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diff --git a/src/functors/analytical/analyticCalcF.h b/src/functors/analytical/analyticCalcF.h
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+/*  This file is part of the OpenLB library
+ *
+ *  Copyright (C) 2012-2018 Lukas Baron, Tim Dornieden, Mathias J. Krause,
+ *  Albert Mink, Adrian Kummerlaender
+ *  E-mail contact: info@openlb.net
+ *  The most recent release of OpenLB can be downloaded at
+ *  <http://www.openlb.net/>
+ *
+ *  This program is free software; you can redistribute it and/or
+ *  modify it under the terms of the GNU General Public License
+ *  as published by the Free Software Foundation; either version 2
+ *  of the License, or (at your option) any later version.
+ *
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU General Public License for more details.
+ *
+ *  You should have received a copy of the GNU General Public
+ *  License along with this program; if not, write to the Free
+ *  Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+ *  Boston, MA  02110-1301, USA.
+*/
+
+#ifndef ANALYTICAL_CALC_F_H
+#define ANALYTICAL_CALC_F_H
+
+
+#include "analyticalBaseF.h"
+#include "utilities/functorPtr.h"
+#include "utilities/arithmetic.h"
+
+
+namespace olb {
+
+/*
+    arithmetic helper classes for AnalyticalF1D, AnalyticalF3D, AnalyticalF3D
+
+    pointwise: difference, plus, multiplication, division
+
+*/
+
+//////////////////////////////// AnalyticCalcF1D ////////////////////////////////
+
+/// arithmetic helper class for analytical 1D functors
+template <typename T, typename S, template<typename> class F>
+class AnalyticCalcF1D : public AnalyticalF1D<T,S> {
+protected:
+  FunctorPtr<AnalyticalF1D<T,S>> _f;
+  FunctorPtr<AnalyticalF1D<T,S>> _g;
+public:
+  AnalyticCalcF1D(FunctorPtr<AnalyticalF1D<T,S>>&& f,
+                  FunctorPtr<AnalyticalF1D<T,S>>&& g);
+
+  AnalyticCalcF1D(T scalar, FunctorPtr<AnalyticalF1D<T,S>>&& g);
+  AnalyticCalcF1D(FunctorPtr<AnalyticalF1D<T,S>>&& f, T scalar);
+
+  bool operator() (T output[], const S input[]) override;
+};
+
+/// addition functor
+template <typename T, typename S>
+using AnalyticCalcPlus1D = AnalyticCalcF1D<T,S,util::plus>;
+
+/// subtraction functor
+template <typename T, typename S>
+using AnalyticCalcMinus1D = AnalyticCalcF1D<T,S,util::minus>;
+
+/// multiplication functor
+template <typename T, typename S>
+using AnalyticCalcMultiplication1D = AnalyticCalcF1D<T,S,util::multiplies>;
+
+/// division functor
+template <typename T, typename S>
+using AnalyticCalcDivision1D = AnalyticCalcF1D<T,S,util::divides>;
+
+//////////////////////////////// AnalyticCalcF2D ////////////////////////////////
+
+/// arithmetic helper class for analytical 2D functors
+template <typename T, typename S, template<typename> class F>
+class AnalyticCalcF2D : public AnalyticalF2D<T,S> {
+protected:
+  FunctorPtr<AnalyticalF2D<T,S>> _f;
+  FunctorPtr<AnalyticalF2D<T,S>> _g;
+public:
+  AnalyticCalcF2D(FunctorPtr<AnalyticalF2D<T,S>>&& f,
+                  FunctorPtr<AnalyticalF2D<T,S>>&& g);
+
+  AnalyticCalcF2D(T scalar, FunctorPtr<AnalyticalF2D<T,S>>&& g);
+  AnalyticCalcF2D(FunctorPtr<AnalyticalF2D<T,S>>&& f, T scalar);
+
+  bool operator() (T output[], const S input[]) override;
+};
+
+/// addition functor
+template <typename T, typename S>
+using AnalyticCalcPlus2D = AnalyticCalcF2D<T,S,util::plus>;
+
+/// subtraction functor
+template <typename T, typename S>
+using AnalyticCalcMinus2D = AnalyticCalcF2D<T,S,util::minus>;
+
+/// multiplication functor
+template <typename T, typename S>
+using AnalyticCalcMultiplication2D = AnalyticCalcF2D<T,S,util::multiplies>;
+
+/// division functor
+template <typename T, typename S>
+using AnalyticCalcDivision2D = AnalyticCalcF2D<T,S,util::divides>;
+
+//////////////////////////////// AnalyticCalcF3D ////////////////////////////////
+
+/// arithmetic helper class for analytical 3D functors
+template <typename T, typename S, template<typename> class F>
+class AnalyticCalcF3D : public AnalyticalF3D<T,S> {
+protected:
+  FunctorPtr<AnalyticalF3D<T,S>> _f;
+  FunctorPtr<AnalyticalF3D<T,S>> _g;
+public:
+  AnalyticCalcF3D(FunctorPtr<AnalyticalF3D<T,S>>&& f,
+                  FunctorPtr<AnalyticalF3D<T,S>>&& g);
+
+  AnalyticCalcF3D(T scalar, FunctorPtr<AnalyticalF3D<T,S>>&& g);
+  AnalyticCalcF3D(FunctorPtr<AnalyticalF3D<T,S>>&& f, T scalar);
+
+  bool operator() (T output[], const S input[]) override;
+};
+
+/// addition functor
+template <typename T, typename S>
+using AnalyticCalcPlus3D = AnalyticCalcF3D<T,S,util::plus>;
