Publications

Collis, Samuel S.; Ober, Curtis C.; Overfelt, James R.; Young, Joseph G.

Abstract not provided.

Collis, Samuel S.; Ober, Curtis C.; van Bloemen Waanders, Bart G.

Abstract not provided.

Collis, Samuel S.; Ober, Curtis C.; Overfelt, James R.

Abstract not provided.

Collis, Samuel S.; Ober, Curtis C.; van Bloemen Waanders, Bart G.

This abstract explores the potential advantages of discontinuous Galerkin (DG) methods for the time-domain inversion of media parameters within the earth's interior. In particular, DG methods enable local polynomial refinement to better capture localized geological features within an area of interest while also allowing the use of unstructured meshes that can accurately capture discontinuous material interfaces. This abstract describes our initial findings when using DG methods combined with Runge-Kutta time integration and adjoint-based optimization algorithms for full-waveform inversion. Our initial results suggest that DG methods allow great flexibility in matching the media characteristics (faults, ocean bottom and salt structures) while also providing higher fidelity representations in target regions. Time-domain inversion using discontinuous Galerkin on unstructured meshes and with local polynomial refinement is shown to better capture localized geological features and accurately capture discontinuous-material interfaces. These approaches provide the ability to surgically refine representations in order to improve predicted models for specific geological features. Our future work will entail automated extensions to directly incorporate local refinement and adaptive unstructured meshes within the inversion process.

Society of Exploration Geophysicists International Exposition and 80th Annual Meeting 2010, SEG 2010

Smith, Thomas M.; Collis, Samuel S.; Ober, Curtis C.; Overfelt, James R.; Schwaiger, Hans F.

Motivated by the needs of seismic inversion and building on our prior experience for fluid-dynamics systems, we present a high-order discontinuous Galerkin (DG) Runge-Kutta method applied to isotropic, linearized elasto-dynamics. Unlike other DG methods recently presented in the literature, our method allows for inhomogeneous material variations within each element that enables representation of realistic earth models — a feature critical for future use in seismic inversion. Likewise, our method supports curved elements and hybrid meshes that include both simplicial and nonsimplicial elements. We demonstrate the capabilities of this method through a series of numerical experiments including hybrid mesh discretizations of the Marmousi2 model as well as a modified Marmousi2 model with a oscillatory ocean bottom that is exactly captured by our discretization.

Ober, Curtis C.

Over the past several years, verifying and validating complex codes at Sandia National Laboratories has become a major part of code development. These aspects tackle two important parts of simulation modeling: determining if the models have been correctly implemented - verification, and determining if the correct models have been selected - validation. In this talk, we will focus on verification and discuss the basics of code verification and its application to a few codes and problems at Sandia.

Knupp, Patrick K.; Ober, Curtis C.

Abstract not provided.

Weirs, Vincent G.; Lemke, Raymond W.; Robinson, Allen C.; Ober, Curtis C.; Banks, Jeffrey W.; Love, Edward L.; Scovazzi, Guglielmo S.; Shadid, John N.; Hanshaw, Heath L.

Abstract not provided.

Ober, Curtis C.; Bova, S.W.

Abstract not provided.

Knupp, Patrick K.; Ober, Curtis C.; Bond, Ryan B.

Abstract not provided.

Collection of Technical Papers - 44th AIAA Aerospace Sciences Meeting

Hooper, Russell H.; Smith, Thomas M.; Ober, Curtis C.

We demonstrate use of a Jacobian-Free Newton-Krylov solver to enable strong thermal coupling at the interface between a solid body and an external compressible fluid. Our method requires only information typically used in loose coupling based on successive substitution and is implemented within a multi-physics framework. We present results for two external flows over thermally conducting solid bodies obtained using both loose and strong coupling strategies. Performance of the two strategies is compared to elucidate both advantages and caveats associated with strong coupling.

Hooper, Russell H.; Ober, Curtis C.; Lorber, Alfred L.

Abstract not provided.

Hooper, Russell H.; Ober, Curtis C.; Lorber, Alfred L.

Abstract not provided.

Hooper, Russell H.; Ober, Curtis C.

Abstract not provided.

Hooper, Russell H.; Ober, Curtis C.; Lorber, Alfred L.

Abstract not provided.

Bartlett, Roscoe B.; Collis, Samuel S.; Keiter, Eric R.; Ober, Curtis C.

