DataTransferKit - Multiphysics Solution Transfer Services  2.0
DTK_WendlandBasis_impl.hpp
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1 //---------------------------------------------------------------------------//
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33 //---------------------------------------------------------------------------//
39 //---------------------------------------------------------------------------//
40 
41 #ifndef DTK_WENDLANDBASIS_IMPL_HPP
42 #define DTK_WENDLANDBASIS_IMPL_HPP
43 
44 #include <cmath>
45 #include <limits>
46 
47 namespace DataTransferKit
48 {
49 //---------------------------------------------------------------------------//
54 //---------------------------------------------------------------------------//
55 template <>
56 inline double WendlandBasis<0>::evaluateValue( const double radius,
57  const double x ) const
58 {
59  double xval = x / radius;
60  double onemx = 1.0 - xval;
61  return ( xval < 1.0 ) ? onemx * onemx : 0.0;
62 }
63 
64 //---------------------------------------------------------------------------//
69 //---------------------------------------------------------------------------//
70 template <>
71 inline double WendlandBasis<0>::evaluateGradient( const double radius,
72  const double x ) const
73 {
74  double xval = x / radius;
75  return ( xval < 1.0 ) ? 2.0 * xval - 2.0 : 0.0;
76 }
77 
78 //---------------------------------------------------------------------------//
83 //---------------------------------------------------------------------------//
84 template <>
85 inline double WendlandBasis<2>::evaluateValue( const double radius,
86  const double x ) const
87 {
88  double xval = x / radius;
89  double onemx = 1.0 - xval;
90  double onemx2 = onemx * onemx;
91  return ( xval < 1.0 ) ? onemx2 * onemx2 * ( 4.0 * xval + 1.0 ) : 0.0;
92 }
93 
94 //---------------------------------------------------------------------------//
99 //---------------------------------------------------------------------------//
100 template <>
101 inline double WendlandBasis<2>::evaluateGradient( const double radius,
102  const double x ) const
103 {
104  double xval = x / radius;
105  double xmone = xval - 1.0;
106  return ( xval < 1.0 ) ? 20.0 * xval * xmone * xmone * xmone : 0.0;
107 }
108 
109 //---------------------------------------------------------------------------//
114 //---------------------------------------------------------------------------//
115 template <>
116 inline double WendlandBasis<4>::evaluateValue( const double radius,
117  const double x ) const
118 {
119  double xval = x / radius;
120  double onemx = 1.0 - xval;
121  double onemx2 = onemx * onemx;
122  return ( xval < 1.0 )
123  ? onemx2 * onemx2 * onemx2 *
124  ( 35.0 * xval * xval + 18.0 * xval + 3.0 )
125  : 0.0;
126 }
127 
128 //---------------------------------------------------------------------------//
133 //---------------------------------------------------------------------------//
134 template <>
135 inline double WendlandBasis<4>::evaluateGradient( const double radius,
136  const double x ) const
137 {
138  double xval = x / radius;
139  double xmone = xval - 1.0;
140  double xmone2 = xmone * xmone;
141  return ( xval < 1.0 )
142  ? 56.0 * xval * xmone2 * xmone2 * xmone * ( 5.0 * xval + 1 )
143  : 0.0;
144 }
145 
146 //---------------------------------------------------------------------------//
151 //---------------------------------------------------------------------------//
152 template <>
153 inline double WendlandBasis<6>::evaluateValue( const double radius,
154  const double x ) const
155 {
156  double xval = x / radius;
157  double onemx = 1.0 - xval;
158  double onemx2 = onemx * onemx;
159  double onemx4 = onemx2 * onemx2;
160  double xs = xval * xval;
161  return ( xval < 1.0 )
162  ? onemx4 * onemx4 *
163  ( 32.0 * xs * xval + 25.0 * xs + 8.0 * xval + 1.0 )
164  : 0.0;
165 }
166 
167 //---------------------------------------------------------------------------//
172 //---------------------------------------------------------------------------//
173 template <>
174 inline double WendlandBasis<6>::evaluateGradient( const double radius,
175  const double x ) const
176 {
177  double xval = x / radius;
178  double xmone = xval - 1.0;
179  double xmone2 = xmone * xmone;
180  double xmone4 = xmone2 * xmone2;
181  return ( xval < 1.0 )
182  ? 22.0 * xval * xmone4 * xmone2 * xmone *
183  ( 16.0 * xval * xval + 7.0 * xval + 1.0 )
184  : 0.0;
185 }
186 
187 //---------------------------------------------------------------------------//
188 
189 } // end namespace DataTransferKit
190 
191 //---------------------------------------------------------------------------//
192 
193 #endif // end DTK_WENDLANDBASIS_IMPL_HPP
194 
195 //---------------------------------------------------------------------------//
196 // end DTK_WendlandBasis_impl.hpp
197 //---------------------------------------------------------------------------//
DataTransferKit::WendlandBasis
Wendland compactly supported radial basis function.
Definition: DTK_WendlandBasis.hpp:58
DataTransferKit
DTK_BasicEntitySet.cpp.
Definition: DTK_BasicEntitySet.cpp:48
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