MeshQuad4.h

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#ifndef GOOSEFEM_MESHQUAD4_H
#define GOOSEFEM_MESHQUAD4_H
 
#include "Mesh.h"
#include "config.h"
 
namespace GooseFEM {
namespace Mesh {
 
namespace Quad4 {
 
// pre-allocation
namespace Map {
class FineLayer2Regular;
}
 
class Regular : public RegularBase2d<Regular> {
public:
    Regular() = default;
 
    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 = 4;
 
        GOOSEFEM_ASSERT(m_nelx >= 1);
        GOOSEFEM_ASSERT(m_nely >= 1);
 
        m_nnode = (m_nelx + 1) * (m_nely + 1);
        m_nelem = m_nelx * m_nely;
    }
 
    array_type::tensor<size_t, 2> elementgrid() const
    {
        return xt::arange<size_t>(m_nelem).reshape({m_nely, m_nelx});
    }
 
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 elementType_impl() const
    {
        return ElementType::Quad4;
    }
 
    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, 3) = (iy + 1) * (m_nelx + 1) + (ix);
                ret(ielem, 2) = (iy + 1) * (m_nelx + 1) + (ix + 1);
                ++ielem;
            }
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesBottomEdge_impl() const
    {
        return xt::arange<size_t>(m_nelx + 1);
    }
 
    array_type::tensor<size_t, 1> nodesTopEdge_impl() const
    {
        return xt::arange<size_t>(m_nelx + 1) + m_nely * (m_nelx + 1);
    }
 
    array_type::tensor<size_t, 1> nodesLeftEdge_impl() const
    {
        return xt::arange<size_t>(m_nely + 1) * (m_nelx + 1);
    }
 
    array_type::tensor<size_t, 1> nodesRightEdge_impl() const
    {
        return xt::arange<size_t>(m_nely + 1) * (m_nelx + 1) + m_nelx;
    }
 
    array_type::tensor<size_t, 1> nodesBottomOpenEdge_impl() const
    {
        return xt::arange<size_t>(1, m_nelx);
    }
 
    array_type::tensor<size_t, 1> nodesTopOpenEdge_impl() const
    {
        return xt::arange<size_t>(1, m_nelx) + m_nely * (m_nelx + 1);
    }
 
    array_type::tensor<size_t, 1> nodesLeftOpenEdge_impl() const
    {
        return xt::arange<size_t>(1, m_nely) * (m_nelx + 1);
    }
 
    array_type::tensor<size_t, 1> nodesRightOpenEdge_impl() const
    {
        return xt::arange<size_t>(1, m_nely) * (m_nelx + 1) + m_nelx;
    }
 
    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; 
};
 
class FineLayer : public RegularBase2d<FineLayer> {
public:
    FineLayer() = default;
 
    FineLayer(size_t nelx, size_t nely, double h = 1.0, size_t nfine = 1)
    {
        this->init(nelx, nely, h, nfine);
    }
 
    template <class C, class E, std::enable_if_t<xt::is_xexpression<C>::value, bool> = true>
    FineLayer(const C& coor, const E& conn)
    {
        this->init_by_mapping(coor, conn);
    }
 
    const array_type::tensor<size_t, 1>& elemrow_nhx() const
    {
        return m_nhx;
    }
 
    const array_type::tensor<size_t, 1>& elemrow_nhy() const
    {
        return m_nhy;
    }
 
    const array_type::tensor<int, 1>& elemrow_type() const
    {
        return m_refine;
    }
 
    const array_type::tensor<size_t, 1>& elemrow_nelem() const
    {
        return m_layer_nelx;
    }
 
    array_type::tensor<size_t, 1> elementsMiddleLayer() const
    {
        size_t nely = m_nhy.size();
        size_t iy = (nely - 1) / 2;
        return m_startElem(iy) + xt::arange<size_t>(m_layer_nelx(iy));
    }
 
    array_type::tensor<size_t, 1> elementsLayer(size_t layer) const
    {
        GOOSEFEM_ASSERT(layer < m_layer_nelx.size());
        size_t n = m_layer_nelx(layer);
        if (m_refine(layer) != -1) {
            n *= 4;
        }
        return m_startElem(layer) + xt::arange<size_t>(n);
    }
 
    array_type::tensor<size_t, 1> elementgrid_ravel(
        std::vector<size_t> start_stop_rows,
        std::vector<size_t> start_stop_cols
    ) const
    {
        GOOSEFEM_ASSERT(start_stop_rows.size() == 0 || start_stop_rows.size() == 2);
        GOOSEFEM_ASSERT(start_stop_cols.size() == 0 || start_stop_cols.size() == 2);
 
        std::array<size_t, 2> rows;
        std::array<size_t, 2> cols;
 
        if (start_stop_rows.size() == 2) {
            std::copy(start_stop_rows.begin(), start_stop_rows.end(), rows.begin());
            GOOSEFEM_ASSERT(rows[0] <= this->nely());
            GOOSEFEM_ASSERT(rows[1] <= this->nely());
        }
        else {
            rows[0] = 0;
            rows[1] = this->nely();
        }
 
        if (start_stop_cols.size() == 2) {
            std::copy(start_stop_cols.begin(), start_stop_cols.end(), cols.begin());
            GOOSEFEM_ASSERT(cols[0] <= this->nelx());
            GOOSEFEM_ASSERT(cols[1] <= this->nelx());
        }
        else {
            cols[0] = 0;
            cols[1] = this->nelx();
        }
 
        if (rows[0] == rows[1] || cols[0] == cols[1]) {
            array_type::tensor<size_t, 1> ret = xt::empty<size_t>({0});
            return ret;
        }
 
        // Compute dimensions
 
        auto H = xt::cumsum(m_nhy);
        size_t yl = 0;
        if (rows[0] > 0) {
            yl = xt::argmax(H > rows[0])();
        }
        size_t yu = xt::argmax(H >= rows[1])();
        size_t hx = std::max(m_nhx(yl), m_nhx(yu));
        size_t xl = (cols[0] - cols[0] % hx) / hx;
        size_t xu = (cols[1] - cols[1] % hx) / hx;
 
        // Allocate output
 
        size_t N = 0;
 
        for (size_t i = yl; i <= yu; ++i) {
            // no refinement
            size_t n = (xu - xl) * hx / m_nhx(i);
            // refinement
            if (m_refine(i) != -1) {
                n *= 4;
            }
            N += n;
        }
 
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({N});
 
