Dear Sandeep, Look for routines intp_rst, grad_rstd, etc., and calls to them in convect.f and induct.f There are several routines that map onto the finer GL mesh from the base GLL mesh. The metrics, J*dr/dx, J*dr/dy, etc., are already on the fine mesh and collocated with the quadrature weight on that fine mesh when they are constructed (in set_dealias_rx in induct.f). The mathematics of these procedure is described in Sec. 3 of Stabilization of the spectral element method in convection dominated flows by recovery of skew-symmetry * Johan Malm, * Philipp Schlatter * Paul F. Fischer * Dan S. Henningson NOTE: After you create your nonlinear source term, you should divide the value each point x_{ijke} by bm1(i,j,k,e), because Nek multiplies the entry in qvol by bm1(i,j,k,e). In your case, however, you've already accounted for the mass matrix by incorporated the mass matrix on the fine-GL points. I would set up your u x nabla term via a call to userchk and store the result (already divided by bm1), then just dereference it inside qvol. via: subroutine qvol(i,j,k,eg) ... ... common /mynonlin/ s(lx1,ly1,lz1,lelt,ldim) integer e,eg e=gllel(eg) qvol=s(i,j,k,e,ifield-2) return end or something like that. The time step will all be correct and you will get 2nd or 3rd-order accuracy in time via Nek's standard BDFk/EXTk hth, Paul ________________________________ From: Nek5000-users <[email protected]> on behalf of [email protected] <[email protected]> Sent: Wednesday, May 23, 2018 4:50:19 AM To: [email protected] Subject: [Nek5000-users] dealias; mass matrix; interp_rstd Dear Neks, I solve \partial A/\partial t = \nabla^2 A + u x Curl A, where A = (s1,s2,s3) I solve three scalar equations with respective components of u x Curl A as forcing terms in qvol. I would like to compute the dealiased product of u x Curl A I build my code based on kov_stokes_test.usr and subroutines in induct.f I compute local curl, project curl and U onto fine mesh, perform product and project the product back to coarse mesh using interp_rstd However, I am not sure about the multiplication of mass matrices for the product in these subroutines. I attach my usr, rea and SIZE files. Your suggestions are welcome. Thanks, Sandeep