Support for Numpy 2.1 and OpenMDAO 3.35 (#450)

sabakhshi · kanekosh · eytanadler · web-flow · commit b5ac8778b33d · 2025-01-17T11:38:58.000-05:00
* Add support for numpy2 and OpenMDAO 3.35

* Fix b-spline interpolation for mid_panel x_interp points. Compatible with openMDAO 3.35 and later

* Bump OAS version and required OpenMDAO version. Update docs

* Removed openmdao version constraint

* also removed numpy version constraint

* Add support for numpy2 and OpenMDAO 3.35

* Fix b-spline interpolation for mid_panel x_interp points. Compatible with openMDAO 3.35 and later

* Bump OAS version and required OpenMDAO version. Update docs

* Removed openmdao version constraint

* also removed numpy version constraint

* Update b-spline component for structures and retrain all tests

* Flake 8 fix

* Docs updates

* Change MPhys capitalization

---------

Co-authored-by: Shugo Kaneko &lt;49300827+kanekosh@users.noreply.github.com&gt;
Co-authored-by: Eytan Adler &lt;63426601+eytanadler@users.noreply.github.com&gt;
diff --git a/.github/build_real.sh b/.github/build_real.sh
@@ -1,4 +1,5 @@
 #!/bin/bash
 set -e
 sed -i '/mphys/d' "$HOME/.config/pip/constraints.txt" # Remove the pip constraint on the mphys version
+sed -i '/numpy/d; /openmdao/d' "$HOME/.config/pip/constraints.txt"  # Remove the pip constraint on the numpy and openmdao version
 pip install .[testing,mphys]
diff --git a/README.md b/README.md
@@ -98,7 +98,7 @@ The oldest and latest versions of the dependencies that we test regularly are th
 | Python             | 3.8    | 3.11   |
 | NumPy              | 1.20   | latest |
 | SciPy              | 1.6.0  | latest |
-| OpenMDAO           | 3.15   | latest |
+| OpenMDAO           | 3.35   | latest |
 | Matplotlib         | latest | latest |
 | MPhys (optional)   | 2.0.0  | latest |
 | pyGeo (optional)   | 1.6.0  | latest |
diff --git a/openaerostruct/__init__.py b/openaerostruct/__init__.py
@@ -1 +1 @@
-__version__ = "2.9.1"
+__version__ = "2.10.0"
diff --git a/openaerostruct/aerodynamics/eval_mtx.py b/openaerostruct/aerodynamics/eval_mtx.py
@@ -210,7 +210,7 @@ def setup(self):
                 (num_eval_points, nx - 1, ny - 1, 3, 3)
             )
             aic_base = np.einsum("ijkl,m->ijklm", vel_mtx_indices, np.ones(3, int))
-            aic_len = np.sum(np.product(aic_base.shape))
+            aic_len = np.sum(np.prod(aic_base.shape))
 
             if ground_effect:
                 # mirrored surface along the x mesh direction
diff --git a/openaerostruct/docs/installation.rst b/openaerostruct/docs/installation.rst
@@ -44,7 +44,7 @@ The oldest and latest versions of the dependencies that we test regularly are th
       - 1.6.0
       - latest
     * - OpenMDAO
-      - 3.15
+      - 3.35
       - latest
     * - Matplotlib
       - latest
@@ -55,6 +55,9 @@ The oldest and latest versions of the dependencies that we test regularly are th
     * - OpenVSP (optional)
       - 3.27.1
       - 3.27.1
+    * - MPhys (optional)
+      - 2.0
+      - latest
 
 If you are unfamiliar with OpenMDAO and wish to modify the internals of OpenAeroStruct, you should examine the OpenMDAO documentation at http://openmdao.org/twodocs/versions/latest/index.html. The tutorials provided with OpenMDAO are helpful to understand the basics of using OpenMDAO to solve an optimization problem.
 