        // Write output
 
        N = 0;
 
        for (size_t i = yl; i <= yu; ++i) {
            // no refinement
            size_t n = (xu - xl) * hx / m_nhx(i);
            size_t h = hx;
            // refinement
            if (m_refine(i) != -1) {
                n *= 4;
                h *= 4;
            }
            array_type::tensor<size_t, 1> e =
                m_startElem(i) + xl * h / m_nhx(i) + xt::arange<size_t>(n);
            xt::view(ret, xt::range(N, N + n)) = e;
            N += n;
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1>
    elementgrid_around_ravel(size_t e, size_t size, bool periodic = true)
    {
        GOOSEFEM_WIP_ASSERT(periodic == true);
 
        size_t iy = xt::argmin(m_startElem <= e)() - 1;
        size_t nel = m_layer_nelx(iy);
 
        GOOSEFEM_WIP_ASSERT(iy == (m_nhy.size() - 1) / 2);
 
        auto H = xt::cumsum(m_nhy);
 
        if (2 * size >= H(H.size() - 1)) {
            return xt::arange<size_t>(this->nelem());
        }
 
        size_t hy = H(iy);
        size_t l = xt::argmax(H > (hy - size - 1))();
        size_t u = xt::argmax(H >= (hy + size))();
        size_t lh = 0;
        if (l > 0) {
            lh = H(l - 1);
        }
        size_t uh = H(u);
 
        size_t step = xt::amax(m_nhx)();
        size_t relx = (e - m_startElem(iy)) % step;
        size_t mid = (nel / step - (nel / step) % 2) / 2 * step + relx;
        size_t nroll = (nel - (nel - mid + e - m_startElem(iy)) % nel) / step;
        size_t dx = m_nhx(u);
        size_t xl = 0;
        size_t xu = nel;
        if (mid >= size) {
            xl = mid - size;
        }
        if (mid + size < nel) {
            xu = mid + size + 1;
        }
        xl = xl - xl % dx;
        xu = xu - xu % dx;
        if (mid - xl < size) {
            if (xl < dx) {
                xl = 0;
            }
            else {
                xl -= dx;
            }
        }
        if (xu - mid < size) {
            if (xu > nel - dx) {
                xu = nel;
            }
            else {
                xu += dx;
            }
        }
 
        auto ret = this->elementgrid_ravel({lh, uh}, {xl, xu});
        auto map = this->roll(nroll);
        return xt::view(map, xt::keep(ret));
    }
 
    // -
    array_type::tensor<size_t, 1>
    elementgrid_leftright(size_t e, size_t left, size_t right, bool periodic = true)
    {
        GOOSEFEM_WIP_ASSERT(periodic == true);
 
        size_t iy = xt::argmin(m_startElem <= e)() - 1;
        size_t nel = m_layer_nelx(iy);
 
        GOOSEFEM_WIP_ASSERT(iy == (m_nhy.size() - 1) / 2);
 
        size_t step = xt::amax(m_nhx)();
        size_t relx = (e - m_startElem(iy)) % step;
        size_t mid = (nel / step - (nel / step) % 2) / 2 * step + relx;
        size_t nroll = (nel - (nel - mid + e - m_startElem(iy)) % nel) / step;
        size_t dx = m_nhx(iy);
        size_t xl = 0;
        size_t xu = nel;
        if (mid >= left) {
            xl = mid - left;
        }
        if (mid + right < nel) {
            xu = mid + right + 1;
        }
        xl = xl - xl % dx;
        xu = xu - xu % dx;
        if (mid - xl < left) {
            if (xl < dx) {
                xl = 0;
            }
            else {
                xl -= dx;
            }
        }
        if (xu - mid < right) {
            if (xu > nel - dx) {
                xu = nel;
            }
            else {
                xu += dx;
            }
        }
 
        auto H = xt::cumsum(m_nhy);
        size_t yl = 0;
        if (iy > 0) {
            yl = H(iy - 1);
        }
        auto ret = this->elementgrid_ravel({yl, H(iy)}, {xl, xu});
        auto map = this->roll(nroll);
        return xt::view(map, xt::keep(ret));
    }
 
    array_type::tensor<size_t, 1> roll(size_t n)
    {
        auto conn = this->conn();
        size_t nely = static_cast<size_t>(m_nhy.size());
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({m_nelem});
 
        // loop over all element layers
        for (size_t iy = 0; iy < nely; ++iy) {
 
            // no refinement
            size_t shift = n * (m_layer_nelx(iy) / m_layer_nelx(0));
            size_t nel = m_layer_nelx(iy);
 
            // refinement
            if (m_refine(iy) != -1) {
                shift = n * (m_layer_nelx(iy) / m_layer_nelx(0)) * 4;
                nel = m_layer_nelx(iy) * 4;
            }
 
            // element numbers of the layer, and roll them
            auto e = m_startElem(iy) + xt::arange<size_t>(nel);
            xt::view(ret, xt::range(m_startElem(iy), m_startElem(iy) + nel)) = xt::roll(e, shift);
        }
 
        return ret;
    }
 
private:
    friend class RegularBase<FineLayer>;
    friend class RegularBase2d<FineLayer>;
    friend class GooseFEM::Mesh::Quad4::Map::FineLayer2Regular;
 
    size_t nelx_impl() const
    {
        return xt::amax(m_layer_nelx)();
    }
 
    size_t nely_impl() const
    {
        return xt::sum(m_nhy)();
    }
 
    ElementType elementType_impl() const
    {
        return ElementType::Quad4;
    }
 
    array_type::tensor<double, 2> coor_impl() const
    {
        // allocate output
        array_type::tensor<double, 2> ret = xt::empty<double>({m_nnode, m_ndim});
 
        // current node, number of element layers
        size_t inode = 0;
        size_t nely = static_cast<size_t>(m_nhy.size());
 
        // y-position of each main node layer (i.e. excluding node layers for refinement/coarsening)
        // - allocate
        array_type::tensor<double, 1> y = xt::empty<double>({nely + 1});
        // - initialize
        y(0) = 0.0;
        // - compute
        for (size_t iy = 1; iy < nely + 1; ++iy) {
            y(iy) = y(iy - 1) + m_nhy(iy - 1) * m_h;
        }
 
        // loop over element layers (bottom -> middle) : add bottom layer (+ refinement layer) of
        // nodes
 
        for (size_t iy = 0;; ++iy) {
            // get positions along the x- and z-axis
            array_type::tensor<double, 1> x = xt::linspace<double>(0.0, m_Lx, m_layer_nelx(iy) + 1);
 
