Provide CUDA GPU implementation of GMGPolar by mknaranja · Pull Request #76 · SciCompMod/GMGPolar

mknaranja · 2025-04-04T18:31:32Z

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Tests for new functionality has been added
A local test was succesful

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Are new methods referenced? Did you provide further documentation?

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For documentation: Please write or update the Readme in the current working directory!

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Is the code clean of development artifacts e.g., unnecessary comments, prints, ...
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mknaranja · 2025-04-04T18:49:30Z

.vscode/launch.json

@@ -0,0 +1,15 @@
+{


mknaranja · 2025-04-04T18:49:34Z

.vscode/settings.json

@@ -0,0 +1,88 @@
+{


mknaranja · 2025-04-04T18:49:38Z

.vscode/c_cpp_properties.json

@@ -0,0 +1,16 @@
+{


mknaranja · 2025-04-04T18:50:34Z

README.md

@@ -1,96 +1,109 @@
-GMGPolar
-=======
+GMGPolar using CUDA


Readme should contain with and without CUDA

mknaranja · 2025-04-04T18:51:12Z

include/test_cases/CartesianR2GyroSonnendruckerCircular.h

@@ -1,57 +0,0 @@
-#pragma once


files should not be removed but just not compiled when compiling with CUDA

mknaranja · 2025-04-04T18:52:19Z

include/InputFunctions/sourceTerm.h

+    double rhs_f(const double& r, const double& theta, const double& sin_theta, const double& cos_theta) const
+    {
+        double temp = sqrt(inverse_aspect_ratio_epsilon * (inverse_aspect_ratio_epsilon + 2.0 * (r/Rmax) * cos_theta) + 1.0);        
+        return 0.4096 * pow((r/Rmax), 6.0) * pow(((r/Rmax) - 1.0), 6.0) * cos(11.0 * theta) / (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) - pow((r/Rmax), 4.0) * (4.5056 * (r/Rmax) * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * pow(((r/Rmax) - 1.0), 6.0) * (((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)) * (1.0 / 2.0 * (((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)) * (4.0 * inverse_aspect_ratio_epsilon * sin_theta * pow(cos_theta, 2.0) / pow((temp * temp), 2.0) + 2.0 * ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * ((-ellipticity_e) * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) + 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) + 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp)) + 2.0 * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - ellipticity_e * inverse_aspect_ratio_epsilon * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * inverse_aspect_ratio_epsilon * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp))) - 1.0 / 2.0 * ((-2.0) * inverse_aspect_ratio_epsilon * pow(cos_theta, 3.0) / pow((temp * temp), 2.0) + (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * ((-2.0) * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) + 4.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) + 4.0 * ellipticity_e * inverse_aspect_ratio_epsilon * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp))) * (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) - 1.0 / 2.0 * ((-2.0) * inverse_aspect_ratio_epsilon * pow(sin_theta, 2.0) * cos_theta / pow((temp * temp), 2.0) + ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 4.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp))) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) * sin(11.0 * theta) / pow(((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))), (3.0 / 2.0)) + 4.5056 * (r/Rmax) * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * pow(((r/Rmax) - 1.0), 6.0) * (2.0 * inverse_aspect_ratio_epsilon * sin_theta * pow(cos_theta, 2.0) / pow((temp * temp), 2.0) + ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * ((-ellipticity_e) * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) + 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) + 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp)) + (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - ellipticity_e * inverse_aspect_ratio_epsilon * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * inverse_aspect_ratio_epsilon * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp))) * sin(11.0 * theta) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) + 27.0336 * (r/Rmax) * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * pow(((r/Rmax) - 1.0), 5.0) * (((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)) * sin(11.0 * theta) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) + (r/Rmax) * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * (12.288 * (r/Rmax) * pow(((r/Rmax) - 1.0), 4.0) * cos(11.0 * theta) + 17.2032 * pow(((r/Rmax) - 1.0), 5.0) * cos(11.0 * theta)) * (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) + (r/Rmax) * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * (2.4576 * (r/Rmax) * pow(((r/Rmax) - 1.0), 5.0) * cos(11.0 * theta) + 2.4576 * pow(((r/Rmax) - 1.0), 6.0) * cos(11.0 * theta)) * ((-2.0) * inverse_aspect_ratio_epsilon * pow(sin_theta, 2.0) * cos_theta / pow((temp * temp), 2.0) + ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 4.