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Title:Stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition
Author(s):Reichert, Adam H.
Director of Research:Heath, Michael T.; Bodony, Daniel J.
Doctoral Committee Chair(s):Heath, Michael T.; Bodony, Daniel J.
Doctoral Committee Member(s):Olson, Luke N.; Henshaw, William; Gropp, William D.
Department / Program:Computer Science
Discipline:Computer Science
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(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.
Issue Date:2011-08-25
Rights Information:Copyright 2011 Adam H. Reichert
Date Available in IDEALS:2011-08-25
Date Deposited:2011-08

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