Browsing by Author "Symes, William"

Now showing 1 - 7 of 7
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    Accelerated Plane-wave Discontinuous Galerkin for Heterogeneous Scattering Problems
    (2015-04-23) Atcheson, Thomas Reid; Warburton, Timothy; Symes, William; Sorensen, Dan; Sarkar, Vivek
    This thesis considers algorithmic and computational acceleration of numerical wave modelling at high frequencies. Numerical propagation of linear waves at high frequencies poses a significant challenge to modern simulation techniques. Despite the fact that potential practical benefits led a great deal of attention to this problem, current research has yet to provide a general and performant method to solve it. I consider finite element as a possible solution because it can handle geometric complex- ity of heterogeneous domains, but unfortunately it suffers from the “pollution” effect which imposes a prohobitively large memory requirement to handle high frequencies. One recent step towards enabling the finite element method to solve high frequency wave propagation in the frequency domain involves using a plane-wave basis rather than the standard polynomial basis. This allows highly compressed representations of scattering waves but otherwise appeared to limit users to nearly-homogeneous prob- lems. This thesis explores the use of plane-waves in a discontinuous Galerkin method (PWDG) for highly heterogeneous problems possibly containing a point source. The low-memory nature of PWDG and the fact that its expressions can be computed in an entirely symbolic manner without quadratures furthermore permits an efficient graphics processing unit (GPU) implementation such that problems with very high frequencies can be solved on a single workstation. This thesis includes computational results demonstrating results for frequencies in excess of 100 hertz on the Marmousi model, solved using only a single GPU.
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    Discretization of Multipole Sources in a Finite Difference Setting for Wave Propagation Problems
    (2018-06-20) Bencomo, Mario J.; Symes, William
    Seismic sources are commonly idealized as point-sources due to their small spatial extent relative to seismic wavelengths. The acoustic isotropic point-radiator is inadequate as a model of seismic wave generation for seismic sources that are known to exhibit directivity. Therefore, accurate modeling of seismic wavefields must include source representations generating anisotropic radiation patterns. Such seismic sources can be modeled as linear combinations of multipole point-sources. In this paper we present a method for discretizing multipole sources in a finite difference setting, an extension of the moment matching conditions developed for the Dirac delta function in other applications. We also provide the necessary analysis and numerical evidence to demonstrate the accuracy of our singular source approximations. In particular, we develop a weak convergence theory for the discretization of a family of symmetric hyperbolic systems of first-order partial differential equations, with singular source terms, solved via staggered-grid finite difference methods. Numerical experiments demonstrate a stronger result than what is presented in our convergence theory, namely, optimal convergence rates of numerical solutions are achieved point-wise in space away from the source if an appropriate source discretization is used.
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    Full-waveform inversion via source-receiver extension
    (Society of Exploration Geophysicists, 2017) Huang, Guanghui; Nammour, Rami; Symes, William
    Full-waveform inversion produces highly resolved images of the subsurface and quantitative estimation of seismic wave velocity, provided that its initial model is kinematically accurate at the longest data wavelengths. If this initialization constraint is not satisfied, iterative model updating tends to stagnate at kinematically incorrect velocity models producing suboptimal images. The source-receiver extension overcomes this “cycle-skip” pathology by modeling each trace with its own proper source wavelet, permitting a good data fit throughout the inversion process. Because source wavelets should be constant (or vary systematically) across a shot gather, a measure of source trace dependence, for example, the mean square of the signature-deconvolved wavelet scaled by time lag, can be minimized to update the velocity model. For kinematically simple data, such measures of wavelet variance are mathematically equivalent to traveltime misfit. Thus, the model obtained by source-receiver extended inversion is close to that produced by traveltime tomography, even though the process uses no picked times. For more complex data, in which energy travels from source to receiver by multiple raypaths, Green’s function spectral notches may lead to slowly decaying trace-dependent wavelets with energy at time lags unrelated to traveltime error. Tikhonov regularization of the data-fitting problem suppresses these large-lag signals. Numerical examples suggest that this regularized formulation of source-receiver extended inversion is capable of recovering reasonably good velocity models from synthetic transmission and reflection data without stagnation at suboptimal models encountered by standard full-waveform inversion, but with essentially the same computational cost.