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp))) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) + (r/Rmax) * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * (2.4576 * (r/Rmax) * pow(((r/Rmax) - 1.0), 5.0) * cos(11.0 * theta) + 2.4576 * pow(((r/Rmax) - 1.0), 6.0) * cos(11.0 * theta)) * (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (1.0 / 2.0 * (((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)) * (4.0 * inverse_aspect_ratio_epsilon * sin_theta * pow(cos_theta, 2.0) / pow((temp * temp), 2.0) + 2.0 * ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * ((-ellipticity_e) * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) + 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) + 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp)) + 2.0 * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - ellipticity_e * inverse_aspect_ratio_epsilon * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * inverse_aspect_ratio_epsilon * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp))) - 1.0 / 2.0 * ((-2.0) * inverse_aspect_ratio_epsilon * pow(cos_theta, 3.0) / pow((temp * temp), 2.0) + (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * ((-2.0) * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) + 4.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) + 4.0 * ellipticity_e * inverse_aspect_ratio_epsilon * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp))) * (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) - 1.0 / 2.0 * ((-2.0) * inverse_aspect_ratio_epsilon * pow(sin_theta, 2.0) * cos_theta / pow((temp * temp), 2.0) + ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 4.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp))) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) / pow(((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))), (3.0 / 2.0)) - 22.6762679055362 * (r/Rmax) * pow(((r/Rmax) - 1.0), 6.0) * (((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)) * sin(11.0 * theta) / ((208.641975308642 * pow(((r/Rmax) - 0.769230769230769), 2.0) + 1.0) * sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp)))) - 5.03290747193186 * (r/Rmax) * (2.4576 * (r/Rmax) * pow(((r/Rmax) - 1.0), 5.0) * cos(11.0 * theta) + 2.4576 * pow(((r/Rmax) - 1.0), 6.0) * cos(11.0 * theta)) * (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) / ((208.641975308642 * pow(((r/Rmax) - 0.769230769230769), 2.0) + 1.0) * sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp)))) + 27.0336 * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * pow(((r/Rmax) - 1.0), 6.0) * (((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)) * sin(11.0 * theta) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) - 49.5616 * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * pow(((r/Rmax) - 1.0), 6.0) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp)) * cos(11.0 * theta) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) - 4.5056 * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * pow(((r/Rmax) - 1.0), 6.0) * (2.0 * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) / pow((temp * temp), 2.0) + (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * (2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 4.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 4.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + 2.0 * ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) - 2.0 * sin_theta * cos_theta / (temp * temp)) * sin(11.0 * theta) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) - 4.5056 * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * pow(((r/Rmax) - 1.0), 6.0) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp)) * (1.0 / 2.0 * (((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)) * ((-4.0) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta / pow((temp * temp), 2.0) + 2.0 * ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) + 2.0 * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * ((-ellipticity_e) * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 3.0) * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) + 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 3.0) * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 3.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) - ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) + 2.0 * pow(sin_theta, 2.0) / (temp * temp) - 2.0 * pow(cos_theta, 2.0) / (temp * temp)) - 1.0 / 2.0 * (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (2.0 * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) / pow((temp * temp), 2.0) + (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * (2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 4.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 4.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + 2.0 * ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) - 2.0 * sin_theta * cos_theta / (temp * temp)) - 1.0 / 2.0 * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp)) * (2.0 * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 3.0) / pow((temp * temp), 2.0) + ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * ((-2.0) * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 3.0) * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) + 4.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 3.0) * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 6.