Code for the Paper "The Shifted Proper Orthogonal Decomposition: a Mode Decomposition for Multiple Transport Phenomena"

The aim of this code is to run the numerical examples from [1]. We stress that this is a proof-of-concept code and not tested or optimized for productional purposes. 

The files which are the most relevant ones for the user are

sPOD.m:   					main file,
config_sPOD.m: 					specifies the case,
parameter.m:        				specifies the parameters for the corresponding case,
subspaceDecompositionBySPODiteration.m: 	performs the sPOD algorithm as described in [1].

The folder structure is as follows. The folder USER contains the parameter files for all implemented cases. Also other case-specific files like scripts for generating snapshot data and for plots can be found here. All other functions and scripts are contained in LIB. The folder DATA contains the snapshot data of the cases "twoCrossingShocks" and "vortexPair". Another folder named RESULTS might be created when running the examples (depending on the specified parameters) and contains results of the sPOD algorithm.

The specified parameters are chosen such that the results of [1] can be reproduced. The only exception is that the mesh coarsening factor in the vortex pair case is chosen to be 4 to perform the computations based on a snapshot matrix with reduced resolution. This results in significantly smaller computation times and storage requirements, though the results presented in [1] are based on the full mesh. This parameter can be adjusted in the parameter file of the case "vortexPair". The associated variable is called params.data.meshCoarseningFactor.

Authors:
  Julius Reiss, reiss@tnt.tu-berlin.de
  Philipp Schulze, pschulze@math.tu-berlin.de

Reference:
  [1] J. Reiss, P. Schulze, J. Sesterhenn, V. Mehrmann: The Shifted Proper Orthogonal
      Decomposition: a Mode Decomposition for Multiple Transport Phenomena (2018)