Hi there,

For 10-noded tetrahedral elements (4 on corners and 6 on mid-edges), I am wondering if there is any consistent way of lumping the mass matrix?

Thanks in advance.

Tony

In FEM (or FVEM), one of the most common pratices for the lumping is as follow:

For each equation associated to a dof, the coefficients off the main diagonal are added together with the one on the main diagonal. Then, these coeffcients (the ones off the main diagonal) are set to zero. This procedure is independant from the type of element being used.

Note: This procedure can only be done with the local mass matrix.

Regards

Thanks kindly for your reply.

But to my understanding, the row-sum technique only makes sense for linear elements. Right? If you apply this method to quadratic elements (I am using 6-noded triangles and 10-noded tetrahedras), you may get negative mass for some nodes.

I tried the closed NewtonCotes quadrature rule, but this does not work either. However, it does work for 7-noded triangles and 11-noded tetrahedras (one additional node at the centroid).

Thanks anyway.

Tony