+
+/// subtraction functor
+template <typename T, typename S>
+using AnalyticCalcMinus3D = AnalyticCalcF3D<T,S,util::minus>;
+
+/// multiplication functor
+template <typename T, typename S>
+using AnalyticCalcMultiplication3D = AnalyticCalcF3D<T,S,util::multiplies>;
+
+/// division functor
+template <typename T, typename S>
+using AnalyticCalcDivision3D = AnalyticCalcF3D<T,S,util::divides>;
+
+
+/**
+ * \name Arithmetic for functors managed by std::shared_ptr
+ * \{
+ **/
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator+(std::shared_ptr<AnalyticalF1D<T,S>> lhs, std::shared_ptr<AnalyticalF1D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator+(std::shared_ptr<AnalyticalF1D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator+(T lhs, std::shared_ptr<AnalyticalF1D<T,S>> rhs);
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator-(std::shared_ptr<AnalyticalF1D<T,S>> lhs, std::shared_ptr<AnalyticalF1D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator-(std::shared_ptr<AnalyticalF1D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator-(T lhs, std::shared_ptr<AnalyticalF1D<T,S>> rhs);
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator*(std::shared_ptr<AnalyticalF1D<T,S>> lhs, std::shared_ptr<AnalyticalF1D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator*(std::shared_ptr<AnalyticalF1D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator*(T lhs, std::shared_ptr<AnalyticalF1D<T,S>> rhs);
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator/(std::shared_ptr<AnalyticalF1D<T,S>> lhs, std::shared_ptr<AnalyticalF1D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator/(std::shared_ptr<AnalyticalF1D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF1D<T,S>> operator/(T lhs, std::shared_ptr<AnalyticalF1D<T,S>> rhs);
+
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator+(std::shared_ptr<AnalyticalF2D<T,S>> lhs, std::shared_ptr<AnalyticalF2D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator+(std::shared_ptr<AnalyticalF2D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator+(T lhs, std::shared_ptr<AnalyticalF2D<T,S>> rhs);
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator-(std::shared_ptr<AnalyticalF2D<T,S>> lhs, std::shared_ptr<AnalyticalF2D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator-(std::shared_ptr<AnalyticalF2D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator-(T lhs, std::shared_ptr<AnalyticalF2D<T,S>> rhs);
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator*(std::shared_ptr<AnalyticalF2D<T,S>> lhs, std::shared_ptr<AnalyticalF2D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator*(std::shared_ptr<AnalyticalF2D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator*(T lhs, std::shared_ptr<AnalyticalF2D<T,S>> rhs);
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator/(std::shared_ptr<AnalyticalF2D<T,S>> lhs, std::shared_ptr<AnalyticalF2D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator/(std::shared_ptr<AnalyticalF2D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF2D<T,S>> operator/(T lhs, std::shared_ptr<AnalyticalF2D<T,S>> rhs);
+
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator+(std::shared_ptr<AnalyticalF3D<T,S>> lhs, std::shared_ptr<AnalyticalF3D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator+(std::shared_ptr<AnalyticalF3D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator+(T lhs, std::shared_ptr<AnalyticalF3D<T,S>> rhs);
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator-(std::shared_ptr<AnalyticalF3D<T,S>> lhs, std::shared_ptr<AnalyticalF3D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator-(std::shared_ptr<AnalyticalF3D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator-(T lhs, std::shared_ptr<AnalyticalF3D<T,S>> rhs);
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator*(std::shared_ptr<AnalyticalF3D<T,S>> lhs, std::shared_ptr<AnalyticalF3D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator*(std::shared_ptr<AnalyticalF3D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator*(T lhs, std::shared_ptr<AnalyticalF3D<T,S>> rhs);
+
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator/(std::shared_ptr<AnalyticalF3D<T,S>> lhs, std::shared_ptr<AnalyticalF3D<T,S>> rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator/(std::shared_ptr<AnalyticalF3D<T,S>> lhs, T rhs);
+template <typename T, typename S>
+std::shared_ptr<AnalyticalF3D<T,S>> operator/(T lhs, std::shared_ptr<AnalyticalF3D<T,S>> rhs);
+
+///\}
+
+
+} // end namespace olb
+
+#endif