An improved high order finite difference method for non-conforming grid interfaces for the wave equation
For computational scientists solving wave equations on complex grids, this work removes a stability barrier for high order methods, though it is an incremental improvement over existing approaches.
The paper extends a high order finite difference method for the wave equation to non-conforming grid interfaces, achieving provable stability for sixth order accuracy by constructing new penalty terms that bypass the norm-contracting condition. Numerical experiments confirm improved stability and accuracy.
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.