Silent error detection in numerical time-stepping schemes

This web page contains code and data used in the paper "Silent error detection in numerical time-stepping schemes" by Austin R. Benson, Sven Schmit, and Rob Schreiber.

• The paper is available here.
• Slides from Austin's talk at SIAM PP 2014 are available here.

Disclaimer

This experimental code is published in connection with a scientific publication, Silent error detection in numerical time-stepping schemes, by Austin R. Benson, Sven Schmit, and Robert Schreiber, to appear in International Journal of High Performance Computing Applications. This code is made available solely to allow the readers of that publication to verify and reproduce the results described. This experimental code is published "as is", with no representation, warranty, indemnification of any kind. Hewlett-Packard excludes all liability that may result from the use of this experimental code in any form.

Code

• All of the code: silent_errors_code.zip


• After downloading the data (see below), you can regenerate all of the figures in the paper by running paper_plots.m. Thanks to the wonderful blog post by David Gleich and Tammy Kolda for providing information on creating high-quality graphics in Matlab.

Data

• All of the data is provided in .mat files and is available here: silent_errors_data.zip (43 MB).


• Ordinary differential equations: {AB, RK}_vdp_{2, 3}_{func, prev}.mat.
  'AB' and 'RK' denote whether the data are for Adams-Bashforth (AB) or Runge-Kutta (RK). 2 and 3 denote the value of the damping parameter in the van der Pol equation. 'func' and 'prev' denote whether the corruption was in a function evaluation (func) or in previously computed and stored data (prev). To reproduce the data, run all_ode_gen.m.


• Main results on the heat equation: heat{1, 2, 3}{a, b, c}.mat and heat_results_part{1, 2, 3}.mat.
  The former is pre-computed results for each configuration when no errors occur. The latter contains the data for corruption under Configurations 1, 2, and 3. To reproduce the data, first run heat_gen.m and then run all_heat_exps.m.


• Detection indicators for the heat equation: detector_results.mat.
  To reproduce the data, run detector_gen.m.


• Navier-Stokes equations: ns_{prev, pressure}.mat.
  'prev' and 'pressure' denote whether the corruption was in the previous solution or in the pressure computation. To reproduce the data, run navierstokes_gen.m.

© 2014 Austin Benson