diff --git a/openaerostruct/geometry/geometry_group.py b/openaerostruct/geometry/geometry_group.py
@@ -46,7 +46,10 @@ def setup(self):
                 comp = self.add_subsystem(
                     "t_over_c_bsp",
                     om.SplineComp(
-                        method="bsplines", x_interp_val=x_interp, num_cp=n_cp, interp_options={"order": min(n_cp, 4)}
+                        method="bsplines",
+                        x_interp_val=x_interp,
+                        num_cp=n_cp,
+                        interp_options={"order": min(n_cp, 4), "x_cp_start": 0.0, "x_cp_end": 1.0},
                     ),
                     promotes_inputs=["t_over_c_cp"],
                     promotes_outputs=["t_over_c"],
@@ -110,7 +113,10 @@ def setup(self):
                 comp = self.add_subsystem(
                     "t_over_c_bsp",
                     om.SplineComp(
-                        method="bsplines", x_interp_val=x_interp, num_cp=n_cp, interp_options={"order": min(n_cp, 4)}
+                        method="bsplines",
+                        x_interp_val=x_interp,
+                        num_cp=n_cp,
+                        interp_options={"order": min(n_cp, 4), "x_cp_start": 0, "x_cp_end": 1},
                     ),
                     promotes_inputs=["t_over_c_cp"],
                     promotes_outputs=["t_over_c"],
diff --git a/openaerostruct/structures/tube_group.py b/openaerostruct/structures/tube_group.py
@@ -22,7 +22,10 @@ def setup(self):
             comp = self.add_subsystem(
                 "thickness_bsp",
                 om.SplineComp(
-                    method="bsplines", x_interp_val=x_interp, num_cp=n_cp, interp_options={"order": min(n_cp, 4)}
+                    method="bsplines",
+                    x_interp_val=x_interp,
+                    num_cp=n_cp,
+                    interp_options={"order": min(n_cp, 4), "x_cp_start": 0, "x_cp_end": 1},
                 ),
                 promotes_inputs=["thickness_cp"],
                 promotes_outputs=["thickness"],
@@ -37,7 +40,10 @@ def setup(self):
             comp = self.add_subsystem(
                 "radius_bsp",
                 om.SplineComp(
-                    method="bsplines", x_interp_val=x_interp, num_cp=n_cp, interp_options={"order": min(n_cp, 4)}
+                    method="bsplines",
+                    x_interp_val=x_interp,
+                    num_cp=n_cp,
+                    interp_options={"order": min(n_cp, 4), "x_cp_start": 0, "x_cp_end": 1},
                 ),
                 promotes_inputs=["radius_cp"],
                 promotes_outputs=["radius"],
diff --git a/openaerostruct/structures/wingbox_group.py b/openaerostruct/structures/wingbox_group.py
@@ -20,7 +20,10 @@ def setup(self):
             comp = self.add_subsystem(
                 "spar_thickness_bsp",
                 om.SplineComp(
-                    method="bsplines", x_interp_val=x_interp, num_cp=n_cp, interp_options={"order": min(n_cp, 4)}
+                    method="bsplines",
+                    x_interp_val=x_interp,
+                    num_cp=n_cp,
+                    interp_options={"order": min(n_cp, 4), "x_cp_start": 0, "x_cp_end": 1},
                 ),
                 promotes_inputs=["spar_thickness_cp"],
                 promotes_outputs=["spar_thickness"],
@@ -35,7 +38,10 @@ def setup(self):
             comp = self.add_subsystem(
                 "skin_thickness_bsp",
                 om.SplineComp(
-                    method="bsplines", x_interp_val=x_interp, num_cp=n_cp, interp_options={"order": min(n_cp, 4)}
+                    method="bsplines",
+                    x_interp_val=x_interp,
+                    num_cp=n_cp,
+                    interp_options={"order": min(n_cp, 4), "x_cp_start": 0, "x_cp_end": 1},
                 ),
                 promotes_inputs=["skin_thickness_cp"],
                 promotes_outputs=["skin_thickness"],
diff --git a/setup.py b/setup.py
@@ -53,7 +53,7 @@
     package_data={"openaerostruct": ["tests/*.py", "*/tests/*.py", "*/*/tests/*.py"]},
     install_requires=[
         # Remember to update the oldest versions in the GitHub Actions build, the readme, and in docs/installation.rst
-        "openmdao>=3.15",
+        "openmdao>=3.35",
         "numpy>=1.20",
         "scipy>=1.6.0",
         "matplotlib",
diff --git a/tests/aerodynamics_tests/test_wave_drag.py b/tests/aerodynamics_tests/test_wave_drag.py
@@ -29,7 +29,10 @@ def test(self):
         comp = group.add_subsystem(
             "t_over_c_bsp",
             om.SplineComp(
-                method="bsplines", x_interp_val=x_interp, num_cp=n_cp, interp_options={"order": min(n_cp, 4)}
+                method="bsplines",
+                x_interp_val=x_interp,
+                num_cp=n_cp,
+                interp_options={"order": min(n_cp, 4)},
             ),
             promotes_inputs=["t_over_c_cp"],
             promotes_outputs=["t_over_c"],
diff --git a/tests/integration_tests/test_aero_analysis_no_symmetry_wavedrag.py b/tests/integration_tests/test_aero_analysis_no_symmetry_wavedrag.py
@@ -101,7 +101,7 @@ def test(self):
         prob.run_driver()
 
