On the numerical rank of the off-diagonal blocks of Schur complements of discretized elliptic PDEs. (English) Zbl 1209.65032
Summary: It is shown that the numerical rank of the off-diagonal blocks of certain Schur complements of matrices that arise from the finite-difference discretization of constant coefficient, elliptic PDEs in two spatial dimensions is bounded by a constant independent of the grid size. Moreover, in three-dimensional problems the Schur complements are shown to have off-diagonal blocks whose numerical rank is a slowly growing function.
MSC:
65F05 | Direct numerical methods for linear systems and matrix inversion |
35J25 | Boundary value problems for second-order elliptic equations |
65N06 | Finite difference methods for boundary value problems involving PDEs |