Thank you for the assistance. I got the MTKized system to work
# build initial conditions
u0 = zeros(N*3 + 1)
u0[indices_Tgas] .= Tin
u0[indices_Tsol] .= 20
u0[indices_mflux] = 0.5
u0[indices_RConcentrationSolid] .= 3000
# build mass matrix
Ii = [indices_Tsol; indices_RConcentrationSolid];
Jj = [indices_Tsol; indices_RConcentrationSolid];
V = ones(length(Ii));
Msparse = sparse(Ii,Jj,V, 3*N+1, 3*N+1)
f_DAE = ODEFunction(DiscretizedSystemMassMatrixForm_noDualcache!, mass_matrix=Msparse)
probDAE = ODEProblem(f_DAE,u0,(0.0,1500),p_noDualCache)
de = modelingtoolkitize(probDAE)
# MTKized system back to numerical problem:
probDAE_MTK1 = ODEProblem(de,[],(0.0,1500),p_noDualCache,jac=true,sparse=true)
# solve the numerical problem - works
sol_MTK1 = solve(probDAE_MTK1,QBDF())
# pretty much as fast as solving non-MTKized system with Jacobian sparsity, as in above posts.
@benchmark solve(probDAE_MTK1,QBDF())
To my surpise, the MTKized system does not solve faster than the original system with Jacobian sparsity information, although the MTKized system should use the analytic Jacobian, or am I mistaken?
Anyway. In a next step, I tried to structual_simplify the system and solve it:
# Now try to structural_simplify the system before solving it
de2 = structural_simplify(de)
probDAE_MTK2 = ODEProblem(de2,[],(0.0,1500),p_noDualCache,jac=true,sparse=true)
sol_MTK2 = solve(probDAE_MTK2,QBDF())
Unfortunately, I get an UndefVarError: x201 not defined. Why is that? What can I do to get it to work?
Thank you!