Mass lumping in time dependent problem

[kamensky]

I would avoid setting up a diagonal matrix and then using it in a linear solve, since this introduces unnecessary overhead. It would be equivalent to just keep the diagonal of M_lumped as a vector, then use PETSc’s VecPointwiseDivide function as a linear solver. You can access it through the petsc4py API, assuming you are using FEniCS’s default PETSc linear algebra backend. I wrote up an example of this in my answer to the following question:

Dot(grad(u), grad(u)) has negative values

Hi everyone, I’m using macOS Mojave (10.14.6), miniconda, and FEniCS 2018 with Python. I have a function u: \mathbb{R}^d \rightarrow \mathbb{R}, d = 1, 2. What I want to compute now is the norm / length of its gradient, so | \nabla u| = \sqrt{\nabla u \cdot \nabla u}. Looking only at the dot product, then this should be nonnegative. But if I take u as this function [u] then |\nabla u| and \nabla u \cdot \nabla u should have (possibly hughe) jumps at x = 0.3 and 0.7. Instead I get something li…

See, in particular, the function lumpedProject, which implements lumped-mass L^2 projection of some arbitrary function f using VecPointwiseDivide.