Intrepid2_CellTools_Serial.hpp

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#ifndef __INTREPID2_CELLTOOLS_SERIAL_HPP__
#define __INTREPID2_CELLTOOLS_SERIAL_HPP__

#include "Intrepid2_ConfigDefs.hpp"

#include "Shards_CellTopology.hpp"

#include "Intrepid2_Types.hpp"
#include "Intrepid2_Utils.hpp"
#include "Intrepid2_Kernels.hpp"

#include "Intrepid2_CellData.hpp"

namespace Intrepid2 {

namespace Impl {

class CellTools {
public:

  struct Serial {

    // output:
    //   jacobian (physDim,refDim) - jacobian matrix evaluated at a single point
    // input:
    //   grads    (numNodes,refDim) - hgrad basis grad values evaluated at a single point (C1/C2 element only)
    //   nodes    (numNodes,physDim) - cell element-to-node connectivity
    template<typename jacobianViewType,
    typename basisGradViewType,
    typename nodeViewType>
    KOKKOS_INLINE_FUNCTION
    static void
    computeJacobian(const jacobianViewType  &jacobian, // physDim,refDim
        const basisGradViewType &grads,    // numNodes,refDim
        const nodeViewType      &nodes) {  // numNodes,physDim
      const auto numNodes = nodes.extent(0);

      const auto  physDim = jacobian.extent(0);
      const auto refDim = jacobian.extent(1);

      INTREPID2_TEST_FOR_ABORT( numNodes != grads.extent(0), "grad dimension_0 does not match to cardinality.");
      INTREPID2_TEST_FOR_ABORT(refDim != grads.extent(1), "grad dimension_1 does not match to space dim.");
      INTREPID2_TEST_FOR_ABORT( physDim != nodes.extent(1), "node dimension_1 does not match to space dim.");

      Kernels::Serial::gemm_trans_notrans(1.0, nodes, grads, 0.0, jacobian);
    }

    // output:
    //   point (physDim)   - mapped physical point
    // input:
    //   vals  (numNodes)   - hgrad basis values evaluated at a single point (C1/C2 element only)
    //   nodes (numNodes,physDim) - cell element-to-node connectivity
    template<typename PointViewType,
    typename basisValViewType,
    typename nodeViewType>
    KOKKOS_INLINE_FUNCTION
    static void
    mapToPhysicalFrame(const PointViewType    &point,    // physDim
        const basisValViewType &vals,     // numNodes
        const nodeViewType     &nodes) {  // numNodes,physDim
      const auto numNodes = vals.extent(0);
      const auto physDim = point.extent(0);

      INTREPID2_TEST_FOR_ABORT(numNodes != nodes.extent(0), "nodes dimension_0 does not match to vals dimension_0.");
      INTREPID2_TEST_FOR_ABORT(physDim != nodes.extent(1), "node dimension_1 does not match to space dim.");

      Kernels::Serial::gemv_trans(1.0, nodes, vals, 0.0, point);
    }

    template<typename implBasisType,
    typename refPointViewType,
    typename phyPointViewType,
    typename nodeViewType>
    KOKKOS_INLINE_FUNCTION
    static bool
    mapToReferenceFrame(const refPointViewType &refPoint, // refDim
        const phyPointViewType &physPoint, // physDim
        const nodeViewType &nodes,
        const double tol = tolerence()) {  // numNodes,physDim
      const ordinal_type refDim = refPoint.extent(0);
      const ordinal_type physDim = physPoint.extent(0);
      const ordinal_type numNodes = nodes.extent(0);

      INTREPID2_TEST_FOR_ABORT(refDim > physDim, "the dimension of the reference cell is greater than physical cell dimension.");
      INTREPID2_TEST_FOR_ABORT(physDim != static_cast<ordinal_type>(nodes.extent(1)), "physPoint dimension_0 does not match to space dim.");
      INTREPID2_TEST_FOR_ABORT(numNodes > 27, "function hard-coded to support at most mappings with 27 Dofs");

      typedef typename refPointViewType::non_const_value_type value_type;

      // I want to use view instead of dynrankview
      // NMAX = 27, MAXDIM = 3
      value_type buf[27*3 + 27 + 9 + 9 + 9 + 9 + 3 + 3] = {}, *ptr = &buf[0];
      Kokkos::DynRankView<value_type,
      Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> grads(ptr, numNodes, refDim); ptr += numNodes*refDim;

