Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations

Algorithm 3

NU-DMD for uniform in time data (using on ).

Require: Observables contained in matrix of size

1:                                                                     ⊳Find Fourier coefficients

2: kmeans(A)                                                                              ⊳K-means clustering save distances in D

3: ii 1                                                                                             ⊳counter for next loop

4: for i 1 to column length of D do                                                 ⊳Obtain

5:  if i^th row of D specified distance then

6:    ii^th row of i^th row of

7:    ii ii+ 1

8:  end if

9: end for

10:                                                                                ⊳QR decomposition

11: F                                                           ⊳Initialize function of norm of

12: guess matrix of size                                                   ⊳Intial guess of

13: minimize using                                                           ⊳Use minimization method to find

14: M                                                                                      ⊳Calculate the spatial modes