            // add nodes of the bottom layer of this element
            for (size_t ix = 0; ix < m_layer_nelx(iy) + 1; ++ix) {
                ret(inode, 0) = x(ix);
                ret(inode, 1) = y(iy);
                ++inode;
            }
 
            // stop at middle layer
            if (iy == (nely - 1) / 2) {
                break;
            }
 
            // add extra nodes of the intermediate layer, for refinement in x-direction
            if (m_refine(iy) == 0) {
                // - get position offset in x- and y-direction
                double dx = m_h * static_cast<double>(m_nhx(iy) / 3);
                double dy = m_h * static_cast<double>(m_nhy(iy) / 2);
                // - add nodes of the intermediate layer
                for (size_t ix = 0; ix < m_layer_nelx(iy); ++ix) {
                    for (size_t j = 0; j < 2; ++j) {
                        ret(inode, 0) = x(ix) + dx * static_cast<double>(j + 1);
                        ret(inode, 1) = y(iy) + dy;
                        ++inode;
                    }
                }
            }
        }
 
        // loop over element layers (middle -> top) : add (refinement layer +) top layer of nodes
 
        for (size_t iy = (nely - 1) / 2; iy < nely; ++iy) {
            // get positions along the x- and z-axis
            array_type::tensor<double, 1> x = xt::linspace<double>(0.0, m_Lx, m_layer_nelx(iy) + 1);
 
            // add extra nodes of the intermediate layer, for refinement in x-direction
            if (m_refine(iy) == 0) {
                // - get position offset in x- and y-direction
                double dx = m_h * static_cast<double>(m_nhx(iy) / 3);
                double dy = m_h * static_cast<double>(m_nhy(iy) / 2);
                // - add nodes of the intermediate layer
                for (size_t ix = 0; ix < m_layer_nelx(iy); ++ix) {
                    for (size_t j = 0; j < 2; ++j) {
                        ret(inode, 0) = x(ix) + dx * static_cast<double>(j + 1);
                        ret(inode, 1) = y(iy) + dy;
                        ++inode;
                    }
                }
            }
 
            // add nodes of the top layer of this element
            for (size_t ix = 0; ix < m_layer_nelx(iy) + 1; ++ix) {
                ret(inode, 0) = x(ix);
                ret(inode, 1) = y(iy + 1);
                ++inode;
            }
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 2> conn_impl() const
    {
        // allocate output
        array_type::tensor<size_t, 2> ret = xt::empty<size_t>({m_nelem, m_nne});
 
        // current element, number of element layers, starting nodes of each node layer
        size_t ielem = 0;
        size_t nely = static_cast<size_t>(m_nhy.size());
        size_t bot, mid, top;
 
        // loop over all element layers
        for (size_t iy = 0; iy < nely; ++iy) {
            // - get: starting nodes of bottom(, middle) and top layer
            bot = m_startNode(iy);
            mid = m_startNode(iy) + m_nnd(iy);
            top = m_startNode(iy + 1);
 
            // - define connectivity: no coarsening/refinement
            if (m_refine(iy) == -1) {
                for (size_t ix = 0; ix < m_layer_nelx(iy); ++ix) {
                    ret(ielem, 0) = bot + (ix);
                    ret(ielem, 1) = bot + (ix + 1);
                    ret(ielem, 2) = top + (ix + 1);
                    ret(ielem, 3) = top + (ix);
                    ielem++;
                }
            }
 
            // - define connectivity: refinement along the x-direction (below the middle layer)
            else if (m_refine(iy) == 0 && iy <= (nely - 1) / 2) {
                for (size_t ix = 0; ix < m_layer_nelx(iy); ++ix) {
                    // -- bottom element
                    ret(ielem, 0) = bot + (ix);
                    ret(ielem, 1) = bot + (ix + 1);
                    ret(ielem, 2) = mid + (2 * ix + 1);
                    ret(ielem, 3) = mid + (2 * ix);
                    ielem++;
                    // -- top-right element
                    ret(ielem, 0) = bot + (ix + 1);
                    ret(ielem, 1) = top + (3 * ix + 3);
                    ret(ielem, 2) = top + (3 * ix + 2);
                    ret(ielem, 3) = mid + (2 * ix + 1);
                    ielem++;
                    // -- top-center element
                    ret(ielem, 0) = mid + (2 * ix);
                    ret(ielem, 1) = mid + (2 * ix + 1);
                    ret(ielem, 2) = top + (3 * ix + 2);
                    ret(ielem, 3) = top + (3 * ix + 1);
                    ielem++;
                    // -- top-left element
                    ret(ielem, 0) = bot + (ix);
                    ret(ielem, 1) = mid + (2 * ix);
                    ret(ielem, 2) = top + (3 * ix + 1);
                    ret(ielem, 3) = top + (3 * ix);
                    ielem++;
                }
            }
 
            // - define connectivity: coarsening along the x-direction (above the middle layer)
            else if (m_refine(iy) == 0 && iy > (nely - 1) / 2) {
                for (size_t ix = 0; ix < m_layer_nelx(iy); ++ix) {
                    // -- lower-left element
                    ret(ielem, 0) = bot + (3 * ix);
                    ret(ielem, 1) = bot + (3 * ix + 1);
                    ret(ielem, 2) = mid + (2 * ix);
                    ret(ielem, 3) = top + (ix);
                    ielem++;
                    // -- lower-center element
                    ret(ielem, 0) = bot + (3 * ix + 1);
                    ret(ielem, 1) = bot + (3 * ix + 2);
                    ret(ielem, 2) = mid + (2 * ix + 1);
                    ret(ielem, 3) = mid + (2 * ix);
                    ielem++;
                    // -- lower-right element
                    ret(ielem, 0) = bot + (3 * ix + 2);
                    ret(ielem, 1) = bot + (3 * ix + 3);
                    ret(ielem, 2) = top + (ix + 1);
                    ret(ielem, 3) = mid + (2 * ix + 1);
                    ielem++;
                    // -- upper element
                    ret(ielem, 0) = mid + (2 * ix);
                    ret(ielem, 1) = mid + (2 * ix + 1);
                    ret(ielem, 2) = top + (ix + 1);
                    ret(ielem, 3) = top + (ix);
                    ielem++;
                }
            }
        }
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesBottomEdge_impl() const
    {
        return m_startNode(0) + xt::arange<size_t>(m_layer_nelx(0) + 1);
    }
 
    array_type::tensor<size_t, 1> nodesTopEdge_impl() const
    {
        size_t nely = m_nhy.size();
        return m_startNode(nely) + xt::arange<size_t>(m_layer_nelx(nely - 1) + 1);
    }
 
    array_type::tensor<size_t, 1> nodesLeftEdge_impl() const
    {
        size_t nely = m_nhy.size();
 
