A Multilevel Approach for Trace System in HDG Discretizations

Understand

We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods.

• The key is to blend ideas from nested dissection, domain decomposition, and high-order characteristic of HDG discretizations.
• Specifically, we first create a coarse solver by eliminating and/or limiting the front growth in nested dissection.
• This is accomplished by projecting the trace data into a sequence of same or high-order polynomials on a set of increasingly $h-$coarser edges/faces.