Stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition

High order finite difference methods;Overlapping domain decomposition;Numerical stability;Generalized summation-by-parts

Reichert, Adam H.

关键词: High order finite difference methods;    Overlapping domain decomposition;    Numerical stability;    Generalized summation-by-parts;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/26201/Reichert_Adam.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Overlapping domain decomposition methods, otherwise known as overset or chimera methods, are useful approaches for simplifying the discretizations of partial differential equations in or around complex geometries. While in wide use, the methods are prone to numerical instability unless numerical diffusion or some other form of regularization is used. This is especially true for higher-order methods. To address this, high-order, provably stable, overlapping domain decomposition methods are derived for hyperbolic initial-boundary-value problems. The overlap is treated by splitting the domain into pieces and using newly derived generalized summation-by-parts derivative operators and polynomial interpolation. Numerical regularization is not required for stability in the linear limit. Applications to linear and nonlinear problems in one and two dimensions are presented and new high-order generalized summation-by-parts derivative operators are derived.