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({nely + 1});
 
        size_t i = 0;
        size_t j = (nely + 1) / 2;
        size_t k = (nely - 1) / 2;
        size_t l = nely;
 
        xt::view(ret, xt::range(i, j)) = xt::view(m_startNode, xt::range(i, j));
        xt::view(ret, xt::range(k + 1, l + 1)) = xt::view(m_startNode, xt::range(k + 1, l + 1));
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesRightEdge_impl() const
    {
        size_t nely = m_nhy.size();
 
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({nely + 1});
 
        size_t i = 0;
        size_t j = (nely + 1) / 2;
        size_t k = (nely - 1) / 2;
        size_t l = nely;
 
        xt::view(ret, xt::range(i, j)) =
            xt::view(m_startNode, xt::range(i, j)) + xt::view(m_layer_nelx, xt::range(i, j));
 
        xt::view(ret, xt::range(k + 1, l + 1)) = xt::view(m_startNode, xt::range(k + 1, l + 1)) +
                                                 xt::view(m_layer_nelx, xt::range(k, l));
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesBottomOpenEdge_impl() const
    {
        return m_startNode(0) + xt::arange<size_t>(1, m_layer_nelx(0));
    }
 
    array_type::tensor<size_t, 1> nodesTopOpenEdge_impl() const
    {
        size_t nely = m_nhy.size();
 
        return m_startNode(nely) + xt::arange<size_t>(1, m_layer_nelx(nely - 1));
    }
 
    array_type::tensor<size_t, 1> nodesLeftOpenEdge_impl() const
    {
        size_t nely = m_nhy.size();
 
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({nely - 1});
 
        size_t i = 0;
        size_t j = (nely + 1) / 2;
        size_t k = (nely - 1) / 2;
        size_t l = nely;
 
        xt::view(ret, xt::range(i, j - 1)) = xt::view(m_startNode, xt::range(i + 1, j));
        xt::view(ret, xt::range(k, l - 1)) = xt::view(m_startNode, xt::range(k + 1, l));
 
        return ret;
    }
 
    array_type::tensor<size_t, 1> nodesRightOpenEdge_impl() const
    {
        size_t nely = m_nhy.size();
 
        array_type::tensor<size_t, 1> ret = xt::empty<size_t>({nely - 1});
 
        size_t i = 0;
        size_t j = (nely + 1) / 2;
        size_t k = (nely - 1) / 2;
        size_t l = nely;
 
        xt::view(ret, xt::range(i, j - 1)) = xt::view(m_startNode, xt::range(i + 1, j)) +
                                             xt::view(m_layer_nelx, xt::range(i + 1, j));
 
        xt::view(ret, xt::range(k, l - 1)) = xt::view(m_startNode, xt::range(k + 1, l)) +
                                             xt::view(m_layer_nelx, xt::range(k, l - 1));
 
        return ret;
    }
 
    size_t nodesBottomLeftCorner_impl() const
    {
        return m_startNode(0);
    }
 
    size_t nodesBottomRightCorner_impl() const
    {
        return m_startNode(0) + m_layer_nelx(0);
    }
 
    size_t nodesTopLeftCorner_impl() const
    {
        size_t nely = m_nhy.size();
        return m_startNode(nely);
    }
 
    size_t nodesTopRightCorner_impl() const
    {
        size_t nely = m_nhy.size();
        return m_startNode(nely) + m_layer_nelx(nely - 1);
    }
 
    double m_h; 
    size_t m_nelem; 
    size_t m_nnode; 
    size_t m_nne; 
    size_t m_ndim; 
    double m_Lx; 
    array_type::tensor<size_t, 1> m_layer_nelx; 
    array_type::tensor<size_t, 1> m_nhx; 
    array_type::tensor<size_t, 1> m_nhy; 
    array_type::tensor<size_t, 1> m_nnd; 
    array_type::tensor<int, 1> m_refine; 
    array_type::tensor<size_t, 1> m_startElem; 
    array_type::tensor<size_t, 1> m_startNode; 
 
    void init(size_t nelx, size_t nely, double h, size_t nfine = 1)
    {
        GOOSEFEM_ASSERT(nelx >= 1ul);
        GOOSEFEM_ASSERT(nely >= 1ul);
 
        m_h = h;
        m_ndim = 2;
        m_nne = 4;
        m_Lx = m_h * static_cast<double>(nelx);
 
        // compute element size in y-direction (use symmetry, compute upper half)
 
        // temporary variables
        size_t nmin, ntot;
        array_type::tensor<size_t, 1> nhx = xt::ones<size_t>({nely});
        array_type::tensor<size_t, 1> nhy = xt::ones<size_t>({nely});
        array_type::tensor<int, 1> refine = -1 * xt::ones<int>({nely});
 
        // minimum height in y-direction (half of the height because of symmetry)
        if (nely % 2 == 0) {
            nmin = nely / 2;
        }
        else {
            nmin = (nely + 1) / 2;
        }
 
        // minimum number of fine layers in y-direction (minimum 1, middle layer part of this half)
        if (nfine % 2 == 0) {
            nfine = nfine / 2 + 1;
        }
        else {
            nfine = (nfine + 1) / 2;
        }
 
        if (nfine < 1) {
            nfine = 1;
        }
 
        if (nfine > nmin) {
            nfine = nmin;
        }
 
        // loop over element layers in y-direction, try to coarsen using these rules:
        // (1) element size in y-direction <= distance to origin in y-direction
        // (2) element size in x-direction should fit the total number of elements in x-direction
        // (3) a certain number of layers have the minimum size "1" (are fine)
        for (size_t iy = nfine;;) {
            // initialize current size in y-direction
            if (iy == nfine) {
                ntot = nfine;
            }
            // check to stop
            if (iy >= nely || ntot >= nmin) {
                nely = iy;
                break;
            }
 
