A numerical algorithm for the diffusion equation using 3D FEM and the Arnoldi method (Q1971588)

From the mathematical point of view the authors build up a numerical scheme in order to solve the Boltzmann transport equation in its simplest form. They use the classical finite element method (FEM) in order to transform the above equation into a generalized state space equation. They employ the Krylov subspace method to compute the impulse response of the system (the exponential of a large matrix). Consequently, they obtain the ``most'' controllable subspace. Then they use the Arnoldi algorithm to find its orthogonal. However, the work seems to be extremely interesting from the medical technology point of view.