Publications

Glusa, Christian A.; D'Elia, Marta D.; Antil, Harbir A.; Weiss, Chester J.; van Bloemen Waanders, Bart G.

Abstract not provided.

SIAM Journal on Scientific Computing

Glusa, Christian A.; ANTIL, HARBIR; D'Elia, Marta D.; van Bloemen Waanders, Bart G.; Weiss, Chester J.

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in geophysical electromagnetics. We establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales as well as the best possible solver for the classical integer-order Helmholtz equation. We conclude with several illustrative examples that confirm our theoretical findings.

El-Kady, I.; Reinke, Charles M.; van Bloemen Waanders, Bart G.; