Scalar Field: Offline

Offline phase of the Empirical Interpolation Method applied to scalar fields

Preparation

The structure of the case study folder is the following

>> ./Study_case
	>> /Folder_1  
		>> /0
		>> ...
		>> /constant
		>> /system
			controlDict
			blockMeshDict
			...
			EIMsolverDict  <--- Dictionary needed for the input parameters					
	>> /Folder_2

The EIMsolverDict must be put inside ./Study_case/Folder_1/system/

An example of EIMsolverDict can be found in “application/EIM/ScalarEIM_Offline”, which requires the following entries:

Offline_parameters
{
	field        T;               <---- ScalarField on which EIM is performed 
	error        0.001;           <---- relative L_infinity error desidered
	maxBasis     20;              <---- Max number of EIM basis functions
	foldersList  (
			"Folder_1" 
			"Folder_2") ; <---- List of folder names containig the snapshots
}

Usage

Inside ./Study_case/Folder_1 launch

ScalarEIM_Offline

To include folder “0” use

ScalarEIM_Offline -withZero

To perform on a specified region (for multi-region cases) use

ScalarEIM_Offline -region <regionName>

Results

The Magic Functions, Magic Points and all the other .txt files are saved in a separate folder called EIM_(fieldName), which has the classical OpenFOAM structure.

>> ./Study_case
	>> /Folder_1  				 		
	>> /Folder_2		
	>> /EIM_T		
		>> /0		        
				TMagicFunction0
				TMagicFunction1
				TMagicFunction2
				...
									
		>> /system			
		>> /constant
				TMagicPoints
			
		>> /T_EIM_Offline_files
				Lebesgue_constant.txt
				max_relative_L_infinity_error.txt
				max_absolute_L_infinity_error.txt
				MagicParameter.txt

The absolute and relative error are computed as

\[E_M^{\infty} = || \phi-\mathcal{I}_M[\phi]||_{L^\infty}\qquad \epsilon_M^\infty = \frac{|| \phi-\mathcal{I}_M[\phi]||_{L^\infty}}{||\phi||_{L^\infty}}\]