Heat Equation

Description: Discretization of the Heat Equation

This benchmark represents a discretized one-dimensional heat equation model. More details can be found in .

For a large-scale heat equation example see the steel profile benchmark.

Origin

This benchmark is part of the SLICOT Benchmark Examples for Model Reduction .

Data

The system matrices $A$, $B$, $C$, $E$ are available from the SLICOT benchmarks page: heat-disc.zip and are stored as MATLAB .mat file.

Dimensions

System structure:

$\begin{array}{rcl}E\dot{x}(t)& =& Ax(t)+Bu(t)\\ y(t)& =& Cx(t)\end{array}$

System dimensions:

$A\in {\mathbb{ℝ}}^{200\times 200}$, $B\in {\mathbb{ℝ}}^{200\times 1}$, $C\in {\mathbb{ℝ}}^{1\times 200}$, $E\in {\mathbb{ℝ}}^{200\times 200}$.

Citation

To cite this benchmark, use the following references:

• For the benchmark itself and its data:

Niconet e.V., SLICOT - Subroutine Library in Systems and Control Theory, http://www.slicot.org

@MANUAL{slicot_heat,
 title =        {{SLICOT} - Subroutine Library in Systems and Control Theory},
 organization = {Niconet e.V.}
 address =      {\url{http://www.slicot.org}},
 key =          {SLICOT}
}

• For the background on the benchmark:

@TECHREPORT{morChaV92,
 author =       {Y. Chahlaoui, P. Van Dooren},
 title =        {A collection of Benchmark examples for model reduction of linear time invariant dynamical systems},
 institution =  {SLICOT Working Note},
 number =       {2002-2},
 year =         {2002},
 url =          {http://eprints.maths.manchester.ac.uk/1040/1/ChahlaouiV02a.pdf}
}