volume.hh

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#ifndef DUMUX_GEOMETRY_VOLUME_HH
#define DUMUX_GEOMETRY_VOLUME_HH
 
#include <cmath>
#include <limits>
#include <type_traits>
 
#include <dune/common/exceptions.hh>
#include <dune/geometry/type.hh>
#include <dune/geometry/quadraturerules.hh>
 
#include <dumux/common/math.hh>
 
namespace Dumux {
 
template<int dim, class CornerF>
auto convexPolytopeVolume(Dune::GeometryType type, const CornerF& c)
{
    using ctype = typename std::decay_t<decltype(c(0))>::value_type;
    static constexpr int coordDim = std::decay_t<decltype(c(0))>::dimension;
    static_assert(coordDim >= dim, "Coordinate dimension has to be larger than geometry dimension");
 
    // not implemented for coordinate dimension larger than 3
    if constexpr (coordDim > 3)
        return std::numeric_limits<ctype>::quiet_NaN();
 
    if constexpr (dim == 0)
        return 1.0;
 
    else if constexpr (dim == 1)
        return (c(1)-c(0)).two_norm();
 
    else if constexpr (dim == 2)
    {
        if (type == Dune::GeometryTypes::triangle)
        {
            if constexpr (coordDim == 2)
            {
                // make sure we are using positive volumes
                // the cross product of edge vectors might be negative,
                // depending on the element orientation
                using std::abs;
                return 0.5*abs(Dumux::crossProduct(c(1)-c(0), c(2)-c(0)));
            }
            else // coordDim == 3
                return 0.5*Dumux::crossProduct(c(1)-c(0), c(2)-c(0)).two_norm();
 
        }
        else if (type == Dune::GeometryTypes::quadrilateral)
        {
            if constexpr (coordDim == 2)
            {
                // make sure we are using positive volumes
                // the cross product of diagonals might be negative,
                // depending on the element orientation
                using std::abs;
                return 0.5*abs(Dumux::crossProduct(c(3)-c(0), c(2)-c(1)));
            }
            else // coordDim == 3
                return 0.5*Dumux::crossProduct(c(3)-c(0), c(2)-c(1)).two_norm();
 
        }
        else
            return std::numeric_limits<ctype>::quiet_NaN();
    }
 
    else if constexpr (dim == 3)
    {
        if (type == Dune::GeometryTypes::tetrahedron)
        {
            using std::abs;
            return 1.0/6.0 * abs(
                Dumux::tripleProduct(c(3)-c(0), c(1)-c(0), c(2)-c(0))
            );
        }
        else if (type == Dune::GeometryTypes::hexahedron)
        {
            // after Grandy 1997, Efficient computation of volume of hexahedron
            const auto v = c(7)-c(0);
            using std::abs;
            return 1.0/6.0 * (
                abs(Dumux::tripleProduct(v, c(1)-c(0), c(3)-c(5)))
                + abs(Dumux::tripleProduct(v, c(4)-c(0), c(5)-c(6)))
                + abs(Dumux::tripleProduct(v, c(2)-c(0), c(6)-c(3)))
            );
        }
        else if (type == Dune::GeometryTypes::pyramid)
        {
            // 1/3 * base * height
            // for base see case Dune::GeometryTypes::quadrilateral above
            // = 1/3 * (1/2 * norm(ADxBC)) * ((ADxBC)/norm(AD x BC) ⋅ AE)
            // = 1/6 * (AD x BC) ⋅ AE
            using std::abs;
            return 1.0/6.0 * abs(
                Dumux::tripleProduct(c(3)-c(0), c(2)-c(1), c(4)-c(0))
            );
        }
        else if (type == Dune::GeometryTypes::prism)
        {
            // compute as sum of a pyramid (0-1-3-4-5) and a tetrahedron (2-0-1-5)
            using std::abs;
            return 1.0/6.0 * (
                abs(Dumux::tripleProduct(c(3)-c(1), c(4)-c(0), c(5)-c(0)))
                + abs(Dumux::tripleProduct(c(5)-c(2), c(0)-c(2), c(1)-c(2)))
            );
        }
        else
            return std::numeric_limits<ctype>::quiet_NaN();
    }
    else
        return std::numeric_limits<ctype>::quiet_NaN();
}
 
template<class Geometry>
auto convexPolytopeVolume(const Geometry& geo)
{
    const auto v = convexPolytopeVolume<Geometry::mydimension>(
        geo.type(), [&](unsigned int i){ return geo.corner(i); }
    );
 
    // fall back to the method of the geometry if no specialized
    // volume function is implemented for the geometry type
    return std::isnan(v) ? geo.volume() : v;
}
 
template<class Geometry>
auto volume(const Geometry& geo, unsigned int integrationOrder = 4)
{
    using ctype = typename Geometry::ctype;
    ctype volume = 0.0;
    const auto rule = Dune::QuadratureRules<ctype, Geometry::mydimension>::rule(geo.type(), integrationOrder);
    for (const auto& qp : rule)
        volume += geo.integrationElement(qp.position())*qp.weight();
    return volume;
}
 
template<class Geometry, class Transformation>
auto volume(const Geometry& geo, Transformation transformation, unsigned int integrationOrder = 4)
{
    using ctype = typename Geometry::ctype;
    ctype volume = 0.0;
    const auto rule = Dune::QuadratureRules<ctype, Geometry::mydimension>::rule(geo.type(), integrationOrder);
    for (const auto& qp : rule)
        volume += transformation.integrationElement(geo, qp.position())*qp.weight();
    return volume;
}
 
} // end namespace Dumux
 
#endif