!--------------------------------------------------------------------------
   !---------------------------- curl_laplacian ----------------------------------
   !$OMP DO SCHEDULE(STATIC)
   DO ij = 1, dual_num
      ! this VLOOP iterates over dual cell edges
      SELECT CASE(dual_deg(ij))
      CASE(3)
         edge1 = dual_edge(1,ij)
         edge2 = dual_edge(2,ij)
         edge3 = dual_edge(3,ij)
         sign1 = dual_ne(1,ij)
         sign2 = dual_ne(2,ij)
         sign3 = dual_ne(3,ij)
         !DIR$ SIMD
         DO l = 1, llm
            etav = 0.d0
            etav = etav + sign1*u(l,edge1)
            etav = etav + sign2*u(l,edge2)
            etav = etav + sign3*u(l,edge3)
            qv(l,ij) = etav/Av(ij)
         END DO
      CASE(4)
         edge1 = dual_edge(1,ij)
         edge2 = dual_edge(2,ij)
         edge3 = dual_edge(3,ij)
         edge4 = dual_edge(4,ij)
         sign1 = dual_ne(1,ij)
         sign2 = dual_ne(2,ij)
         sign3 = dual_ne(3,ij)
         sign4 = dual_ne(4,ij)
         !DIR$ SIMD
         DO l = 1, llm
            etav = 0.d0
            etav = etav + sign1*u(l,edge1)
            etav = etav + sign2*u(l,edge2)
            etav = etav + sign3*u(l,edge3)
            etav = etav + sign4*u(l,edge4)
            qv(l,ij) = etav/Av(ij)
         END DO
      CASE DEFAULT
         !DIR$ SIMD
         DO l = 1, llm
            etav = 0.d0
            DO iedge = 1, dual_deg(ij)
               edge = dual_edge(iedge,ij)
               etav = etav + dual_ne(iedge,ij)*u(l,edge)
            END DO
            qv(l,ij) = etav/Av(ij)
         END DO
      END SELECT
   END DO
   !$OMP END DO
   !$OMP DO SCHEDULE(STATIC)
   DO edge = 1, edge_num
      ij_up = up(edge)
      ij_down = down(edge)
      !DIR$ SIMD
      DO l = 1, llm
         curlcurl(l,edge) = 1.*(qv(l,ij_down)-qv(l,ij_up))*(1./le_de(edge))
      END DO
   END DO
   !$OMP END DO
   !---------------------------- curl_laplacian ----------------------------------
   !--------------------------------------------------------------------------