Scientific Computing is the study of methods and procedures to approximate solutions to mathematical problems. Often, we have to approximate solutions because computing the optimal solution takes too long or is not possible to due machine floating point inaccuracy.
The notes in this repo explain how to model physical phenomena as mathematical models. It then models explains how they are used to derive numerical models, which are solved to discover some information about the physical phenomena.
Solving these models takes an enourmous amount of numerical computation. To speed the computation, the models are often solved in parallel, across multiple machines. Methods of distributing work across multiple machines is also covered in these nodes.
git clone https://github.com/DonaldWhyte/notes-parallel-scientific-computing.git
The notes are written in LaTeX. To build the notes, first install LaTeX and pdflatex. This document explains how to install LaTeX on Windows, Mac OS X and various Linux distributions.
Afterwards, navigate into the cloned repository and execute the build script:
cd notes-parallel-scientific-computing
make docs
This will build two PDF documents in the current working directory:
parallel-scientific-computing.pdf-- main document that contains almost all the notesparallel-cw2.pdf-- document comparing the performance of various numeric solvers (e.g. Jacobi, Gauss-Seidel, SOR)
The test programs are written in C. All the test programs are located in
directories within CourseworkWorksheets. To build them, run make programs.
The programs use OpenMPI for parallelism. This means they use mpicc for
building and mpiexec to execute the programs across multiple machines.
You'll need to install OpenMPI to build and run the programs. Instructions on how to install OpenMPI for some platforms is specified below. If your platform is not lsited, then check out the OpenMPI website for instructions on how to install OpenMPI on your platform.
brew install open-mpi
yum install openmpi openmpi-devel environment-modules
module add openmpi-x86_64
Simply run make or make all to build all test programs and documents.
To just build the test programs, run make programs.
The distributed test programs use mpiexec, since several processes are
executed across multiple machines. mpiexec takes a text file that contains
the hostnames of all hosts that can be used to run the distributed programs.
The text file has the format:
hostname1
hostname2
...
hostname4
This repo's makefiles pass mpiexec the path to a host list file. This is
machines.txt at the root fo this repository. You must add the hostnames of
all your worker machinres to machines.txt to run any of the test programs.
After filling in machines.txt, navigate to the directory that contains the program you want to run (e.g. CourseworkWorksheets/worksheet0).
To run that program with the default number of nodes (4), then simply type
make run. To specify the number of nodes/processes to use, type:
make run NUM_NODES=<numberOfNodes>
You can also override the default machines list file path to use a file at a
different location. This can be done using the HOSTFILE argument, like so:
make run HOSTFILE=<pathToMachinesListTextFile>
Credit to University of Leeds and Matthew Hubbard for doing a great job teaching me the fundamentals of parallel scientific computation.