2017/02/07 by Siyang Wang, Wang, Siyang
Engineering · Mathematics · #65M06 #65M12 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1702.02056
openalex publication_date 2017/02/07 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28
This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators being norm-contracting, which is satisfied by the second and fourth order operators, but not by the sixth order operator. We construct new penalty terms to impose interface conditions such that the stability proof does not require the norm-contracting condition. As a consequence, the sixth order accurate scheme is also provably stable. Numerical experiments demonstrate the improved stability and accuracy property.