From: guido Date: Fri, 7 Jul 2000 21:43:32 +0000 (+0000) Subject: new high order closed Newton-Cotes formulae X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=5671617ab1b63a7b53908eb651127a02e4ef0559;p=dealii-svn.git new high order closed Newton-Cotes formulae git-svn-id: https://svn.dealii.org/trunk@3142 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/base/include/base/quadrature_lib.h b/deal.II/base/include/base/quadrature_lib.h index 4446712a0b..a2868f65e3 100644 --- a/deal.II/base/include/base/quadrature_lib.h +++ b/deal.II/base/include/base/quadrature_lib.h @@ -169,5 +169,28 @@ class QTrapez : public Quadrature QTrapez (); }; +/** + * Milne-rule. Closed Newton-Cotes formula, exact for polynomials of degree 5. + * See Stoer: Einführung in die Numerische Mathematik I, p. 102 + */ +template +class QMilne : public Quadrature +{ + public: + QMilne (); +}; + + +/** + * Weddle-rule. Closed Newton-Cotes formula, exact for polynomials of degree 7. + * See Stoer: Einführung in die Numerische Mathematik I, p. 102 + */ +template +class QWeddle : public Quadrature +{ + public: + QWeddle (); +}; + #endif diff --git a/deal.II/base/source/quadrature_lib.cc b/deal.II/base/source/quadrature_lib.cc index b4bc6549f3..2a0bcdce55 100644 --- a/deal.II/base/source/quadrature_lib.cc +++ b/deal.II/base/source/quadrature_lib.cc @@ -286,6 +286,21 @@ QMidpoint<1>::QMidpoint () : }; +template <> +QTrapez<1>::QTrapez () : + Quadrature<1> (2) +{ + static const double xpts[] = { 0.0, 1.0 }; + static const double wts[] = { 0.5, 0.5 }; + + for (unsigned int i=0; i(xpts[i]); + weights[i] = wts[i]; + }; +}; + + template <> QSimpson<1>::QSimpson () : Quadrature<1> (3) @@ -302,11 +317,28 @@ QSimpson<1>::QSimpson () : template <> -QTrapez<1>::QTrapez () : - Quadrature<1> (2) +QMilne<1>::QMilne () : + Quadrature<1> (5) { - static const double xpts[] = { 0.0, 1.0 }; - static const double wts[] = { 0.5, 0.5 }; + static const double xpts[] = { 0.0, .25, .5, .75, 1.0 }; + static const double wts[] = { 7./90., 32./90., 12./90., 32./90., 7./90. }; + + for (unsigned int i=0; i(xpts[i]); + weights[i] = wts[i]; + }; +}; + + +template <> +QWeddle<1>::QWeddle () : + Quadrature<1> (7) +{ + static const double xpts[] = { 0.0, 1./6., 1./3., .5, 2./3., 5./6., 1.0 }; + static const double wts[] = { 41./840., 216./840., 27./840., 272./840., + 27./840., 216./840., 41./840. + }; for (unsigned int i=0; i::QTrapez () : }; + // construct the quadrature formulae in higher dimensions by // tensor product of lower dimensions template @@ -369,8 +402,10 @@ template class QGauss6<2>; template class QGauss7<2>; template class QGauss8<2>; template class QMidpoint<2>; -template class QSimpson<2>; template class QTrapez<2>; +template class QSimpson<2>; +template class QMilne<2>; +template class QWeddle<2>; template class QGauss2<3>; template class QGauss3<3>; @@ -380,5 +415,7 @@ template class QGauss6<3>; template class QGauss7<3>; template class QGauss8<3>; template class QMidpoint<3>; -template class QSimpson<3>; template class QTrapez<3>; +template class QSimpson<3>; +template class QMilne<3>; +template class QWeddle<3>;