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High-order high-performance computing algorithms for wave propagation in heterogeneous media
Morgenstern, Charles O.
Morgenstern, Charles O.
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2016
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Understanding the propagation of waves using computer models is important for several applications. Major challenges for developing efficient wave propagation computer models include incorporating heterogeneous and unbounded wave propagation media, and high-frequency data. Such models lead to very large and poorly conditioned indefinite linear systems. The main focus of this thesis is to address these challenges through several mathematical and high-performance computing techniques. Our novel algorithms include developing and implementing unbounded heterogeneous media models using a hybrid of finite element and boundary element methods (FEM/BEMs). For incorporating heterogeneous media, high-frequency input data, and hybrid models, large scale simulations are needed in conjunction with iterative methods for indefinite systems. We develop efficient computer models through innovative preconditioned iterative high-order FEMs. Our implementation includes multigrid and domain decomposition algorithms, and multiple- and high-frequency simulations in two- and three-dimensional heterogeneous media with non-smooth and curved boundaries. Indefiniteness is a major computational bottleneck for wave propagation models that have been investigated for several decades. In addition to our efficient methods for the standard indefinite systems, we develop, analyze, and implement a new class of sign-definite high-order preconditioned wave propagation computer models. Our sign-definite iterative models require a small number of iterations which is independent of the frequency of the wave propagation. We demonstrate our many novel algorithms developed in this thesis using high-performance parallel computing implementations.
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