1 // -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2 // vi: set et ts=4 sw=2 sts=2:
3
4 #include <algorithm>
5 #include <limits>
6 #include <iostream>
7 #include <type_traits>
8
9 #include <config.h>
10
11 #include <dune/common/quadmath.hh>
12 #include <dune/geometry/referenceelements.hh>
13 #include <dune/geometry/quadraturerules.hh>
14 #include <dune/geometry/quadraturerules/compositequadraturerule.hh>
15 #include <dune/geometry/refinement.hh>
16
17 bool success = true;
18
19 template <class ctype, std::enable_if_t<std::numeric_limits<ctype>::is_specialized, int> = 0>
20 ctype eps ()
21 {
22 return std::numeric_limits<ctype>::epsilon();
23 }
24
25 template <class ctype, std::enable_if_t<!std::numeric_limits<ctype>::is_specialized, int> = 0>
26 ctype eps ()
27 {
28 return std::numeric_limits<float>::epsilon();
29 }
30
31 /*
32 This is a simple accuracy test on the reference element. It integrates
33 x^p and y^p with the quadrature rule of order p, which should give
34 an exact result.
35 */
36
37 /*
38 Exact (analytical) solution on different reference elements.
39 */
40
41 template <class ctype, int dim>
42 ctype analyticalSolution (Dune::GeometryType t, int p, int direction )
43 {
44 using Dune::GeometryType;
45 ctype exact=0;
46
47 if (t.isCube())
48 {
49 exact = ctype( 1 )/(p+1);
50 return exact;
51 }
52
53 if (t.isSimplex())
54 {
55 /* 1/(prod(k=1..dim,(p+k)) */
56 exact = ctype( 1 );
57 for( int k = 1; k <= dim; ++k )
58 exact *= p+k;
59 exact = ctype( 1 ) / exact;
60 return exact;
61 }
62
63 if (t.isPrism())
64 {
65 const int pdim = (dim > 0 ? dim-1 : 0);
66 if( direction < dim-1 )
67 {
68 Dune::GeometryType nt = Dune::GeometryTypes::simplex( dim-1 );
69 if( dim > 0 )
70 exact = analyticalSolution< ctype, pdim >( nt, p, direction );
71 else
72 exact = ctype( 1 );
73 }
74 else
75 exact = ctype( 1 ) / ctype( Dune::Factorial< pdim >::factorial * (p+1));
76 return exact;
77 }
78
79 if (t.isPyramid())
80 {
81 switch( direction )
82 {
83 case 0 :
84 case 1 :
85 exact = ctype( 1 )/((p+3)*(p+1));
86 break;
87 case 2 :
88 exact = ctype( 2 )/((p+1)*(p+2)*(p+3));
89 break;
90 };
91 return exact;
92 }
93
94 DUNE_THROW(Dune::NotImplemented, __func__ << " for " << t);
95 return exact;
96 }
97
98 template<class QuadratureRule>
checkQuadrature(const QuadratureRule & quad)99 void checkQuadrature(const QuadratureRule &quad)
100 {
101 using std::pow; using std::abs;
102 using namespace Dune;
103 typedef typename QuadratureRule::CoordType ctype;
104 const unsigned int dim = QuadratureRule::d;
105 const unsigned int p = quad.order();
106 const Dune::GeometryType& t = quad.type();
107 FieldVector<ctype,dim> integral(0);
108 for (typename QuadratureRule::iterator qp=quad.begin(); qp!=quad.end(); ++qp)
109 {
110 // pos of integration point
111 const FieldVector< ctype, dim > &x = qp->position();
112 const ctype weight = qp->weight();
113
114 for (unsigned int d=0; d<dim; d++)
115 integral[d] += weight*pow(x[d], p);
116 }
117
118 ctype maxRelativeError = 0;
119 for(unsigned int d=0; d<dim; d++)
120 {
121 ctype exact = analyticalSolution<ctype,dim>(t,p,d);
122 ctype relativeError = abs(integral[d] - exact) / (abs(integral[d]) + abs(exact));
123 if (relativeError > maxRelativeError)
124 maxRelativeError = relativeError;
125 }
126 ctype epsilon = pow(2.0,p)*p*eps<ctype>();
