Low-rank approximation of elliptic boundary value problems with high-contrast coefficients
Provides theoretical justification for robust numerical methods in high-contrast elliptic problems, which is important for computational science and engineering applications.
The paper proves that degenerate approximations to Green's function for elliptic problems with high-contrast coefficients converge independently of the contrast in suitable norms, enabling fast hierarchical matrix methods without coefficient adaptation.
We analyze the convergence of degenerate approximations to Green's function of elliptic boundary value problems with high-contrast coefficients. It is shown that the convergence is independent of the contrast if the error is measured with respect to suitable norms. This lays ground to fast methods (so-called hierarchical matrix approximations) which do not have to be adapted to the coefficients.