         assert_near_equal(prob["aero_point_0.CL"][0], 0.46419154063077483, 1e-6)
-        assert_near_equal(prob["aero_point_0.CD"][0], 0.020863555824806052, 1e-6)
+        assert_near_equal(prob["aero_point_0.CD"][0], 0.020404720588811737, 1e-6)
         assert_near_equal(prob["aero_point_0.CM"][1], -1.8595708973535592, 1e-6)
 
 
diff --git a/tests/integration_tests/test_aero_opt_wavedrag.py b/tests/integration_tests/test_aero_opt_wavedrag.py
@@ -112,7 +112,7 @@ def test(self):
         assert_opt_successful(self, optResult)
 
         assert_near_equal(prob["aero_point_0.CL"][0], 0.5, 1e-6)
-        assert_near_equal(prob["aero_point_0.CD"][0], 0.021353004050991248, 1e-6)
+        assert_near_equal(prob["aero_point_0.CD"][0], 0.020825781122528385, 1e-6)
         assert_near_equal(prob["aero_point_0.CM"][1], -2.0819892547514067, 1e-6)
 
 
diff --git a/tests/integration_tests/test_aerostruct.py b/tests/integration_tests/test_aerostruct.py
@@ -150,7 +150,7 @@ def test(self):
         assert_near_equal(prob["AS_point_0.beta"], 0.0)
         assert_opt_successful(self, optResult)
 
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 92523.945549167, 1e-8)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 92523.9636052887, 1e-8)
 
 
 if __name__ == "__main__":
diff --git a/tests/integration_tests/test_aerostruct_analysis.py b/tests/integration_tests/test_aerostruct_analysis.py
@@ -137,8 +137,8 @@ def test(self):
 
         prob.run_model()
 
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 263398.25938918366, 1e-4)
-        assert_near_equal(prob["AS_point_0.CM"][1], -0.6462808405237332, 1e-5)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 241347.34494621187, 1e-4)
+        assert_near_equal(prob["AS_point_0.CM"][1], -0.7040800097095121, 1e-5)
 
 
 if __name__ == "__main__":
diff --git a/tests/integration_tests/test_aerostruct_analysis_Sref.py b/tests/integration_tests/test_aerostruct_analysis_Sref.py
@@ -139,8 +139,8 @@ def test(self):
 
         prob.run_model()
 
-        assert_near_equal(prob["AS_point_0.CL"][0], 1.6210175228727655, 1e-6)
-        assert_near_equal(prob["AS_point_0.CM"][1], -1.8365760768848112, 1e-5)
+        assert_near_equal(prob["AS_point_0.CL"][0], 1.619784221965875, 1e-6)
+        assert_near_equal(prob["AS_point_0.CM"][1], -2.0008904315028193, 1e-5)
 
 
 if __name__ == "__main__":
diff --git a/tests/integration_tests/test_aerostruct_analysis_compressible.py b/tests/integration_tests/test_aerostruct_analysis_compressible.py
@@ -139,8 +139,8 @@ def test(self):
 
         prob.run_model()
 
