From dc2ee7a8b7ba9b5761caf3078fbb4d998a8807b2 Mon Sep 17 00:00:00 2001
From: wolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Date: Wed, 18 Jul 2001 09:50:43 +0000
Subject: [PATCH] FourierSine and FourierCosineFunction

git-svn-id: https://svn.dealii.org/trunk@4849 0785d39b-7218-0410-832d-ea1e28bc413d
---
 deal.II/base/include/base/function_lib.h | 118 ++++++++++++++++++
 deal.II/base/source/function_lib.cc      | 149 +++++++++++++++++++++++
 deal.II/doc/news/2001/c-3-1.html         |   7 +-
 3 files changed, 273 insertions(+), 1 deletion(-)

diff --git a/deal.II/base/include/base/function_lib.h b/deal.II/base/include/base/function_lib.h
index 1172b3a2e8..10c42f8e52 100644
--- a/deal.II/base/include/base/function_lib.h
+++ b/deal.II/base/include/base/function_lib.h
@@ -525,5 +525,123 @@ class JumpFunction : public Function<dim>
 
 
 
+/**
+ * Given a wavenumber vector generate a cosine function. The
+ * wavenumber coefficient is given as a @p{d}-dimensional point @p{k}
+ * in Fourier space, and the function is then recovered as @p{f(x) =
+ * \prod_i cos(k_i x_i) = Re(\exp(i k.x))}.
+ *
+ * The class has its name from the fact that it resembles one
+ * component of a Fourier cosine decomposition.
+ *
+ * @author Wolfgang Bangerth, 2001
+ */
+template <int dim>
+class FourierCosineFunction : public Function<dim> 
+{
+  public:
+				     /**
+				      * Constructor. Take the Fourier
+				      * coefficients in each space
+				      * direction as argument.
+				      */
+    FourierCosineFunction (const Point<dim> &fourier_coefficients);
+    
+				     /**
+				      * Return the value of the
+				      * function at the given
+				      * point. Unless there is only
+				      * one component (i.e. the
+				      * function is scalar), you
+				      * should state the component you
+				      * want to have evaluated; it
+				      * defaults to zero, i.e. the
+				      * first component.
+				      */
+    virtual double value (const Point<dim>   &p,
+			  const unsigned int  component = 0) const;
+
+				     /**
+				      * Return the gradient of the
+				      * specified component of the
+				      * function at the given point.
+				      */
+    virtual Tensor<1,dim> gradient (const Point<dim>   &p,
+				    const unsigned int  component = 0) const;
+
+				     /**
+				      * Compute the Laplacian of a
+				      * given component at point @p{p}.
+				      */
+    virtual double laplacian (const Point<dim>   &p,
+			      const unsigned int  component = 0) const;
+  private:
+				     /**
+				      * Stored Fourier coefficients.
+				      */
+    const Point<dim> fourier_coefficients;
+};
+
+
+
+/**
+ * Given a wavenumber vector generate a sine function. The
+ * wavenumber coefficient is given as a @p{d}-dimensional point @p{k}
+ * in Fourier space, and the function is then recovered as @p{f(x) =
+ * \prod_i sin(k_i x_i) = Im(\exp(i k.x))}.
+ *
+ * The class has its name from the fact that it resembles one
+ * component of a Fourier sine decomposition.
+ *
+ * @author Wolfgang Bangerth, 2001
+ */
+template <int dim>
+class FourierSineFunction : public Function<dim> 
+{
+  public:
+				     /**
+				      * Constructor. Take the Fourier
+				      * coefficients in each space
+				      * direction as argument.
+				      */
+    FourierSineFunction (const Point<dim> &fourier_coefficients);
+    
+				     /**
+				      * Return the value of the
+				      * function at the given
+				      * point. Unless there is only
+				      * one component (i.e. the
+				      * function is scalar), you
+				      * should state the component you
+				      * want to have evaluated; it
+				      * defaults to zero, i.e. the
+				      * first component.
+				      */
+    virtual double value (const Point<dim>   &p,
+			  const unsigned int  component = 0) const;
+
+				     /**
+				      * Return the gradient of the
+				      * specified component of the
+				      * function at the given point.
+				      */
+    virtual Tensor<1,dim> gradient (const Point<dim>   &p,
+				    const unsigned int  component = 0) const;
+
+				     /**
+				      * Compute the Laplacian of a
+				      * given component at point @p{p}.
+				      */
+    virtual double laplacian (const Point<dim>   &p,
+			      const unsigned int  component = 0) const;
+  private:
+				     /**
+				      * Stored Fourier coefficients.
+				      */
+    const Point<dim> fourier_coefficients;
+};
+
+
+
 
 #endif
diff --git a/deal.II/base/source/function_lib.cc b/deal.II/base/source/function_lib.cc
index 36c52c679a..5da39ec8f9 100644
--- a/deal.II/base/source/function_lib.cc
+++ b/deal.II/base/source/function_lib.cc
@@ -1112,6 +1112,148 @@ JumpFunction<dim>::memory_consumption () const
 };
 
