Doing a few fewer matrix multiplications in 3D RBC setup

Author: brownbaerchen

pySDC/helpers/spectral_helper.py

@@ -257,7 +257,7 @@ class ChebychevHelper(SpectralHelper1D):
     that moves to Chebychev U basis during differentiation, which is sparse. When using this technique, problems need to
     be formulated in first order formulation.
 
-    This implementation is largely based on the Dedalus paper (arXiv:1905.10388).
+    This implementation is largely based on the Dedalus paper (https://doi.org/10.1103/PhysRevResearch.2.023068).
     """
 
     def __init__(self, *args, x0=-1, x1=1, **kwargs):

pySDC/implementations/problem_classes/RayleighBenard3D.py

@@ -158,17 +158,19 @@ def __init__(
         self.nu = (Ra / Prandtl) ** (-1 / 2.0)
 
         # construct operators
+        _D = U02 @ (Dxx + Dyy) + Dzz
         L_lhs = {
             'p': {'u': U01 @ Dx, 'v': U01 @ Dy, 'w': Dz},  # divergence free constraint
-            'u': {'p': U02 @ Dx, 'u': -self.nu * (U02 @ (Dxx + Dyy) + Dzz)},
-            'v': {'p': U02 @ Dy, 'v': -self.nu * (U02 @ (Dxx + Dyy) + Dzz)},
-            'w': {'p': U12 @ Dz, 'w': -self.nu * (U02 @ (Dxx + Dyy) + Dzz), 'T': -U02 @ Id},
-            'T': {'T': -self.kappa * (U02 @ (Dxx + Dyy) + Dzz)},
+            'u': {'p': U02 @ Dx, 'u': -self.nu * _D},
+            'v': {'p': U02 @ Dy, 'v': -self.nu * _D},
+            'w': {'p': U12 @ Dz, 'w': -self.nu * _D, 'T': -U02 @ Id},
+            'T': {'T': -self.kappa * _D},
         }
         self.setup_L(L_lhs)
 
         # mass matrix
-        M_lhs = {i: {i: U02 @ Id} for i in ['u', 'v', 'w', 'T']}
+        _U02 = U02 @ Id
+        M_lhs = {i: {i: _U02} for i in ['u', 'v', 'w', 'T']}
         self.setup_M(M_lhs)
 
         # BCs