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 224121.12881258246, 1e-4)
-        assert_near_equal(prob["AS_point_0.CM"][1], -0.9083682371351329, 1e-5)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 205383.27093443452, 1e-4)
+        assert_near_equal(prob["AS_point_0.CM"][1], -0.9867712621195601, 1e-5)
 
 
 if __name__ == "__main__":
diff --git a/tests/integration_tests/test_aerostruct_engine_thrusts.py b/tests/integration_tests/test_aerostruct_engine_thrusts.py
@@ -156,8 +156,8 @@ def test(self):
         print(prob["AS_point_0.fuelburn"][0])
         print(prob["AS_point_0.CM"][1])
 
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 263992.6780138112, 1e-4)
-        assert_near_equal(prob["AS_point_0.CM"][1], -0.6438933659444002, 1e-5)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 241937.85848709388, 1e-4)
+        assert_near_equal(prob["AS_point_0.CM"][1], -0.7013413978098743, 1e-5)
 
 
 if __name__ == "__main__":
diff --git a/tests/integration_tests/test_aerostruct_groundeffect.py b/tests/integration_tests/test_aerostruct_groundeffect.py
@@ -152,7 +152,7 @@ def test(self):
         optResult = prob.run_driver()
         assert_opt_successful(self, optResult)
         # the fuel burn should be less in ground effect
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 86980.04655202407, 1e-6)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 86980.21117717, 1e-6)
         totals = prob.check_totals(
             of=["AS_point_0.L_equals_W", "AS_point_0.fuelburn", "AS_point_0.wing_perf.failure"],
             wrt=["wing.twist_cp", "alpha", "height_agl"],
diff --git a/tests/integration_tests/test_aerostruct_point_loads.py b/tests/integration_tests/test_aerostruct_point_loads.py
@@ -150,8 +150,8 @@ def test(self):
 
         prob.run_model()
 
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 264106.7825178142, 1e-4)
-        assert_near_equal(prob["AS_point_0.CM"][1], -0.6436834908660709, 1e-5)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 242051.20185901612, 1e-4)
+        assert_near_equal(prob["AS_point_0.CM"][1], -0.7010846868817897, 1e-5)
 
 
 if __name__ == "__main__":
diff --git a/tests/integration_tests/test_aerostruct_wingbox_+weight_analysis.py b/tests/integration_tests/test_aerostruct_wingbox_+weight_analysis.py
@@ -400,8 +400,8 @@ def test(self):
 
         prob.run_model()
 
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 87333.56998786073, 1e-5)
-        assert_near_equal(prob["wing.structural_mass"][0], 34500.40422127632, 1e-5)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 85296.25551779529, 1e-5)
+        assert_near_equal(prob["wing.structural_mass"][0], 29707.645593713547, 1e-5)
 
 
 if __name__ == "__main__":
diff --git a/tests/integration_tests/test_aerostruct_wingbox_analysis.py b/tests/integration_tests/test_aerostruct_wingbox_analysis.py
@@ -401,9 +401,9 @@ def test(self):
         print(prob["wing.structural_mass"][0] / 1.25)
         print(prob["AS_point_0.wing_perf.failure"][0])
 
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 87760.55423816708, 1e-5)
-        assert_near_equal(prob["wing.structural_mass"][0], 34500.40422127632, 1e-5)
-        assert_near_equal(prob["AS_point_0.wing_perf.failure"][0], -0.15727437869018163, 1e-5)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 87095.16845081086, 1e-5)
+        assert_near_equal(prob["wing.structural_mass"][0], 29707.645593713547, 1e-5)
+        assert_near_equal(prob["AS_point_0.wing_perf.failure"][0], 0.004148750437858817, 1e-5)
 
 
 if __name__ == "__main__":
diff --git a/tests/integration_tests/test_aerostruct_wingbox_fuel_vol_constraint_opt.py b/tests/integration_tests/test_aerostruct_wingbox_fuel_vol_constraint_opt.py
@@ -435,8 +435,8 @@ def test(self):
 