      Kokkos::DynRankView<value_type,
      Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> vals(ptr, numNodes); ptr += numNodes;

      Kokkos::DynRankView<value_type,
      Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> jac(ptr, physDim, refDim); ptr += physDim*refDim;

      Kokkos::DynRankView<value_type,
      Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> metric(ptr, refDim, refDim); ptr += refDim*refDim;

      Kokkos::DynRankView<value_type,
      Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> invMetric(ptr, refDim, refDim); ptr += refDim*refDim;

      Kokkos::DynRankView<value_type,
      Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> invDf(ptr, refDim, physDim); ptr += refDim*physDim;

      Kokkos::DynRankView<value_type,
      Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> tmpPhysPoint(ptr, physDim); ptr += physDim;

      Kokkos::DynRankView<value_type,
      Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> oldRefPoint(ptr, refDim); ptr += refDim;

      // set initial guess
      for (ordinal_type j=0;j<refDim;++j) oldRefPoint(j) = 0;

      double xphyNorm = Kernels::Serial::norm(physPoint, NORM_ONE);

      bool converged = false;
      for (ordinal_type iter=0;iter<Parameters::MaxNewton;++iter) {
        // xtmp := F(oldRefPoint);
        implBasisType::template Serial<OPERATOR_VALUE>::getValues(vals, oldRefPoint);
        mapToPhysicalFrame(tmpPhysPoint, vals, nodes);
        Kernels::Serial::z_is_axby(tmpPhysPoint, 1.0, physPoint, -1.0, tmpPhysPoint);  //residual  xtmp := physPoint - F(oldRefPoint);
        double residualNorm = Kernels::Serial::norm(tmpPhysPoint, NORM_ONE);
        if (residualNorm < tol*xphyNorm) {
          converged = true;
          break;
        }

        // DF^{-1}
        implBasisType::template Serial<OPERATOR_GRAD>::getValues(grads, oldRefPoint);
        CellTools::Serial::computeJacobian(jac, grads, nodes);

        if(physDim == refDim) { //jacobian inverse
          Kernels::Serial::inverse(invDf, jac);
        } else { //jacobian is not square, we compute the pseudo-inverse (jac^T jac)^{-1} jac^T
          Kernels::Serial::gemm_trans_notrans(1.0, jac, jac, 0.0, metric);
          Kernels::Serial::inverse(invMetric, metric);
          Kernels::Serial::gemm_notrans_trans(1.0, invMetric, jac, 0.0, invDf);
        }

        // Newton
        Kernels::Serial::gemv_notrans(1.0, invDf, tmpPhysPoint, 0.0, refPoint); // refPoint := DF^{-1}( physPoint - F(oldRefPoint))
        Kernels::Serial::z_is_axby(refPoint, 1.0, oldRefPoint,  1.0, refPoint); // refPoint += oldRefPoint

        // temporarily overwriting oldRefPoint with oldRefPoint-refPoint
        Kernels::Serial::z_is_axby(oldRefPoint, 1.0, oldRefPoint, -1.0, refPoint);

        double err = Kernels::Serial::norm(oldRefPoint, NORM_ONE);
        if (err < tol) {
          converged = true;
          break;
        }

        Kernels::Serial::copy(oldRefPoint, refPoint);
      }
      return converged;
    }

    template<typename refEdgeTanViewType, typename ParamViewType>
    KOKKOS_INLINE_FUNCTION
    static void
    getReferenceEdgeTangent(const refEdgeTanViewType refEdgeTangent,
        const ParamViewType edgeParametrization,
        const ordinal_type edgeOrdinal ) {

      ordinal_type dim = edgeParametrization.extent(1);
      for(ordinal_type i = 0; i < dim; ++i) {
        refEdgeTangent(i) = edgeParametrization(edgeOrdinal, i, 1);
      }
    }

    template<typename refFaceTanViewType, typename ParamViewType>
    KOKKOS_INLINE_FUNCTION
    static void
    getReferenceFaceTangent(const refFaceTanViewType refFaceTanU,
        const refFaceTanViewType refFaceTanV,
        const ParamViewType faceParametrization,
        const ordinal_type faceOrdinal) {

