Tutorial 4: Parallel solution of the heat transport equation

In this exercise, we will parallelize the three-dimensional solution of the heat transport equation from tutorial 3. The goals are to

• …understand how to work with MPI-parallel programs.
• …understand how domain decomposition work with FFTs.

Three-dimensional steady-state problem

We will in this tutorial look back at the 3D variant of the implicit (steady-state) heat transport problem. The steady-state equation for which $\partial T/\partial t=0$, i.e. the solution where the temperature field does not change anymore, is given by

\[R \equiv \alpha \nabla^2 T + \dot{q}_S=0.\]

Note that $R$ is called the residual and the objective of a numerical solution of these equations is to minimize the residual given an approximation to the function $T(x)$.

muGrid and muFFT

We now need to switch to a library that support MPI-parallelization. We will use muGrid and muFFT, which provide an abstraction layer to a variety of FFT implementation. You can find the relevant information here:

• muGrid repository, muGrid documentation
• muFFT repository, muFFT documentation

Task 1: Read the manual

Look at the documentation of muGrid and muFFT and familarize yourself with these libraries.

Task 2: Serial solver with muFFT

Convert your serial solver to use muFFT.

Task 3: Parallel solver with muFFT

Parallelize your solver.