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    High order discontinuous Galerkin methods for simulating miscible displacement process in porous media with a focus on minimal regularity
    (2015-04-20) Li, Jizhou; Riviere, Beatrice M.; Symes, William; Hirasaki, George; Warburton, Timothy; Heinkenschloss, Matthias
    In my thesis, I formulate, analyze and implement high order discontinuous Galerkin methods for simulating miscible displacement in porous media. The analysis concerning the stability and convergence under the minimal regularity assumption is established to provide theoretical foundations for using discontinuous Galerkin discretization to solve miscible displacement problems. The numerical experiments demonstrate the robustness and accuracy of the proposed methods. The performance study for large scale simulations with highly heterogeneous porous media suggests strong scalability which indicates the efficiency of the numerical algorithm. The simulations performed using the algorithms for physically unstable flow show that higher order methods proposed in thesis are more suitable for simulating such phenomenon than the commonly used cell-center finite volume method.
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    High performance high-order numerical methods: applications in ocean modeling
    (2015-08-27) Gandham, Rajesh; Warburton, Timothy; Symes, William; Bradshaw, Stephen; Beatrice, Riviere
    This thesis presents high-order numerical methods for time-dependent simulations of oceanic wave propagation on modern many-core hardware architecture. Simulation of the waves such as tsunami, is challenging because of the varying fluid depths, propagation in many regions, requirement of high resolution near the shore, complex nonlinear wave phenomenon, and necessity of faster than real-time predictions. This thesis addresses issues related to stability, accuracy, and efficiency of the numerical simulation of these waves. For the simulation of tsunami waves, a two-dimensional nonlinear shallow water PDE model is considered. Discontinuous Galerkin (DG) methods on unstructured triangular meshes are used for the numerical solution of the model. These methods are not stable for nonlinear problems. To address the stability of these methods, a total variational bounded slope limiter in conjunction with a positive preserving scheme is developed, in particular for unstructured triangular meshes. Accuracy and stability of the methods are verified with test cases found in literature. These methods are also validated using 2004 Indian Ocean tsunami data to demonstrate faster than real-time simulation capability for practical problems using a commodity workstation. For accurate modeling of tsunami and ocean waves, in general, a three-dimensional hydrostatic incompressible Navier-Stokes model along with free surface conditions is considered. DG discretizations on unstructured prismatic elements are used for the numerical solutions. These prismatic elements are obtained by extruding the triangular meshes from ocean free surface to the ocean bottom. The governing equations are represented in a fixed sigma coordinate reference system. The limiting procedure, time-stepping method, accelerated implementations are adopted from two-dimensional formulations. The runtime performance of this three-dimensional method is compared with the performance of the two-dimensional shallow water model, to give an estimate of computational overhead in moving forward to three-dimensional models in practical ocean modeling applications. A GPU accelerated unsmooth aggregation algebraic method is developed. Algebraic multi-grid method is used as a linear solver in many engineering applications such as computational fluid dynamics. The developed method involves a setup stage and a solution stage. This method is parallelized for both stages unlike most of the methods that are parallelized only for the solution stage. Efficiency of the setup is crucial in these applications since the setup has to be performed many times. The efficiency of the method is demonstrated using a sequence of downsized problems. The computational kernels are expressed in an extensive multi-threading library OCCA. Using OCCA, the developed implementations achieve portability across various hardware architectures such as GPUs, CPUs, and multi-threading programming models OpenCL, CUDA, and OpenMP. The optimal performance of these kernels across various thread models and hardware architecture is compared.
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    Terahertz Multistatic Reflection Imaging
    (2002-07-01) Dorney, Timothy D.; Symes, William; Baraniuk, Richard G.; Mittleman, Daniel M.; Digital Signal Processing (http://dsp.rice.edu/)
    We describe a new imaging method using single-cycle pulses of terahertz (THz) radiation. This technique emulates the data collection and image processing procedures developed for geophysical prospecting and is made possible by the availability of fiber-coupled THz receiver antennas. We use a migration procedure to solve the inverse problem; this permits us to reconstruct the location, the shape, and the refractive index of targets. We show examples for both metallic and dielectric model targets, and we perform velocity analysis on dielectric targets to estimate the refractive indices of imaged components. These results broaden the capabilities of THz imaging systems and also demonstrate the viability of the THz system as a test bed for the exploration of new seismic processing methods.
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    Terahertz Reflection Imaging using Kirchhoff Migration
    (2001-10-01) Dorney, Timothy D.; Johnson, Jon L.; Rudd, J. Van; Baraniuk, Richard G.; Symes, William; Mittleman, Daniel M.; Digital Signal Processing (http://dsp.rice.edu/)
    We describe a new imaging method that uses single-cycle pulses of terahertz (THz) radiation. This technique emulates data-collection and image-processing procedures developed for geophysical prospecting and is made possible by the availability of fiber-coupled THz receiver antennas. We use a simple migration procedure to solve the inverse problem; this permits us to reconstruct the location and shape of targets. These results demonstrate the feasibility of the THz system as a test-bed for the exploration of new seismic processing methods involving complex model systems.