Browsing by Author "Vargas, Arturo"

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    Hermite Methods for the Simulation of Wave Propagation
    (2017-05) Vargas, Arturo
    Simulations of wave propagation play a crucial role in science and engineering. In applications of geophysics, they are the engine of many seismic imaging algorithms. For electrical engineers, they can be a useful tool for the design of radars and antennas. In these applications achieving high fidelity, simulations are challenging due to the inherent issues in modeling highly oscillatory waves and the associated high computational cost of high-resolution simulations. Thus the ideal numerical method should be able to capture high-frequency waves and be suitable for parallel computing. In both seismic applications and computational electromagnetics the Yee scheme, a finite difference time domain (FDTD) method, is the method of choice for structured grids. The scheme has the benefit of being easy to implement but performs poorly in the presence of high-frequency waves. High order accurate FDTD methods may be derived but ultimately rely on neighboring grid points when approximating derivative. In contrast to FDTD methods, the Hermite methods of Goodrich and co-authors (2006) use Hermite interpolation and a staggered (dual) grid to construct high order accurate numerical methods for first order hyperbolic equations. These methods achieve high order approximations in both time and space by reconstructing local polynomials within cells of the computational domain and employing Hermite-Taylor time stepping. The resulting schemes are able to evolve the solution locally within a cell making them ideal for parallel computing. Building on the original Hermite methods this thesis focuses on two goals: (1) the development of new Hermite methods and (2) their implementation on modern computing architectures. To accomplish the first objective, this thesis presents two variations of Hermite methods which are designed to simplify the scheme while preserving the favorable features. The first variation is a family of Hermite methods which do not require a dual grid. These methods eliminate the need for storing dual coefficients while maintaining optimal convergence rates. The second type of variation are Hermite methods which use leapfrog time-stepping. These schemes propagate the solution with less computation than the original scheme and may be used for either first or second order equations. To address the second objective, this thesis presents algorithms which take advantage of the many-core architecture of graphics processing units (GPU). As threedimensional simulations can easily exceed the memory of a single GPU, techniques for partitioning the data across multiple GPUs are presented. Finally, this thesis presents numerical results and performance studies which confim the accuracy and efficiency of the proposed Hermite methods for linear and nonlinear wave equations.
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    Hermite Methods for the Simulation of Wave Propagation
    (2017-04-20) Vargas, Arturo; Warburton, Timothy; Gillman, Adrianna
    Simulations of wave propagation play a crucial role in science and engineering. In applications of geophysics, they are the engine of many seismic imaging algorithms. For electrical engineers, they can be a useful tool for the design of radars and antennas. In these applications achieving high fidelity, simulations are challenging due to the inherent issues in modeling highly oscillatory waves and the associated high computational cost of high-resolution simulations. Thus the ideal numerical method should be able to capture high-frequency waves and be suitable for parallel computing. In both seismic applications and computational electromagnetics the Yee scheme, a finite difference time domain (FDTD) method, is the method of choice for structured grids. The scheme has the benefit of being easy to implement but performs poorly in the presence of high-frequency waves. High order accurate FDTD methods may be derived but ultimately rely on neighboring grid points when approximating derivative. In contrast to FDTD methods, the Hermite methods of Goodrich and co-authors (2006) use Hermite interpolation and a staggered (dual) grid to construct high order accurate numerical methods for first order hyperbolic equations. These methods achieve high order approximations in both time and space by reconstructing local polynomials within cells of the computational domain and employing Hermite-Taylor time stepping. The resulting schemes are able to evolve the solution locally within a cell making them ideal for parallel computing. Building on the original Hermite methods this thesis focuses on two goals: (1) the development of new Hermite methods and (2) their implementation on modern computing architectures. To accomplish the first objective, this thesis presents two variations of Hermite methods which are designed to simplify the scheme while preserving the favorable features. The first variation is a family of Hermite methods which do not require a dual grid. These methods eliminate the need for storing dual coefficients while maintaining optimal convergence rates. The second type of variation are Hermite methods which use leapfrog time-stepping. These schemes propagate the solution with less computation than the original scheme and may be used for either first or second order equations. To address the second objective, this thesis presents algorithms which take advantage of the many-core architecture of graphics processing units (GPU). As three-dimensional simulations can easily exceed the memory of a single GPU, techniques for partitioning the data across multiple GPUs are presented. Finally, this thesis presents numerical results and performance studies which confirm the accuracy and efficiency of the proposed Hermite methods for linear and nonlinear wave equations.
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    Radial MILO: A 4D Image Registration Algorithm Based on Filtering Block Match Data via l1-minimization
    (2015-04-21) Vargas, Arturo; Zhang, Yin; Castillo, Edward; Tapia, Richard; Warburton, Tim
    Minimal l1 Perturbation to Block Match Data (MILO) is a spatially accurate image registration algorithm developed for thoracic CT inhale/exhale images. The MILO algorithm consists of three components: (1) creating an initial estimate for voxel displacement via a Mutual Minimizing Block Matching Algorithm (MMBM), (2) a filtering step based on l1 minimization and a uniform B-spline parameterization, and (3) recovering a full displacement field based on the filtered estimates. This thesis presents a variation of MILO for 4DCT images. In practice, the use of uniform B-splines has led to rank deficient linear systems due to the spline's inability to conform to non-structured MMBM estimates. In order to adaptively conform to the data an octree is paired with radial functions. The l1 minimization problem had previously been addressed by employing QR factorization, which required substantial storage. As an alternative a block coordinate descent algorithm is employed, relieving the need for QR factorization. Furthermore, by modeling voxel trajectories as quadratic functions in time, the proposed method is able to register multiple images.