dominate.

For weak scaling, memory use stays close to constant and these super-scalar increases aren't seen but the communications overhead stays constant relative to the computational overhead, and scaling remains good.

Other Issues to Consider

System libraries and settings can also have a significant effect on performance.

The use of the HugePage library can make memory access more efficient. The implementation of this is very system specific and the details will not be expanded here.

Variation in clock speed, such as SpeedStep or Turbo Boost, is also available on some hardware and care needs to be taken that the settings are known.

Many systems also allow some level of hyperthreading at a core level. These usually share floating point units and for a code like TeaLeaf, which is floating point intensive and light on integer operations, are unlikely to produce a benefit and more likely to reduce performance.

TeaLeaf is considered a memory bound code. Most data does not stay in cache very long before it is replaced. For this reason, memory speed can have a significant effect on performance. For the same reason, the same is true of hardware caches.

Testing the Results

Even though bitwise answers cannot be expected across systems, answers should be very close, though the iterative nature of the solves and the dependence on reduction in the MPI can affect this. A summary print of state variables is printed out by default every ten diffusion steps and then at the end of the run. This print gives average value of the volume, mass, density, internal energy and temperature. Only temperature should vary with step count because all boundaries are zero flux and there is no material motion. If mass, volume or enegry do not stay constant through a run, then something is seriously wrong.

There is a set of benchmarks contained in the folder Benchmarks to use for testing ranging from small quick tests that can be run on a laptop to full node runs


A mini-app to solve the heat conduction equation




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