127 if (p==0)
128 epsilon = 2.0*eps<ctype>();
129 if (maxRelativeError > epsilon) {
130 std::cerr << "Error: Quadrature for " << t << " and order=" << p << " failed" << std::endl;
131 for (unsigned int d=0; d<dim; d++)
132 {
133 ctype exact = analyticalSolution<ctype,dim>(t,p,d);
134 ctype relativeError = abs(integral[d] - exact) / (abs(integral[d]) + abs(exact));
135 std::cerr << " relative error " << relativeError << " in direction " << d << " (exact = " << exact << " numerical = " << integral[d] << ")" << std::endl;
136 }
137 success = false;
138 }
139 }
140
141 template<class QuadratureRule>
checkWeights(const QuadratureRule & quad)142 void checkWeights(const QuadratureRule &quad)
143 {
144 using std::abs;
145 typedef typename QuadratureRule::CoordType ctype;
146 const unsigned int dim = QuadratureRule::d;
147 const unsigned int p = quad.order();
148 const Dune::GeometryType& t = quad.type();
149 typedef typename QuadratureRule::iterator QuadIterator;
150 ctype volume = 0;
151 QuadIterator qp = quad.begin();
152 QuadIterator qend = quad.end();
153 for (; qp!=qend; ++qp)
154 {
155 volume += qp->weight();
156 }
157 if (abs(volume - Dune::ReferenceElements<ctype, dim>::general(t).volume())
158 > quad.size()*eps<ctype>())
159 {
160 std::cerr << "Error: Quadrature for " << t << " and order=" << p
161 << " does not sum to volume of RefElem" << std::endl;
162 std::cerr << "\tSums to " << volume << "( RefElem.volume() = "
163 << Dune::ReferenceElements<ctype, dim>::general(t).volume()
164 << ")" << "(difference " << volume -
165 Dune::ReferenceElements<ctype, dim>::general(t).volume()
166 << ")" << std::endl;
167 success = false;
168 }
169 }
170
171 template<class ctype, int dim>
check(Dune::GeometryType type,unsigned int maxOrder,Dune::QuadratureType::Enum qt=Dune::QuadratureType::GaussLegendre)172 void check(Dune::GeometryType type,
173 unsigned int maxOrder,
174 Dune::QuadratureType::Enum qt = Dune::QuadratureType::GaussLegendre)
175 {
176 typedef Dune::QuadratureRule<ctype, dim> Quad;
177 std::string qt_str = "";
178 switch (qt) {
179 case Dune::QuadratureType::GaussLegendre: qt_str = "GaussLegendre"; break;
180 case Dune::QuadratureType::GaussJacobi_1_0: qt_str = "GaussJacobi_1_0"; break;
181 case Dune::QuadratureType::GaussJacobi_2_0: qt_str = "GaussJacobi_2_0"; break;
182 case Dune::QuadratureType::GaussJacobi_n_0: qt_str = "GaussJacobi_n_0"; break;
183 case Dune::QuadratureType::GaussLobatto: qt_str = "GaussLobatto"; break;
184 case Dune::QuadratureType::GaussRadauLeft: qt_str = "GaussRadauLeft"; break;
185 case Dune::QuadratureType::GaussRadauRight: qt_str = "GaussRadauRight"; break;
186 default: qt_str = "unknown";
187 }
188 std::cout << "check(Quadrature of type " << qt_str << ")" << std::endl;
189 for (unsigned int p=0; p<=maxOrder; ++p)
190 {
191 const Quad & quad = Dune::QuadratureRules<ctype,dim>::rule(type, p, qt);
192 if (quad.type() != type || unsigned(quad.order()) < p) {
193 std::cerr << "Error: Type mismatch! Requested Quadrature for " << type
194 << " and order=" << p << "." << std::endl
195 << "\tGot Quadrature for " << quad.type() << " and order="
196 << quad.order() << std::endl;
197 success = false;
198 return;
199 }
200 checkWeights(quad);
201 checkQuadrature(quad);
202 }