            // rules (1,2) satisfied: coarsen in x-direction
            if (3 * nhy(iy) <= ntot && nelx % (3 * nhx(iy)) == 0 && ntot + nhy(iy) < nmin) {
                refine(iy) = 0;
                nhy(iy) *= 2;
                auto vnhy = xt::view(nhy, xt::range(iy + 1, _));
                auto vnhx = xt::view(nhx, xt::range(iy, _));
                vnhy *= 3;
                vnhx *= 3;
            }
 
            // update the number of elements in y-direction
            ntot += nhy(iy);
            // proceed to next element layer in y-direction
            ++iy;
            // check to stop
            if (iy >= nely || ntot >= nmin) {
                nely = iy;
                break;
            }
        }
 
        // symmetrize, compute full information
 
        // allocate mesh constructor parameters
        m_nhx = xt::empty<size_t>({nely * 2 - 1});
        m_nhy = xt::empty<size_t>({nely * 2 - 1});
        m_refine = xt::empty<int>({nely * 2 - 1});
        m_layer_nelx = xt::empty<size_t>({nely * 2 - 1});
        m_nnd = xt::empty<size_t>({nely * 2});
        m_startElem = xt::empty<size_t>({nely * 2 - 1});
        m_startNode = xt::empty<size_t>({nely * 2});
 
        // fill
        // - lower half
        for (size_t iy = 0; iy < nely; ++iy) {
            m_nhx(iy) = nhx(nely - iy - 1);
            m_nhy(iy) = nhy(nely - iy - 1);
            m_refine(iy) = refine(nely - iy - 1);
        }
        // - upper half
        for (size_t iy = 0; iy < nely - 1; ++iy) {
            m_nhx(iy + nely) = nhx(iy + 1);
            m_nhy(iy + nely) = nhy(iy + 1);
            m_refine(iy + nely) = refine(iy + 1);
        }
 
        // update size
        nely = m_nhx.size();
 
        // compute the number of elements per element layer in y-direction
        for (size_t iy = 0; iy < nely; ++iy) {
            m_layer_nelx(iy) = nelx / m_nhx(iy);
        }
 
        // compute the number of nodes per node layer in y-direction
        for (size_t iy = 0; iy < (nely + 1) / 2; ++iy) {
            m_nnd(iy) = m_layer_nelx(iy) + 1;
        }
        for (size_t iy = (nely - 1) / 2; iy < nely; ++iy) {
            m_nnd(iy + 1) = m_layer_nelx(iy) + 1;
        }
 
        // compute mesh dimensions
 
        // initialize
        m_nnode = 0;
        m_nelem = 0;
        m_startNode(0) = 0;
 
        // loop over element layers (bottom -> middle, elements become finer)
        for (size_t i = 0; i < (nely - 1) / 2; ++i) {
            // - store the first element of the layer
            m_startElem(i) = m_nelem;
            // - add the nodes of this layer
            if (m_refine(i) == 0) {
                m_nnode += (3 * m_layer_nelx(i) + 1);
            }
            else {
                m_nnode += (m_layer_nelx(i) + 1);
            }
            // - add the elements of this layer
            if (m_refine(i) == 0) {
                m_nelem += (4 * m_layer_nelx(i));
            }
            else {
                m_nelem += (m_layer_nelx(i));
            }
            // - store the starting node of the next layer
            m_startNode(i + 1) = m_nnode;
        }
 
        // loop over element layers (middle -> top, elements become coarser)
        for (size_t i = (nely - 1) / 2; i < nely; ++i) {
            // - store the first element of the layer
            m_startElem(i) = m_nelem;
            // - add the nodes of this layer
            if (m_refine(i) == 0) {
                m_nnode += (5 * m_layer_nelx(i) + 1);
            }
            else {
                m_nnode += (m_layer_nelx(i) + 1);
            }
            // - add the elements of this layer
            if (m_refine(i) == 0) {
                m_nelem += (4 * m_layer_nelx(i));
            }
            else {
                m_nelem += (m_layer_nelx(i));
            }
            // - store the starting node of the next layer
            m_startNode(i + 1) = m_nnode;
        }
        // - add the top row of nodes
        m_nnode += m_layer_nelx(nely - 1) + 1;
    }
 
    template <class C, class E>
    void init_by_mapping(const C& coor, const E& conn)
    {
        GOOSEFEM_ASSERT(coor.dimension() == 2);
        GOOSEFEM_ASSERT(conn.dimension() == 2);
        GOOSEFEM_ASSERT(coor.shape(1) == 2);
        GOOSEFEM_ASSERT(conn.shape(1) == 4);
        GOOSEFEM_ASSERT(conn.shape(0) > 0);
        GOOSEFEM_ASSERT(coor.shape(0) >= 4);
        GOOSEFEM_ASSERT(xt::amax(conn)() < coor.shape(0));
 
        if (conn.shape(0) == 1) {
            this->init(1, 1, coor(conn(0, 1), 0) - coor(conn(0, 0), 0));
            GOOSEFEM_CHECK(xt::all(xt::equal(this->conn(), conn)));
            GOOSEFEM_CHECK(xt::allclose(this->coor(), coor));
            return;
        }
 
        // Identify the middle layer
 
        size_t emid = (conn.shape(0) - conn.shape(0) % 2) / 2;
        size_t eleft = emid;
        size_t eright = emid;
 
        while (conn(eleft, 0) == conn(eleft - 1, 1) && eleft > 0) {
            eleft--;
        }
 
        while (conn(eright, 1) == conn(eright + 1, 0) && eright < conn.shape(0) - 1) {
            eright++;
        }
 
        GOOSEFEM_CHECK(xt::allclose(coor(conn(eleft, 0), 0), 0.0));
 
        // Get element sizes along the middle layer
 
        auto n0 = xt::view(conn, xt::range(eleft, eright + 1), 0);
        auto n1 = xt::view(conn, xt::range(eleft, eright + 1), 1);
        auto n2 = xt::view(conn, xt::range(eleft, eright + 1), 2);
        auto dx = xt::view(coor, xt::keep(n1), 0) - xt::view(coor, xt::keep(n0), 0);
        auto dy = xt::view(coor, xt::keep(n2), 1) - xt::view(coor, xt::keep(n1), 1);
        auto hx = xt::amin(dx)();
        auto hy = xt::amin(dy)();
 
        GOOSEFEM_CHECK(xt::allclose(hx, hy));
        GOOSEFEM_CHECK(xt::allclose(dx, hx));
        GOOSEFEM_CHECK(xt::allclose(dy, hy));
 
