Stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition
Reichert, Adam H.
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https://hdl.handle.net/2142/26201
Description
Title
Stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition
Author(s)
Reichert, Adam H.
Issue Date
2011-08-25T22:18:30Z
Director of Research (if dissertation) or Advisor (if thesis)
Heath, Michael T.
Bodony, Daniel J.
Doctoral Committee Chair(s)
Heath, Michael T.
Bodony, Daniel J.
Committee Member(s)
Olson, Luke N.
Henshaw, William
Gropp, William D.
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
High order finite difference methods
Overlapping domain decomposition
Numerical stability
Generalized summation-by-parts
Abstract
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.
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