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https://github.com/cadet/cadet-semi-analytic

Semi-analytic "arbitrary precision" branch of CADET utilizing analytical solutions in Laplace domain and numerical inversion for models with linear isotherm.
https://github.com/cadet/cadet-semi-analytic

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Semi-analytic "arbitrary precision" branch of CADET utilizing analytical solutions in Laplace domain and numerical inversion for models with linear isotherm.

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README 

        
[![DOI](https://zenodo.org/badge/38963550.svg)](https://doi.org/10.5281/zenodo.14066869)



# CADET - Semi Analytic Extension



The Chromatography Analysis and Design Toolkit (CADET) is developed at the Institute of Bio- and Geosciences 1 (IBG-1) of Forschungszentrum Jülich (FZJ) under supervision of Prof. Eric von Lieres.

This is the semi-analytic extension of the [CADET-Core project](https://github.com/cadet/cadet-core), of which both are freely distributed (under the terms of the GPLv3) as a contribution to the scientific community.

If you find it useful for your own work, we would appreciate acknowledgements of this software and citations of our papers:



* S. Leweke, E. von Lieres (2016): [Fast arbitrary order moments and arbitrary precision solution of the general rate model of column liquid chromatography with linear isotherm](https://doi.org/10.1016/j.compchemeng.2015.09.009), Computers & Chemical Engineering, 84, 350–362.



Please note that the results from the referenced publication can be reproduced exactly using version 1 of the software, which can be [accessed on zenodo](https://doi.org/10.5281/zenodo.14066870).



## Features



* Processes a comprehensive family of chromatography models ([2D GRM, GRM, LRMP, LRM, CSTR](https://cadet.github.io/master/modelling/index.html)) with one component and linear isotherm

* Fast arbitrary order moments using the Laplace transform of the model, algorithmic differentiation, and extrapolation

* Arbitrary inlet profiles via piecewise cubic polynomials in moment calculation

* Arbitrary precision solution of the model using a numerical inverse Laplace transform (can optionally be combined with extrapolation)

* Proven error bounds in case of quasi-stationary binding

* Suited for dynamic and quasi-stationary binding

* Shared memory parallelization using OpenMP

* Supports XML and HDF5 as input formats, CSV for output

* Command line interface

* Multi-platform: Works on Windows, Linux, and Mac OS X



## Get and build CADET-semi-analytic



CADET-semi-analytic has been successfully built and run on the following platforms:



* Windows

* Linux

* Mac OS X



### Dependencies



* A C++11 capable compiler with OpenMP support (e.g., GCC >= 4.7, Clang >= 3.7, MS Visual Studio >= 2010)

* [CMake](http://cmake.org/)

* [HDF5](http://www.hdfgroup.org/HDF5/)

* [GMP](https://gmplib.org/)

* [MPFR](http://www.mpfr.org/)

* [MPC](http://www.multiprecision.org/)

* [MPFR C++](http://www.holoborodko.com/pavel/mpfr) (header-only, distributed along with CADET-semi-analytic)

* [quadpack++](http://sourceforge.net/projects/quadpackpp) (header-only, distributed along with CADET-semi-analytic)

* [CppAD](http://www.coin-or.org/CppAD/) (header-only, distributed along with CADET-semi-analytic)

* [TCLAP: Templatized C++ Command Line Parser](http://sourceforge.net/projects/tclap/) (header-only, distributed along with CADET-semi-analytic)

* [pugixml](http://code.google.com/p/pugixml/) (distributed along with CADET-semi-analytic)

* Optionally: [FADBAD++](http://www.fadbad.com/) (distributed along with CADET-semi-analytic)



### Building



1. Download and build the requirements. Note that CADET-semi-analytic needs the HDF5-C++ library which is not built by default (use `--enable-cxx` when calling `./configure`).

2. Get the [latest source code](https://github.com/modsim/cadet-semi-analytic/archive/master.zip) of CADET-semi-analytic

3. Unpack to the folder `casema/code`

4. Create a new folder `casema/build` and change to it

5. Call `cmake` and use the environment variables `GMP_ROOT`, `MPFR_ROOT`, `MPC_ROOT`, and `HDF5_ROOT` to point CMake to the top level directories of the installed libraries if it does not find them automatically. Use `-DCMAKE_INSTALL_PREFIX` to tell CMake the installation directory and `DCMAKE_CXX_COMPILER` if you want to use a non-default compiler. On Linux a suitable command might look like this (paths need to be adjusted):



  ```

	GMP_ROOT=libs/gmp/ MPFR_ROOT=libs/mpfr/ MPC_ROOT=libs/mpc/ HDF5_ROOT=libs/hdf5/ cmake -DCMAKE_INSTALL_PREFIX=install/ -DCMAKE_CXX_COMPILER=g++-4.8 -DCMAKE_C_COMPILER=gcc-4.8 ../code

  ```

  Note that you need to pass the switch `-DUSE_FADBAD=ON` in order to enable FADBAD++ support.

6. After CMake has successfully run, the software is compiled and installed by executing `make install`



## Using CADET-semi-analytic



CADET-semi-analytic uses the [CADET file format](https://cadet.github.io/master/interface/index.html). However, it is limited to one component and linear isotherms. Example can be found in [CADET-Verification](https://github.com/cadet/CADET-Verification).



Suppose your model is contained in the HDF5 file `model.h5`, then you can compute the chromatogram via the command

  ```

	casema-cli.exe model.h5 -o chromatogram.csv -e 1e-100 -p 250 -P 20 -t 4

  ```

  where no extrapolation method is used and, hence, the convergence detection tolerances are set to 0.

  This command also requests the usage of 250 decimal digits precision arithmetics (but only 20 digits of them are written to file), parallelization using 4 threads, and the total error to be less than 10^(-100).

  Extrapolation is enabled by adding `-x MET` to the command line, where `MET` is one of `ide`, `ads`, `wem`, `wrm`, `iad`, `lum`, `ltm`, `ibt`, `btm`, `nam`, `rem`, or `sgr`.

  The results are written to the file `chromatogram.csv`.



Alternatively, you can choose to write the output to the H5 input file, following the CADET file format.

Note, however, that in this mode, the output precision is constrained by the H5 format, which does not support arbitrary precision, and is instead limited by the numerical limits of the C++ double type.

  ```

	casema-cli.exe model.h5 -e 1e-100 -p 250 -P 20 -t 4

  ```