        // Extract shape and initialise
 
        size_t nelx = eright - eleft + 1;
        size_t nely = static_cast<size_t>((coor(coor.shape(0) - 1, 1) - coor(0, 1)) / hx);
        this->init(nelx, nely, hx);
        GOOSEFEM_CHECK(xt::all(xt::equal(this->conn(), conn)));
        GOOSEFEM_CHECK(xt::allclose(this->coor(), coor));
        GOOSEFEM_CHECK(
            xt::all(xt::equal(this->elementsMiddleLayer(), eleft + xt::arange<size_t>(nelx)))
        );
    }
};
 
namespace Map {
 
class RefineRegular {
public:
    RefineRegular() = default;
 
    RefineRegular(const GooseFEM::Mesh::Quad4::Regular& mesh, size_t nx, size_t ny)
        : m_coarse(mesh), m_nx(nx), m_ny(ny)
    {
        m_fine = Regular(nx * m_coarse.nelx(), ny * m_coarse.nely(), m_coarse.h());
 
        array_type::tensor<size_t, 2> elmat_coarse = m_coarse.elementgrid();
        array_type::tensor<size_t, 2> elmat_fine = m_fine.elementgrid();
 
        m_coarse2fine = xt::empty<size_t>({m_coarse.nelem(), nx * ny});
 
        for (size_t i = 0; i < elmat_coarse.shape(0); ++i) {
            for (size_t j = 0; j < elmat_coarse.shape(1); ++j) {
                xt::view(m_coarse2fine, elmat_coarse(i, j), xt::all()) = xt::flatten(xt::view(
                    elmat_fine, xt::range(i * ny, (i + 1) * ny), xt::range(j * nx, (j + 1) * nx)
                ));
            }
        }
    }
 
    size_t nx() const
    {
        return m_nx;
    }
 
    size_t ny() const
    {
        return m_ny;
    }
 
    GooseFEM::Mesh::Quad4::Regular coarseMesh() const
    {
        return m_coarse;
    }
 
    GooseFEM::Mesh::Quad4::Regular fineMesh() const
    {
        return m_fine;
    }
 
    const array_type::tensor<size_t, 2>& map() const
    {
        return m_coarse2fine;
    }
 
    [[deprecated]]
    GooseFEM::Mesh::Quad4::Regular getCoarseMesh() const
    {
        return m_coarse;
    }
 
    [[deprecated]]
    GooseFEM::Mesh::Quad4::Regular getFineMesh() const
    {
        return m_fine;
    }
 
    [[deprecated]]
    const array_type::tensor<size_t, 2>& getMap() const
    {
        return m_coarse2fine;
    }
 
    template <class T, size_t rank>
    array_type::tensor<T, rank> meanToCoarse(const array_type::tensor<T, rank>& data) const
    {
        GOOSEFEM_ASSERT(data.shape(0) == m_coarse2fine.size());
 
        std::array<size_t, rank> shape;
        std::copy(data.shape().cbegin(), data.shape().cend(), &shape[0]);
        shape[0] = m_coarse2fine.shape(0);
 
        array_type::tensor<T, rank> ret = xt::empty<T>(shape);
 
        for (size_t i = 0; i < m_coarse2fine.shape(0); ++i) {
            auto e = xt::view(m_coarse2fine, i, xt::all());
            auto d = xt::view(data, xt::keep(e));
            xt::view(ret, i) = xt::mean(d, 0);
        }
 
        return ret;
    }
 
    template <class T, size_t rank, class S>
    array_type::tensor<T, rank> averageToCoarse(
        const array_type::tensor<T, rank>& data,
        const array_type::tensor<S, rank>& weights
    ) const
    {
        GOOSEFEM_ASSERT(data.shape(0) == m_coarse2fine.size());
 
        std::array<size_t, rank> shape;
        std::copy(data.shape().cbegin(), data.shape().cend(), &shape[0]);
        shape[0] = m_coarse2fine.shape(0);
 
        array_type::tensor<T, rank> ret = xt::empty<T>(shape);
 
        for (size_t i = 0; i < m_coarse2fine.shape(0); ++i) {
            auto e = xt::view(m_coarse2fine, i, xt::all());
            array_type::tensor<T, rank> d = xt::view(data, xt::keep(e));
            array_type::tensor<T, rank> w = xt::view(weights, xt::keep(e));
            xt::view(ret, i) = xt::average(d, w, {0});
        }
 
        return ret;
    }
 
    template <class T, size_t rank>
    array_type::tensor<T, rank> mapToFine(const array_type::tensor<T, rank>& data) const
    {
        GOOSEFEM_ASSERT(data.shape(0) == m_coarse2fine.shape(0));
 
        std::array<size_t, rank> shape;
        std::copy(data.shape().cbegin(), data.shape().cend(), &shape[0]);
        shape[0] = m_coarse2fine.size();
 
        array_type::tensor<T, rank> ret = xt::empty<T>(shape);
 
        for (size_t e = 0; e < m_coarse2fine.shape(0); ++e) {
            for (size_t i = 0; i < m_coarse2fine.shape(1); ++i) {
                xt::view(ret, m_coarse2fine(e, i)) = xt::view(data, e);
            }
        }
 
        return ret;
    }
 
private:
    GooseFEM::Mesh::Quad4::Regular m_coarse; 
    GooseFEM::Mesh::Quad4::Regular m_fine; 
    size_t m_nx; 
    size_t m_ny; 
    array_type::tensor<size_t, 2> m_coarse2fine; 
};
 
class FineLayer2Regular {
public:
    FineLayer2Regular() = default;
 
    FineLayer2Regular(const GooseFEM::Mesh::Quad4::FineLayer& mesh) : m_finelayer(mesh)
    {
        // ------------
        // Regular-mesh
        // ------------
 
        m_regular = GooseFEM::Mesh::Quad4::Regular(
            xt::amax(m_finelayer.m_layer_nelx)(), xt::sum(m_finelayer.m_nhy)(), m_finelayer.m_h
        );
 
        // -------
        // mapping
        // -------
 
        // allocate mapping
        m_elem_regular.resize(m_finelayer.m_nelem);
        m_frac_regular.resize(m_finelayer.m_nelem);
 
        // alias
        array_type::tensor<size_t, 1> nhx = m_finelayer.m_nhx;
        array_type::tensor<size_t, 1> nhy = m_finelayer.m_nhy;
        array_type::tensor<size_t, 1> nelx = m_finelayer.m_layer_nelx;
        array_type::tensor<size_t, 1> start = m_finelayer.m_startElem;
 