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) - 2.0 * ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) + 2.0 * sin_theta * cos_theta / (temp * temp))) * sin(11.0 * theta) / pow(((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))), (3.0 / 2.0)) - (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * (((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)) * ((-27.0336) * (r/Rmax) * pow(((r/Rmax) - 1.0), 5.0) * sin(11.0 * theta) - 27.0336 * pow(((r/Rmax) - 1.0), 6.0) * sin(11.0 * theta)) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) - (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * (((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)) * (2.4576 * (r/Rmax) * pow(((r/Rmax) - 1.0), 5.0) * cos(11.0 * theta) + 2.4576 * pow(((r/Rmax) - 1.0), 6.0) * cos(11.0 * theta)) * (1.0 / 2.0 * (((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)) * ((-4.0) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta / pow((temp * temp), 2.0) + 2.0 * ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) + 2.0 * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * ((-ellipticity_e) * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 3.0) * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) + 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 3.0) * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 3.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) - ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) + 2.0 * pow(sin_theta, 2.0) / (temp * temp) - 2.0 * pow(cos_theta, 2.0) / (temp * temp)) - 1.0 / 2.0 * (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (2.0 * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * pow(cos_theta, 2.0) / pow((temp * temp), 2.0) + (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * (2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 4.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 4.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + 2.0 * ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) - 2.0 * sin_theta * cos_theta / (temp * temp)) - 1.0 / 2.0 * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp)) * (2.0 * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 3.0) / pow((temp * temp), 2.0) + ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * ((-2.0) * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 3.0) * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) + 4.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 3.0) * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 6.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) - 2.0 * ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) + 2.0 * sin_theta * cos_theta / (temp * temp))) / pow(((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))), (3.0 / 2.0)) + 6.0 * (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * (2.4576 * (r/Rmax) * pow(((r/Rmax) - 1.0), 5.0) * cos(11.0 * theta) + 2.4576 * pow(((r/Rmax) - 1.0), 6.0) * cos(11.0 * theta)) * (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp))) - (0.452961672473868 - 0.348432055749129 * atan(14.4444444444444 * (r/Rmax) - 11.1111111111111)) * (2.4576 * (r/Rmax) * pow(((r/Rmax) - 1.0), 5.0) * cos(11.0 * theta) + 2.4576 * pow(((r/Rmax) - 1.0), 6.0) * cos(11.0 * theta)) * ((-2.0) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * cos_theta / pow((temp * temp), 2.0) + ((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) - 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 2.0) * cos_theta * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 2.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(cos_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) + (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) * ((-ellipticity_e) * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 3.0) * factor_xi / ( pow((2.0 - temp), 2.0) * pow((temp * temp), (3.0 / 2.0))) + 2.0 * ellipticity_e * (inverse_aspect_ratio_epsilon * inverse_aspect_ratio_epsilon) * ((r/Rmax) * (r/Rmax)) * pow(sin_theta, 3.0) * factor_xi / ( pow((2.0 - temp), 3.0) * (temp * temp)) - 3.0 * ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) - ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) + pow(sin_theta, 2.0) / (temp * temp) - pow(cos_theta, 2.0) / (temp * temp)) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp)))) / sqrt((-pow((((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))) * (ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))) - sin_theta * cos_theta / (temp * temp)), 2.0)) + (pow(((-ellipticity_e) * inverse_aspect_ratio_epsilon * (r/Rmax) * pow(sin_theta, 2.0) * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * cos_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(sin_theta, 2.0) / (temp * temp)) * (pow((ellipticity_e * inverse_aspect_ratio_epsilon * (r/Rmax) * sin_theta * cos_theta * factor_xi / ( pow((2.0 - temp), 2.0) * temp) + ellipticity_e * sin_theta * factor_xi / ( (2.0 - temp))), 2.0) + pow(cos_theta, 2.0) / (temp * temp)));


As runtime polymorphism might not be a possibility, this is one hard-coded test case?

Julian Litz and others added 9 commits December 6, 2024 13:09

Initial empty branch for CUDA GPU implementation

a6f7de1

Residual and Smoothertransfered to Cuda

03fffca

Smoother finalized

1699fb6

Extrapolated Smoother done.

bc3418e

Fully working GPU implementation

f5bc750

Some clean-up

dedb857

Update extrapolated_residual.cu

05d84e2

Update compute_exact_error.cu

b1d036b

Removed Debug code

a873467