2016/01/25 by Sriramkrishnan Muralikrishnan, Minh-Binh Tran, Muralikrishnan, Sriramkrishnan +4
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in inverse problems #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1601.06681
10 pages, 5 figures, submitted to 14th Copper mountain conference on iterative methods (student paper competition)
openalex publication_date 2016/01/25 · arxiv created 2016/01/27 · arxiv updated 2016/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a scalable and efficient iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of hyperbolic partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations. In particular, the method is a fixed-point approach that requires only independent element-by-element local solves in each iteration. As such, it is well-suited for current and future computing systems with massive concurrencies. We rigorously show that the proposed method is exponentially convergent in the number of iterations for transport and linearized shallow water equations. Furthermore, the convergence is independent of the solution order. Various 2D and 3D numerical results for steady and time-dependent problems are presented to verify our theoretical findings.