        // 'matrix' of element numbers of the Regular-mesh
        array_type::tensor<size_t, 2> elementgrid = m_regular.elementgrid();
 
        // cumulative number of element-rows of the Regular-mesh per layer of the FineLayer-mesh
        array_type::tensor<size_t, 1> cum_nhy =
            xt::concatenate(xt::xtuple(xt::zeros<size_t>({1}), xt::cumsum(nhy)));
 
        // number of element layers in y-direction of the FineLayer-mesh
        size_t nely = nhy.size();
 
        // loop over layers of the FineLayer-mesh
        for (size_t iy = 0; iy < nely; ++iy) {
            // element numbers of the Regular-mesh along this layer of the FineLayer-mesh
            auto el_new = xt::view(elementgrid, xt::range(cum_nhy(iy), cum_nhy(iy + 1)), xt::all());
 
            // no coarsening/refinement
            // ------------------------
 
            if (m_finelayer.m_refine(iy) == -1) {
                // element numbers of the FineLayer-mesh along this layer
                array_type::tensor<size_t, 1> el_old = start(iy) + xt::arange<size_t>(nelx(iy));
 
                // loop along this layer of the FineLayer-mesh
                for (size_t ix = 0; ix < nelx(iy); ++ix) {
                    // get the element numbers of the Regular-mesh for this element of the
                    // FineLayer-mesh
                    auto block =
                        xt::view(el_new, xt::all(), xt::range(ix * nhx(iy), (ix + 1) * nhx(iy)));
 
                    // write to mapping
                    for (auto& i : block) {
                        m_elem_regular[el_old(ix)].push_back(i);
                        m_frac_regular[el_old(ix)].push_back(1.0);
                    }
                }
            }
 
            // refinement along the x-direction (below the middle layer)
            // ---------------------------------------------------------
 
            else if (m_finelayer.m_refine(iy) == 0 && iy <= (nely - 1) / 2) {
                // element numbers of the FineLayer-mesh along this layer
                // rows: coarse block, columns element numbers per block
                array_type::tensor<size_t, 2> el_old =
                    start(iy) + xt::arange<size_t>(nelx(iy) * 4ul).reshape({-1, 4});
 
                // loop along this layer of the FineLayer-mesh
                for (size_t ix = 0; ix < nelx(iy); ++ix) {
                    // get the element numbers of the Regular-mesh for this block of the
                    // FineLayer-mesh
                    auto block =
                        xt::view(el_new, xt::all(), xt::range(ix * nhx(iy), (ix + 1) * nhx(iy)));
 
                    // bottom: wide-to-narrow
                    {
                        for (size_t j = 0; j < nhy(iy) / 2; ++j) {
                            auto e = xt::view(block, j, xt::range(j, nhx(iy) - j));
 
                            m_elem_regular[el_old(ix, 0)].push_back(e(0));
                            m_frac_regular[el_old(ix, 0)].push_back(0.5);
 
                            for (size_t k = 1; k < e.size() - 1; ++k) {
                                m_elem_regular[el_old(ix, 0)].push_back(e(k));
                                m_frac_regular[el_old(ix, 0)].push_back(1.0);
                            }
 
                            m_elem_regular[el_old(ix, 0)].push_back(e(e.size() - 1));
                            m_frac_regular[el_old(ix, 0)].push_back(0.5);
                        }
                    }
 
                    // top: regular small element
                    {
                        auto e = xt::view(
                            block,
                            xt::range(nhy(iy) / 2, nhy(iy)),
                            xt::range(1 * nhx(iy) / 3, 2 * nhx(iy) / 3)
                        );
 
                        for (auto& i : e) {
                            m_elem_regular[el_old(ix, 2)].push_back(i);
                            m_frac_regular[el_old(ix, 2)].push_back(1.0);
                        }
                    }
 
                    // left
                    {
                        // left-bottom: narrow-to-wide
                        for (size_t j = 0; j < nhy(iy) / 2; ++j) {
                            auto e = xt::view(block, j, xt::range(0, j + 1));
 
                            for (size_t k = 0; k < e.size() - 1; ++k) {
                                m_elem_regular[el_old(ix, 3)].push_back(e(k));
                                m_frac_regular[el_old(ix, 3)].push_back(1.0);
                            }
 
                            m_elem_regular[el_old(ix, 3)].push_back(e(e.size() - 1));
                            m_frac_regular[el_old(ix, 3)].push_back(0.5);
                        }
 
                        // left-top: regular
                        {
                            auto e = xt::view(
                                block,
                                xt::range(nhy(iy) / 2, nhy(iy)),
                                xt::range(0 * nhx(iy) / 3, 1 * nhx(iy) / 3)
                            );
 
                            for (auto& i : e) {
                                m_elem_regular[el_old(ix, 3)].push_back(i);
                                m_frac_regular[el_old(ix, 3)].push_back(1.0);
                            }
                        }
                    }
 
                    // right
                    {
                        // right-bottom: narrow-to-wide
                        for (size_t j = 0; j < nhy(iy) / 2; ++j) {
                            auto e = xt::view(block, j, xt::range(nhx(iy) - j - 1, nhx(iy)));
 
                            m_elem_regular[el_old(ix, 1)].push_back(e(0));
                            m_frac_regular[el_old(ix, 1)].push_back(0.5);
 
                            for (size_t k = 1; k < e.size(); ++k) {
                                m_elem_regular[el_old(ix, 1)].push_back(e(k));
                                m_frac_regular[el_old(ix, 1)].push_back(1.0);
                            }
                        }
 
                        // right-top: regular
                        {
                            auto e = xt::view(
                                block,
                                xt::range(nhy(iy) / 2, nhy(iy)),
                                xt::range(2 * nhx(iy) / 3, 3 * nhx(iy) / 3)
                            );
 
                            for (auto& i : e) {
                                m_elem_regular[el_old(ix, 1)].push_back(i);
                                m_frac_regular[el_old(ix, 1)].push_back(1.0);
                            }
                        }
                    }
                }
            }
 
            // coarsening along the x-direction (above the middle layer)
            else if (m_finelayer.m_refine(iy) == 0 && iy > (nely - 1) / 2) {
                // element numbers of the FineLayer-mesh along this layer
                // rows: coarse block, columns element numbers per block
                array_type::tensor<size_t, 2> el_old =
                    start(iy) + xt::arange<size_t>(nelx(iy) * 4ul).reshape({-1, 4});
 
