Coverage for pySDC/implementations/problem_classes/acoustic_helpers/buildWave1DMatrix.py: 100%

1import numpy as np 

2import scipy.sparse as sp 

3 

4from pySDC.helpers.problem_helper import get_finite_difference_matrix 

5 

6wave_order = 6 

7 

8 

9def getFDMatrix(N, dx, order, stencil_type, bc): 

10 """ 

11 First derivative matrix. Only homogeneous boundary conditions are supported, so the 

12 right hand side contribution returned by the helper has to vanish. 

13 """ 

14 A, b = get_finite_difference_matrix( 

15 derivative=1, order=order, stencil_type=stencil_type, dx=dx, size=N, dim=1, bc=bc 

16 ) 

17 assert np.linalg.norm(b) == 0.0, 'Inhomogeneous boundary conditions are not supported here' 

18 return sp.csc_matrix(A) 

19 

20 

21def getWave1DMatrix(N, dx, bc_left, bc_right): 

22 Id = sp.eye(2 * N) 

23 

24 D_u = getFDMatrix(N, dx, wave_order, 'center', (bc_left[0], bc_right[0])) 

25 D_p = getFDMatrix(N, dx, wave_order, 'center', (bc_left[1], bc_right[1])) 

26 Zero = np.zeros((N, N)) 

27 M1 = sp.hstack((Zero, D_p), format="csc") 

28 M2 = sp.hstack((D_u, Zero), format="csc") 

29 M = sp.vstack((M1, M2), format="csc") 

30 return sp.csc_matrix(Id), sp.csc_matrix(M) 

31 

32 

33def getWave1DAdvectionMatrix(N, dx, order): 

34 Dx = getFDMatrix(N, dx, order, 'upwind', 'periodic') 

35 Zero = np.zeros((N, N)) 

36 M1 = sp.hstack((Dx, Zero), format="csc") 

37 M2 = sp.hstack((Zero, Dx), format="csc") 

38 M = sp.vstack((M1, M2), format="csc") 

39 return sp.csc_matrix(M)