Jussi Enkovaara committed Jul 03, 2018 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 ``````Two dimensional heat equation ============================= This folder contains a code which solves two dimensional heat equation with MPI parallelization. The code features non-blocking point-to-point communication, user defined datatypes, collective communication, and parallel I/O with MPI I/O. Heat (or diffusion) equation is ![img](http://quicklatex.com/cache3/d2/ql_b3f6b8bdc3a8862c73c5a97862afb9d2_l3.png) where **u(x, y, t)** is the temperature field that varies in space and time, and α is thermal diffusivity constant. The two dimensional Laplacian can be discretized with finite differences as ![img](http://quicklatex.com/cache3/2d/ql_59f49ed64dbbe76704e0679b8ad7c22d_l3.png) Given an initial condition (u(t=0) = u0) one can follow the time dependence of the temperature field with explicit time evolution method: ![img](http://quicklatex.com/cache3/9e/ql_9eb7ce5f3d5eccd6cfc1ff5638bf199e_l3.png) Note: Algorithm is stable only when ![img](http://quicklatex.com/cache3/d1/ql_0e7107049c9183d11dbb1e81174280d1_l3.png) The two dimensional grid is decomposed along both dimensions, and the communication of boundary data is overlapped with computation. Restart files are written and read with MPI I/O. Compilation instructions ------------------------ For building and running the example one needs to have the [libpng](http://www.libpng.org/pub/png/libpng.html) library installed. In addition, working MPI environment is required. For Python version mpi4py and matplotlib are needed. Move to proper subfolder (C or Fortran) and modify the top of the **Makefile** according to your environment (proper compiler commands and compiler flags). Code can be build simple with **make** How to run ---------- The number of MPI ranks has to be a factor of the grid dimension (default `````` Jussi Enkovaara committed Jul 03, 2018 60 ``````dimension is 2000). The default initial temperature field is a disk. Initial `````` Jussi Enkovaara committed Jul 03, 2018 61 62 63 64 65 66 67 68 69 70 71 72 73 74 ``````temperature field can be read also from a file, the provided **bottle.dat** illustrates what happens to a cold soda bottle in sauna. * Running with defaults: mpirun -np 4 ./heat_mpi * Initial field from a file: mpirun -np 4 ./heat_mpi bottle.dat * Initial field from a file, given number of time steps: mpirun -np 4 ./heat_mpi bottle.dat 1000 * Defauls pattern with given dimensions and time steps: mpirun -np 4 ./heat_mpi 800 800 1000 The program produces a series of heat_XXXX.png files which show the time development of the temperature field ``````