      // set refFaceTanU -> C_1(*)
      // set refFaceTanV -> C_2(*)
      ordinal_type dim = faceParametrization.extent(1);
      for(ordinal_type i = 0; i < dim; ++i) {
        refFaceTanU(i) = faceParametrization(faceOrdinal, i, 1);
        refFaceTanV(i) = faceParametrization(faceOrdinal, i, 2);
      }
    }

    template<typename edgeTangentViewType, typename ParamViewType, typename jacobianViewType>
    KOKKOS_INLINE_FUNCTION
    static void
    getPhysicalEdgeTangent(const edgeTangentViewType edgeTangent, // physDim
        const ParamViewType edgeParametrization,
        const jacobianViewType jacobian,         // physDim, physDim
        const ordinal_type edgeOrdinal) {
      typedef typename ParamViewType::non_const_value_type value_type;
      const ordinal_type dim = edgeParametrization.extent(1);
      value_type buf[3];
      Kokkos::DynRankView<value_type, Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> refEdgeTangent(&buf[0], dim);

      getReferenceEdgeTangent(refEdgeTangent, edgeParametrization, edgeOrdinal);
      Kernels::Serial::matvec_product(edgeTangent, jacobian, refEdgeTangent);
    }

    template<typename faceTanViewType, typename ParamViewType, typename jacobianViewType>
    KOKKOS_INLINE_FUNCTION
    static void
    getPhysicalFaceTangents( faceTanViewType faceTanU, // physDim
        faceTanViewType faceTanV, // physDim
        const ParamViewType faceParametrization,
        const jacobianViewType jacobian,       // physDim, physDim
        const ordinal_type faceOrdinal) {
      typedef typename ParamViewType::non_const_value_type value_type;
      const ordinal_type dim = faceParametrization.extent(1);
      INTREPID2_TEST_FOR_ABORT(dim != 3,
          "computing face tangents requires dimension 3.");
      value_type buf[6];
      Kokkos::DynRankView<value_type,
      Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> refFaceTanU(&buf[0], dim), refFaceTanV(&buf[3], dim);

      getReferenceFaceTangent(refFaceTanU,
          refFaceTanV,
          faceParametrization,
          faceOrdinal);

      Kernels::Serial::matvec_product_d3(faceTanU, jacobian, refFaceTanU);
      Kernels::Serial::matvec_product_d3(faceTanV, jacobian, refFaceTanV);
    }


    template<typename faceNormalViewType, typename ParamViewType, typename jacobianViewType>
    KOKKOS_INLINE_FUNCTION
    static void
    getPhysicalFaceNormal(const faceNormalViewType faceNormal, // physDim
        const ParamViewType faceParametrization,
        const jacobianViewType jacobian,       // physDim, physDim
        const ordinal_type faceOrdinal) {
      typedef typename ParamViewType::non_const_value_type value_type;
      const ordinal_type dim = faceParametrization.extent(1);
      INTREPID2_TEST_FOR_ABORT(dim != 3,
          "computing face normal requires dimension 3.");
      value_type buf[6];
      Kokkos::DynRankView<value_type,
      Kokkos::AnonymousSpace,
      Kokkos::MemoryUnmanaged> faceTanU(&buf[0], dim), faceTanV(&buf[3], dim);

      getPhysicalFaceTangents(faceTanU, faceTanV,
          faceParametrization,
          jacobian,
          faceOrdinal);
      Kernels::Serial::vector_product_d3(faceNormal, faceTanU, faceTanV);
    }

    template<typename sideNormalViewType, typename ParamViewType, typename jacobianViewType>
    KOKKOS_INLINE_FUNCTION
    static void
    getPhysicalSideNormal(const sideNormalViewType sideNormal, // physDim
        const ParamViewType sideParametrization,
        const jacobianViewType jacobian,       // physDim, physDim
        const ordinal_type sideOrdinal) {
      const ordinal_type dim = sideParametrization.extent(1);
      typedef typename ParamViewType::non_const_value_type value_type;
      switch (dim) {
      case 2: {
        value_type buf[3];
        Kokkos::DynRankView<value_type,
        Kokkos::AnonymousSpace,
        Kokkos::MemoryUnmanaged> edgeTangent(&buf[0], dim);
        getPhysicalEdgeTangent(edgeTangent, sideParametrization, jacobian, sideOrdinal);
        sideNormal(0) =  edgeTangent(1);
        sideNormal(1) = -edgeTangent(0);
        break;
      }
      case 3: {
        getPhysicalFaceNormal(sideNormal, sideParametrization, jacobian, sideOrdinal);
        break;
      }
      default: {
        INTREPID2_TEST_FOR_ABORT(true, "cell dimension is out of range.");
        break;
      }
      }
    }
  };
};
}
}

#endif