         assert_opt_successful(self, optResult)
         assert_near_equal(prob["AS_point_0.fuelburn"][0], 76869.3858256513, 1e-4)
-        assert_near_equal(prob["wing.structural_mass"][0], 14523.135605406405, 1e-4)
-        assert_near_equal(prob["fuel_vol_delta.fuel_vol_delta"][0], 42.99371350246894, 1e-4)
+        assert_near_equal(prob["wing.structural_mass"][0], 14520.819967195273, 1e-4)
+        assert_near_equal(prob["fuel_vol_delta.fuel_vol_delta"][0], 43.02081603846062, 1e-4)
         assert_near_equal(prob["AS_point_0.CL"][0], 0.5, 1e-5)
 
 
diff --git a/tests/integration_tests/test_aerostruct_wingbox_opt.py b/tests/integration_tests/test_aerostruct_wingbox_opt.py
@@ -409,7 +409,7 @@ def test(self):
 
         prob.run_driver()
         assert_near_equal(prob["AS_point_0.fuelburn"][0], 79151.03928720397, 1e-5)
-        assert_near_equal(prob["wing.structural_mass"][0] / 1.25, 13387.705394088985, 1e-5)
+        assert_near_equal(prob["wing.structural_mass"][0] / 1.25, 13388.445732877735, 1e-5)
         assert_near_equal(prob["wing.geometry.span"][0], 60.0, 1e-5)
 
 
diff --git a/tests/integration_tests/test_aerostruct_wingbox_wave_fuel_vol_constraint_opt.py b/tests/integration_tests/test_aerostruct_wingbox_wave_fuel_vol_constraint_opt.py
@@ -432,8 +432,8 @@ def test(self):
         optResult = prob.run_driver()
 
         assert_opt_successful(self, optResult)
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 85374.45357945036, 1e-5)
-        assert_near_equal(prob["wing.structural_mass"][0], 13048.465090719292, 1e-5)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 85400.83793743863, 1e-5)
+        assert_near_equal(prob["wing.structural_mass"][0], 13149.34611487464, 1e-5)
         assert_near_equal(prob["AS_point_0.CL"][0], 0.5, 1e-5)
 
 
diff --git a/tests/integration_tests/test_multipoint_parallel.py b/tests/integration_tests/test_multipoint_parallel.py
@@ -3,7 +3,7 @@
 """
 
 import unittest
-from openmdao.utils.assert_utils import assert_near_equal
+from openmdao.utils.assert_utils import assert_near_equal, assert_check_totals
 
 try:
     from petsc4py import PETSc  # noqa: F401
@@ -379,7 +379,6 @@ def test_multipoint_MPI(self):
 
         # compute derivatives
         start_time = time.time()
-        totals = prob.compute_totals()
         derivs_time = time.time() - start_time
 
         print("I am processor", MPI.COMM_WORLD.rank, ", finished run_model and compute_totals")
@@ -392,17 +391,17 @@ def test_multipoint_MPI(self):
         # OpenMDAO versions before 3.31 use absolute names as dictionary keys, but versions after
         # use user facing (promoted) names. Handle both cases here.
         try:
-            deriv_fuel_sum_spar_thickness = totals[("fuel_sum.fuel_sum", "wing.spar_thickness_cp")]
+            deriv_fuel_sum_spar_thickness = prob.check_totals(
+                of=["fuel_sum.fuel_sum"], wrt=["wing.spar_thickness_cp"], compact_print=True
+            )
         except KeyError:
-            deriv_fuel_sum_spar_thickness = totals[("fuel_sum", "wing.spar_thickness_cp")]
+            deriv_fuel_sum_spar_thickness = prob.check_totals(
+                of=["fuel_sum"], wrt=["wing.spar_thickness_cp"], compact_print=True
+            )
 
         assert_near_equal(MPI.COMM_WORLD.size, 2, 1e-8)
-        assert_near_equal(prob.get_val("fuel_sum", units="kg"), 5663.04182905, 1e-5)
-        assert_near_equal(
-            deriv_fuel_sum_spar_thickness,
-            np.array([[1467.2504797, 2271.82835456, 3133.0901236, 5247.87365798]]),
-            1e-5,
-        )
+        assert_near_equal(prob.get_val("fuel_sum", units="kg"), 5646.50827504, 1e-5)
+        assert_check_totals(deriv_fuel_sum_spar_thickness, rtol=1e-4, atol=1.0)
 
 
 if __name__ == "__main__":
diff --git a/tests/integration_tests/test_multipoint_wingbox_aerostruct.py b/tests/integration_tests/test_multipoint_wingbox_aerostruct.py
@@ -459,8 +459,8 @@ def test(self):
 
         assert_opt_successful(self, optResult)
 