Sensitivity analysis is critically important to numerous analysis algorithms, including large scale optimization, uncertainty quantification,reduced order modeling, and error estimation. Our research focused on developing tools, algorithms and standard interfaces to facilitate the implementation of sensitivity type analysis into existing code and equally important, the work was focused on ways to increase the visibility of sensitivity analysis. We attempt to accomplish the first objective through the development of hybrid automatic differentiation tools, standard linear algebra interfaces for numerical algorithms, time domain decomposition algorithms and two level Newton methods. We attempt to accomplish the second goal by presenting the results of several case studies in which direct sensitivities and adjoint methods have been effectively applied, in addition to an investigation of h-p adaptivity using adjoint based a posteriori error estimation. A mathematical overview is provided of direct sensitivities and adjoint methods for both steady state and transient simulations. Two case studies are presented to demonstrate the utility of these methods. A direct sensitivity method is implemented to solve a source inversion problem for steady state internal flows subject to convection diffusion. Real time performance is achieved using novel decomposition into offline and online calculations. Adjoint methods are used to reconstruct initial conditions of a contamination event in an external flow. We demonstrate an adjoint based transient solution. In addition, we investigated time domain decomposition algorithms in an attempt to improve the efficiency of transient simulations. Because derivative calculations are at the root of sensitivity calculations, we have developed hybrid automatic differentiation methods and implemented this approach for shape optimization for gas dynamics using the Euler equations. The hybrid automatic differentiation method was applied to a first order approximation of the Euler equations and used as a preconditioner. In comparison to other methods, the AD preconditioner showed better convergence behavior. Our ultimate target is to perform shape optimization and hp adaptivity using adjoint formulations in the Premo compressible fluid flow simulator. A mathematical formulation for mixed-level simulation algorithms has been developed where different physics interact at potentially different spatial resolutions in a single domain. To minimize the implementation effort, explicit solution methods can be considered, however, implicit methods are preferred if computational efficiency is of high priority. We present the use of a partial elimination nonlinear solver technique to solve these mixed level problems and show how these formulation are closely coupled to intrusive optimization approaches and sensitivity analyses. Production codes are typically not designed for sensitivity analysis or large scale optimization. The implementation of our optimization libraries into multiple production simulation codes in which each code has their own linear algebra interface becomes an intractable problem. In an attempt to streamline this task, we have developed a standard interface between the numerical algorithm (such as optimization) and the underlying linear algebra. These interfaces (TSFCore and TSFCoreNonlin) have been adopted by the Trilinos framework and the goal is to promote the use of these interfaces especially with new developments. Finally, an adjoint based a posteriori error estimator has been developed for discontinuous Galerkin discretization of Poisson's equation. The goal is to investigate other ways to leverage the adjoint calculations and we show how the convergence of the forward problem can be improved by adapting the grid using adjoint-based error estimates. Error estimation is usually conducted with continuous adjoints but if discrete adjoints are available it may be possible to reuse the discrete version for error estimation. We investigate the advantages and disadvantages of continuous and discrete adjoints through a simple example.

Knupp, Patrick K.; Ober, Curtis C.

Order-of-accuracy verification is necessary to ensure that software correctly solves a given set of equations. One method to verify the order of accuracy of a code is the method of manufactured solutions. In this study, a manufactured solution has been derived and implemented that allows verification of not only the Euler, Navier-Stokes, and Reynolds-Averaged Navier-Stokes (RANS) equation sets, but also some of their associated boundary conditions (BC's): slip, no-slip (adiabatic and isothermal), and outflow (subsonic, supersonic, and mixed). Order-of-accuracy verification has been performed for the Euler and Navier-Stokes equations and these BC's in a compressible computational fluid dynamics code. All of the results shown are on skewed, non-uniform meshes. RANS results will be presented in a future paper. The observed order of accuracy was lower than the expected order of accuracy in two cases. One of these cases resulted in the identification and correction of a coding mistake in the CHAD gradient correction that was reducing the observed order of accuracy. This mistake would have been undetectable on a Cartesian mesh. During the search for the CHAD gradient correction problem, an unrelated coding mistake was found and corrected. The other case in which the observed order of accuracy was less than expected was a test of the slip BC; although no specific coding or formulation mistakes have yet been identified. After the correction of the identified coding mistakes, all of the aforementioned equation sets and BC's demonstrated the expected (or at least acceptable) order of accuracy except the slip condition.

Knupp, Patrick K.; Bond, Ryan B.; Ober, Curtis C.

Abstract not provided.

Knupp, Patrick K.; Ober, Curtis C.

Abstract not provided.

International Journal for Numerical Methods in Fluids

Roy, C.J.; Nelson, C.C.; Smith, T.M.; Ober, Curtis C.

The method of manufactured solutions is used to verify the order of accuracy of two finite-volume Euler and Navier-Stokes codes. The Premo code employs a node-centred approach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe's upwind method with MUSCL extrapolation for the convective terms and central differences for the diffusion terms, thus yielding a numerical scheme that is formally second-order accurate. The method of manufactured solutions is employed to generate exact solutions to the governing Euler and Navier-Stokes equations in two dimensions along with additional source terms. These exact solutions are then used to accurately evaluate the discretization error in the numerical solutions. Through global discretization error analyses, the spatial order of accuracy is observed to be second order for both codes, thus giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised. Examples of coding mistakes discovered using the method are also given. © 2004 John Wiley and Sons, Ltd.

Ober, Curtis C.; Ober, Curtis C.; Payne, Jeffrey L.; Lorber, Alfred L.

Abstract not provided.

Ober, Curtis C.; Womble, David E.

This report describes Salvo, a three-dimensional seismic-imaging software for complex geologies. Regions of complex geology, such as overthrusts and salt structures, can cause difficulties for many seismic-imaging algorithms used in production today. The paraxial wave equation and finite-difference methods used within Salvo can produce high-quality seismic images in these difficult regions. However this approach comes with higher computational costs which have been too expensive for standard production. Salvo uses improved numerical algorithms and methods, along with parallel computing, to produce high-quality images and to reduce the computational and the data input/output (I/O) costs. This report documents the numerical algorithms implemented for the paraxial wave equation, including absorbing boundary conditions, phase corrections, imaging conditions, phase encoding, and reduced-source migration. This report also describes I/O algorithms for large seismic data sets and images and parallelization methods used to obtain high efficiencies for both the computations and the I/O of seismic data sets. Finally, this report describes the required steps to compile, port and optimize the Salvo software, and describes the validation data sets used to help verify a working copy of Salvo.