203 if (dim>0 && (dim>3 || type.isCube() || type.isSimplex()))
204 {
205 type = type.isCube() ? Dune::GeometryTypes::cube(dim-1) : Dune::GeometryTypes::simplex(dim-1);
206 check<ctype,((dim==0) ? 0 : dim-1)>(type , maxOrder, qt);
207 }
208 }
209
210 template<class ctype, int dim>
checkCompositeRule(Dune::GeometryType type,unsigned int maxOrder,unsigned int maxRefinement,Dune::QuadratureType::Enum qt=Dune::QuadratureType::GaussLegendre)211 void checkCompositeRule(Dune::GeometryType type,
212 unsigned int maxOrder,
213 unsigned int maxRefinement,
214 Dune::QuadratureType::Enum qt = Dune::QuadratureType::GaussLegendre)
215 {
216 typedef Dune::QuadratureRule<ctype, dim> BaseQuad;
217 typedef Dune::CompositeQuadratureRule<ctype, dim> Quad;
218
219 for (unsigned int p=0; p<=maxOrder; ++p)
220 {
221 const BaseQuad& baseQuad = Dune::QuadratureRules<ctype,dim>::rule(type, p, qt);
222 Quad quad = Quad(baseQuad, Dune::refinementLevels(maxRefinement));
223
224 checkWeights(quad);
225 checkQuadrature(quad);
226 }
227 if (dim>0 && (dim>3 || type.isCube() || type.isSimplex()))
228 {
229 type = type.isCube() ? Dune::GeometryTypes::cube(dim-1) : Dune::GeometryTypes::simplex(dim-1);
230 check<ctype,((dim==0) ? 0 : dim-1)>(type, maxOrder, qt);
231 }
232 }
233
main(int argc,char ** argv)234 int main (int argc, char** argv)
235 {
236 unsigned int maxOrder = 45;
237 if (argc > 1)
238 {
239 maxOrder = std::atoi(argv[1]);
240 std::cout << "maxOrder = " << maxOrder << std::endl;
241 }
242 try {
243 check<double,4>(Dune::GeometryTypes::cube(4), maxOrder);
244 check<double,4>(Dune::GeometryTypes::cube(4), std::min(maxOrder, unsigned(31)),
245 Dune::QuadratureType::GaussLobatto);
246 check<double,4>(Dune::GeometryTypes::cube(4), std::min(maxOrder, unsigned(30)),
247 Dune::QuadratureType::GaussRadauLeft);
248 check<double,4>(Dune::GeometryTypes::cube(4), std::min(maxOrder, unsigned(30)),
249 Dune::QuadratureType::GaussRadauRight);
250 check<double,4>(Dune::GeometryTypes::simplex(4), maxOrder);
251
252 #if HAVE_LAPACK
253 check<double,4>(Dune::GeometryTypes::simplex(4), maxOrder, Dune::QuadratureType::GaussJacobi_n_0);
254 #else
255 std::cout << "Skip GaussJacobi_n_0 tests as LAPACK has not been found" << std::endl;
256 #endif
257
258 check<double,3>(Dune::GeometryTypes::prism, maxOrder);
259 check<double,3>(Dune::GeometryTypes::pyramid, maxOrder);
260
261 unsigned int maxRefinement = 4;
262
263 checkCompositeRule<double,2>(Dune::GeometryTypes::triangle, maxOrder, maxRefinement);
264
265 #if HAVE_QUADMATH
266 check<Dune::Float128,4>(Dune::GeometryTypes::cube(4), maxOrder);
267 check<Dune::Float128,4>(Dune::GeometryTypes::cube(4), std::min(maxOrder, unsigned(31)),
268 Dune::QuadratureType::GaussLobatto);
269 check<Dune::Float128,4>(Dune::GeometryTypes::cube(4), std::min(maxOrder, unsigned(30)),
270 Dune::QuadratureType::GaussRadauLeft);
271 check<Dune::Float128,4>(Dune::GeometryTypes::cube(4), std::min(maxOrder, unsigned(30)),
272 Dune::QuadratureType::GaussRadauRight);
273 #else
274 std::cout << "Skip Float128 tests as Quadmath is not supported" << std::endl;
275 #endif
276 }
277 catch( const Dune::Exception &e )
278 {
279 std::cerr << e << std::endl;
280 throw;
281 }
282 catch (...) {
283 std::cerr << "Generic exception!" << std::endl;
284 throw;
285 }
286
287 return success ? 0 : 1;
288 }
289