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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Reichert, Adam H.

Contributors dc:contributor

• Bodony, Daniel J.
• Olson, Luke N.
• Heath, Michael T.
• Henshaw, William
• Gropp, William D.

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

Statement dc:rights

• Copyright 2011 Adam H. Reichert

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/26201

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/26201