MeshTri3.h

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#ifndef GOOSEFEM_MESHTRI3_H
#define GOOSEFEM_MESHTRI3_H
 
#include "Mesh.h"
#include "config.h"
 
namespace GooseFEM {
namespace Mesh {
 
namespace Tri3 {
 
class Regular : public RegularBase2d<Regular> {
public:
    Regular(size_t nelx, size_t nely, double h = 1.0)
    {
        m_h = h;
        m_nelx = nelx;
        m_nely = nely;
        m_ndim = 2;
        m_nne = 3;
 
        GOOSEFEM_ASSERT(m_nelx >= 1);
        GOOSEFEM_ASSERT(m_nely >= 1);
 
        m_nnode = (m_nelx + 1) * (m_nely + 1);
        m_nelem = m_nelx * m_nely * 2;
    }
 
private:
    friend class RegularBase<Regular>;
    friend class RegularBase2d<Regular>;
 
    size_t nelx_impl() const
    {
        return m_nelx;
    }
 
    size_t nely_impl() const
    {
        return m_nely;
    }
 
    ElementType getElementType_impl() const
    {
        return ElementType::Tri3;
    }
 
    array_type::tensor<double, 2> coor_impl() const
    {
        array_type::tensor<double, 2> ret = xt::empty<double>({m_nnode, m_ndim});
 
        array_type::tensor<double, 1> x =
            xt::linspace<double>(0.0, m_h * static_cast<double>(m_nelx), m_nelx + 1);
        array_type::tensor<double, 1> y =
            xt::linspace<double>(0.0, m_h * static_cast<double>(m_nely), m_nely + 1);
 
        size_t inode = 0;
 
        for (size_t iy = 0; iy < m_nely + 1; ++iy) {
            for (size_t ix = 0; ix < m_nelx + 1; ++ix) {
                ret(inode, 0) = x(ix);
                ret(inode, 1) = y(iy);
                ++inode;
            }
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 2> conn_impl() const
    {
        array_type::tensor<size_t, 2> ret = xt::empty<size_t>({m_nelem, m_nne});
 
        size_t ielem = 0;
 
        for (size_t iy = 0; iy < m_nely; ++iy) {
            for (size_t ix = 0; ix < m_nelx; ++ix) {
                ret(ielem, 0) = (iy) * (m_nelx + 1) + (ix);
                ret(ielem, 1) = (iy) * (m_nelx + 1) + (ix + 1);
                ret(ielem, 2) = (iy + 1) * (m_nelx + 1) + (ix);
                ++ielem;
                ret(ielem, 0) = (iy) * (m_nelx + 1) + (ix + 1);
                ret(ielem, 1) = (iy + 1) * (m_nelx + 1) + (ix + 1);
                ret(ielem, 2) = (iy + 1) * (m_nelx + 1) + (ix);
                ++ielem;
            }
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesBottomEdge_impl() const
    {
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({m_nelx + 1});
 
        for (size_t ix = 0; ix < m_nelx + 1; ++ix) {
            ret(ix) = ix;
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesTopEdge_impl() const
    {
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({m_nelx + 1});
 
        for (size_t ix = 0; ix < m_nelx + 1; ++ix) {
            ret(ix) = ix + m_nely * (m_nelx + 1);
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesLeftEdge_impl() const
    {
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({m_nely + 1});
 
        for (size_t iy = 0; iy < m_nely + 1; ++iy) {
            ret(iy) = iy * (m_nelx + 1);
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesRightEdge_impl() const
    {
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({m_nely + 1});
 
        for (size_t iy = 0; iy < m_nely + 1; ++iy) {
            ret(iy) = iy * (m_nelx + 1) + m_nelx;
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesBottomOpenEdge_impl() const
    {
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({m_nelx - 1});
 
        for (size_t ix = 1; ix < m_nelx; ++ix) {
            ret(ix - 1) = ix;
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesTopOpenEdge_impl() const
    {
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({m_nelx - 1});
 