                // loop along this layer of the FineLayer-mesh
                for (size_t ix = 0; ix < nelx(iy); ++ix) {
                    // get the element numbers of the Regular-mesh for this block of the
                    // FineLayer-mesh
                    auto block =
                        xt::view(el_new, xt::all(), xt::range(ix * nhx(iy), (ix + 1) * nhx(iy)));
 
                    // top: narrow-to-wide
                    {
                        for (size_t j = 0; j < nhy(iy) / 2; ++j) {
                            auto e = xt::view(
                                block,
                                nhy(iy) / 2 + j,
                                xt::range(1 * nhx(iy) / 3 - j - 1, 2 * nhx(iy) / 3 + j + 1)
                            );
 
                            m_elem_regular[el_old(ix, 3)].push_back(e(0));
                            m_frac_regular[el_old(ix, 3)].push_back(0.5);
 
                            for (size_t k = 1; k < e.size() - 1; ++k) {
                                m_elem_regular[el_old(ix, 3)].push_back(e(k));
                                m_frac_regular[el_old(ix, 3)].push_back(1.0);
                            }
 
                            m_elem_regular[el_old(ix, 3)].push_back(e(e.size() - 1));
                            m_frac_regular[el_old(ix, 3)].push_back(0.5);
                        }
                    }
 
                    // bottom: regular small element
                    {
                        auto e = xt::view(
                            block,
                            xt::range(0, nhy(iy) / 2),
                            xt::range(1 * nhx(iy) / 3, 2 * nhx(iy) / 3)
                        );
 
                        for (auto& i : e) {
                            m_elem_regular[el_old(ix, 1)].push_back(i);
                            m_frac_regular[el_old(ix, 1)].push_back(1.0);
                        }
                    }
 
                    // left
                    {
                        // left-bottom: regular
                        {
                            auto e = xt::view(
                                block,
                                xt::range(0, nhy(iy) / 2),
                                xt::range(0 * nhx(iy) / 3, 1 * nhx(iy) / 3)
                            );
 
                            for (auto& i : e) {
                                m_elem_regular[el_old(ix, 0)].push_back(i);
                                m_frac_regular[el_old(ix, 0)].push_back(1.0);
                            }
                        }
 
                        // left-top: narrow-to-wide
                        for (size_t j = 0; j < nhy(iy) / 2; ++j) {
                            auto e =
                                xt::view(block, nhy(iy) / 2 + j, xt::range(0, 1 * nhx(iy) / 3 - j));
 
                            for (size_t k = 0; k < e.size() - 1; ++k) {
                                m_elem_regular[el_old(ix, 0)].push_back(e(k));
                                m_frac_regular[el_old(ix, 0)].push_back(1.0);
                            }
 
                            m_elem_regular[el_old(ix, 0)].push_back(e(e.size() - 1));
                            m_frac_regular[el_old(ix, 0)].push_back(0.5);
                        }
                    }
 
                    // right
                    {
                        // right-bottom: regular
                        {
                            auto e = xt::view(
                                block,
                                xt::range(0, nhy(iy) / 2),
                                xt::range(2 * nhx(iy) / 3, 3 * nhx(iy) / 3)
                            );
 
                            for (auto& i : e) {
                                m_elem_regular[el_old(ix, 2)].push_back(i);
                                m_frac_regular[el_old(ix, 2)].push_back(1.0);
                            }
                        }
 
                        // right-top: narrow-to-wide
                        for (size_t j = 0; j < nhy(iy) / 2; ++j) {
                            auto e = xt::view(
                                block, nhy(iy) / 2 + j, xt::range(2 * nhx(iy) / 3 + j, nhx(iy))
                            );
 
                            m_elem_regular[el_old(ix, 2)].push_back(e(0));
                            m_frac_regular[el_old(ix, 2)].push_back(0.5);
 
                            for (size_t k = 1; k < e.size(); ++k) {
                                m_elem_regular[el_old(ix, 2)].push_back(e(k));
                                m_frac_regular[el_old(ix, 2)].push_back(1.0);
                            }
                        }
                    }
                }
            }
        }
    }
 
    GooseFEM::Mesh::Quad4::Regular regularMesh() const
    {
        return m_regular;
    }
 
    GooseFEM::Mesh::Quad4::FineLayer fineLayerMesh() const
    {
        return m_finelayer;
    }
 
    // elements of the Regular mesh per element of the FineLayer mesh
    // and the fraction by which the overlap is
 
    std::vector<std::vector<size_t>> map() const
    {
        return m_elem_regular;
    }
 
    std::vector<std::vector<double>> mapFraction() const
    {
        return m_frac_regular;
    }
 
    [[deprecated]]
    GooseFEM::Mesh::Quad4::Regular getRegularMesh() const
    {
        return m_regular;
    }
 
    [[deprecated]]
    GooseFEM::Mesh::Quad4::FineLayer getFineLayerMesh() const
    {
        return m_finelayer;
    }
 
    // elements of the Regular mesh per element of the FineLayer mesh
    // and the fraction by which the overlap is
 
    [[deprecated]]
    std::vector<std::vector<size_t>> getMap() const
    {
        return m_elem_regular;
    }
 
    [[deprecated]]
    std::vector<std::vector<double>> getMapFraction() const
    {
        return m_frac_regular;
    }
 
    template <class T, size_t rank>
    array_type::tensor<T, rank> mapToRegular(const array_type::tensor<T, rank>& data) const
    {
        GOOSEFEM_ASSERT(data.shape(0) == m_finelayer.nelem());
 
        std::array<size_t, rank> shape;
        std::copy(data.shape().cbegin(), data.shape().cend(), &shape[0]);
        shape[0] = m_regular.nelem();
 
        array_type::tensor<T, rank> ret = xt::zeros<T>(shape);
 
        for (size_t e = 0; e < m_finelayer.nelem(); ++e) {
            for (size_t i = 0; i < m_elem_regular[e].size(); ++i) {
                xt::view(ret, m_elem_regular[e][i]) += m_frac_regular[e][i] * xt::view(data, e);
            }
        }
 
        return ret;
    }
 
private:
    GooseFEM::Mesh::Quad4::FineLayer m_finelayer; 
    GooseFEM::Mesh::Quad4::Regular m_regular; 
    std::vector<std::vector<size_t>> m_elem_regular; 
    std::vector<std::vector<double>> m_frac_regular; 
};
 
} // namespace Map
 
} // namespace Quad4
} // namespace Mesh
} // namespace GooseFEM
 
#endif