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 87326.95014538494, 1e-5)
-        assert_near_equal(prob["wing.structural_mass"][0], 32947.84007488438, 1e-5)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 87326.71090049665, 1e-5)
+        assert_near_equal(prob["wing.structural_mass"][0], 32943.97274107966, 1e-5)
         assert_near_equal(prob["AS_point_0.CL"][0], 0.5, 1e-5)
         assert_near_equal(prob["AS_point_1.L_equals_W"][0], 0.0, 1e-5)
 
diff --git a/tests/integration_tests/test_scaneagle.py b/tests/integration_tests/test_scaneagle.py
@@ -207,9 +207,9 @@ def test_opt(self):
         self.prob.run_driver()
 
         assert_near_equal(self.prob["AS_point_0.fuelburn"][0], 4.518756027353296, 1e-5)
-        assert_near_equal(self.prob["wing.twist_cp"], np.array([2.74161203, 12.22389255, 5.0]), 1e-5)
-        assert_near_equal(self.prob["wing.sweep"][0], 18.909083171987344, 1e-5)
-        assert_near_equal(self.prob["alpha"][0], 1.4756577579439902, 1e-5)
+        assert_near_equal(self.prob["wing.twist_cp"], np.array([2.74343152, 12.2239185, 5.0]), 1e-5)
+        assert_near_equal(self.prob["wing.sweep"][0], 18.908583449616266, 1e-5)
+        assert_near_equal(self.prob["alpha"][0], 1.475153325082263, 1e-5)
 
     def test_totals(self):
         # Set up the problem
diff --git a/tests/integration_tests/test_wingbox_analysis.py b/tests/integration_tests/test_wingbox_analysis.py
@@ -332,7 +332,7 @@ def test(self):
         assert_check_partials(data, atol=1e20, rtol=1e-6)
 
         prob.run_driver()
-        assert_near_equal(prob["wing.structural_mass"], 16675.586037621928, 1e-6)
+        assert_near_equal(prob["wing.structural_mass"], 16932.20046986, 1e-6)
 
 
 if __name__ == "__main__":
diff --git a/tests/integration_tests/test_wingbox_distributed_fuel.py b/tests/integration_tests/test_wingbox_distributed_fuel.py
@@ -443,8 +443,8 @@ def test(self):
         print(prob["AS_point_0.fuelburn"][0])
         print(prob["wing.structural_mass"][0] / 1.25)
 
-        assert_near_equal(prob["AS_point_0.fuelburn"][0], 75973.2666251404, 1e-5)
-        assert_near_equal(prob["wing.structural_mass"][0] / 1.25, 12486.89671978072, 1e-4)
+        assert_near_equal(prob["AS_point_0.fuelburn"][0], 75974.26940153482, 1e-5)
+        assert_near_equal(prob["wing.structural_mass"][0] / 1.25, 12487.980814567598, 1e-4)
 
 
 if __name__ == "__main__":

Original file line number	Diff line number	Diff line change
`@@ -1 +1 @@`
`1`		`-__version__ = "2.9.1"`
	`1`	`+__version__ = "2.10.0"`
Original file line number	Diff line number	Diff line change
`@@ -210,7 +210,7 @@ def setup(self):`
`210`	`210`	`(num_eval_points, nx - 1, ny - 1, 3, 3)`
`211`	`211`	`)`
`212`	`212`	`aic_base = np.einsum("ijkl,m->ijklm", vel_mtx_indices, np.ones(3, int))`
`213`		`- aic_len = np.sum(np.product(aic_base.shape))`
	`213`	`+ aic_len = np.sum(np.prod(aic_base.shape))`
`214`	`214`
`215`	`215`	`if ground_effect:`
`216`	`216`	`# mirrored surface along the x mesh direction`