 
+
+
+
+/* ---------------------- FourierSineFunction ----------------------- */
+
+
+template <int dim>
+FourierCosineFunction<dim>::
+FourierCosineFunction (const Point<dim> &fourier_coefficients)
+		:
+		Function<dim> (1),
+                fourier_coefficients (fourier_coefficients)
+{};
+
+
+
+template <int dim>
+double
+FourierCosineFunction<dim>::value (const Point<dim>   &p,
+				   const unsigned int  component) const
+{
+  Assert (component==0, ExcIndexRange(component,0,1));
+  double val=1;
+  for (unsigned int i=0; i<dim; ++i)
+    val *= std::cos(fourier_coefficients[i] * p[i]);
+  return val;
+};
+
+
+
+template <int dim>
+Tensor<1,dim>
+FourierCosineFunction<dim>::gradient (const Point<dim>   &p,
+				      const unsigned int  component) const
+{
+  Assert (component==0, ExcIndexRange(component,0,1));
+  Tensor<1,dim> grad;
+  for (unsigned int i=0; i<dim; ++i)
+    grad[i] = 1;
+
+  for (unsigned int i=0; i<dim; ++i)
+    {
+      const double cos_i = std::cos(fourier_coefficients[i] * p[i]);
+      const double sin_i = std::sin(fourier_coefficients[i] * p[i]);
+      
+      for (unsigned int d=0; d<dim; ++d)
+	if (d==i)
+	  grad[d] *= - fourier_coefficients[i] * sin_i;
+	else
+	  grad[d] *= cos_i;
+    };
+  
+  return grad;
+};
+
+
+
+template <int dim>
+double
+FourierCosineFunction<dim>::laplacian (const Point<dim>   &p,
+				       const unsigned int  component) const
+{
+  Assert (component==0, ExcIndexRange(component,0,1));
+  double val = -(fourier_coefficients*fourier_coefficients);
+  for (unsigned int i=0; i<dim; ++i)
+    val *= std::cos(fourier_coefficients[i] * p[i]);
+  return val;
+};
+
+
+
+
+/* ---------------------- FourierSineFunction ----------------------- */
+
+
+
+template <int dim>
+FourierSineFunction<dim>::
+FourierSineFunction (const Point<dim> &fourier_coefficients)
+		:
+		Function<dim> (1),
+                fourier_coefficients (fourier_coefficients)
+{};
+
+
+
+template <int dim>
+double
+FourierSineFunction<dim>::value (const Point<dim>   &p,
+				 const unsigned int  component) const
+{
+  Assert (component==0, ExcIndexRange(component,0,1));
+  double val=1;
+  for (unsigned int i=0; i<dim; ++i)
+    val *= std::sin(fourier_coefficients[i] * p[i]);
+  return val;
+};
+
+
+
+template <int dim>
+Tensor<1,dim>
+FourierSineFunction<dim>::gradient (const Point<dim>   &p,
+				    const unsigned int  component) const
+{
+  Assert (component==0, ExcIndexRange(component,0,1));
+  Tensor<1,dim> grad;
+  for (unsigned int i=0; i<dim; ++i)
+    grad[i] = 1;
+
+  for (unsigned int i=0; i<dim; ++i)
+    {
+      const double cos_i = std::cos(fourier_coefficients[i] * p[i]);
+      const double sin_i = std::sin(fourier_coefficients[i] * p[i]);
+      
+      for (unsigned int d=0; d<dim; ++d)
+	if (d==i)
+	  grad[d] *= fourier_coefficients[i] * cos_i;
+	else
+	  grad[d] *= sin_i;
+    };
+  
+  return grad;
+};
+
+
+
+template <int dim>
+double
+FourierSineFunction<dim>::laplacian (const Point<dim>   &p,
+				     const unsigned int  component) const
+{
+  Assert (component==0, ExcIndexRange(component,0,1));
+  double val = -(fourier_coefficients*fourier_coefficients);
+  for (unsigned int i=0; i<dim; ++i)
+    val *= std::sin(fourier_coefficients[i] * p[i]);
+  return val;
+};
+
+
+
+
 template class SquareFunction<1>;
 template class SquareFunction<2>;
 template class SquareFunction<3>;
@@ -1130,3 +1272,10 @@ template class ExpFunction<3>;
 template class JumpFunction<1>;
 template class JumpFunction<2>;
 template class JumpFunction<3>;
+template class FourierCosineFunction<1>;
+template class FourierCosineFunction<2>;
+template class FourierCosineFunction<3>;
+template class FourierSineFunction<1>;
+template class FourierSineFunction<2>;
+template class FourierSineFunction<3>;
+
diff --git a/deal.II/doc/news/2001/c-3-1.html b/deal.II/doc/news/2001/c-3-1.html
index 548eecb0f2..d1595b8c44 100644
--- a/deal.II/doc/news/2001/c-3-1.html
+++ b/deal.II/doc/news/2001/c-3-1.html
@@ -158,9 +158,14 @@ documentation, etc</a>.
 <h3>base</h3>
 
 <ol>
-
   <li> <p>
+       New: classes <code class="class">FourierSineFunction</code> and
+       <code class="class">FourierCosineFunction</code>, resembling
+       one mode of a Fourier decomposition.
+       <br>
+       (GK 2001/07/18)
 
+  <li> <p>
        New: class <code class="class">vector2d</code> was introduced
        in analogy to STL class <code class="class">vector</code>. The
        bew class provides a two-dimensional array and replaces the use
-- 
2.39.5