A Hierarchical Preconditioner for Wave Problems in Quasilinear Complexity

This paper introduces a novel, hierarchical preconditioner based on nested dissection and matrix compression. The is intended for continuous discontinuous Galerkin formulations of elliptic problems. We exploit the property that Schur complements arising in such problems can be well approximated by matrices. An approximate factorization computed matrix-free (quasi-)linear number operations. specifically designed to aid process using demonstrate viability range two-dimensional problems, including Helmholtz equation elastic wave equation. Throughout all tests, phenomena with high wavenumbers, generalized minimal residual method (GMRES) proposed converges very low iterations. theoretical cost verified numerical experiments, growth off-diagonal ranks studied both $h$- $p$-refinement.