        for (size_t ix = 1; ix < m_nelx; ++ix) {
            ret(ix - 1) = ix + m_nely * (m_nelx + 1);
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesLeftOpenEdge_impl() const
    {
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({m_nely - 1});
 
        for (size_t iy = 1; iy < m_nely; ++iy) {
            ret(iy - 1) = iy * (m_nelx + 1);
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesRightOpenEdge_impl() const
    {
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({m_nely - 1});
 
        for (size_t iy = 1; iy < m_nely; ++iy) {
            ret(iy - 1) = iy * (m_nelx + 1) + m_nelx;
        }
 
        return ret;
    }
 
    size_t nodesBottomLeftCorner_impl() const
    {
        return 0;
    }
 
    size_t nodesBottomRightCorner_impl() const
    {
        return m_nelx;
    }
 
    size_t nodesTopLeftCorner_impl() const
    {
        return m_nely * (m_nelx + 1);
    }
 
    size_t nodesTopRightCorner_impl() const
    {
        return m_nely * (m_nelx + 1) + m_nelx;
    }
 
    double m_h; 
    size_t m_nelx; 
    size_t m_nely; 
    size_t m_nelem; 
    size_t m_nnode; 
    size_t m_nne; 
    size_t m_ndim; 
};
 
// read / set the orientation (-1/+1) of all triangles
 
inline array_type::tensor<int, 1>
getOrientation(const array_type::tensor<double, 2>& coor, const array_type::tensor<size_t, 2>& conn)
{
    GOOSEFEM_ASSERT(conn.shape(1) == 3ul);
    GOOSEFEM_ASSERT(coor.shape(1) == 2ul);
 
    double k;
    size_t nelem = conn.shape(0);
 
    array_type::tensor<int, 1> ret = xt::empty<int>({nelem});
 
    for (size_t ielem = 0; ielem < nelem; ++ielem) {
        auto v1 =
            xt::view(coor, conn(ielem, 0), xt::all()) - xt::view(coor, conn(ielem, 1), xt::all());
        auto v2 =
            xt::view(coor, conn(ielem, 2), xt::all()) - xt::view(coor, conn(ielem, 1), xt::all());
 
        k = v1(0) * v2(1) - v2(0) * v1(1);
 
        if (k < 0) {
            ret(ielem) = -1;
        }
        else {
            ret(ielem) = +1;
        }
    }
 
    return ret;
}
 
inline array_type::tensor<size_t, 2> setOrientation(
    const array_type::tensor<double, 2>& coor,
    const array_type::tensor<size_t, 2>& conn,
    const array_type::tensor<int, 1>& val,
    int orientation = -1)
{
    GOOSEFEM_ASSERT(conn.shape(1) == 3ul);
    GOOSEFEM_ASSERT(coor.shape(1) == 2ul);
    GOOSEFEM_ASSERT(conn.shape(0) == val.size());
    GOOSEFEM_ASSERT(orientation == -1 || orientation == +1);
 
    UNUSED(coor);
 
    size_t nelem = conn.shape(0);
    array_type::tensor<size_t, 2> ret = conn;
 
    for (size_t ielem = 0; ielem < nelem; ++ielem) {
        if ((orientation == -1 && val(ielem) > 0) || (orientation == +1 && val(ielem) < 0)) {
            std::swap(ret(ielem, 2), ret(ielem, 1));
        }
    }
 
    return ret;
}
 
inline array_type::tensor<size_t, 2> setOrientation(
    const array_type::tensor<double, 2>& coor,
    const array_type::tensor<size_t, 2>& conn,
    int orientation = -1)
{
    GOOSEFEM_ASSERT(conn.shape(1) == 3ul);
    GOOSEFEM_ASSERT(coor.shape(1) == 2ul);
    GOOSEFEM_ASSERT(orientation == -1 || orientation == +1);
 
    array_type::tensor<int, 1> val = getOrientation(coor, conn);
 
    return setOrientation(coor, conn, val, orientation);
}
 
} // namespace Tri3
} // namespace Mesh
} // namespace GooseFEM
 
#endif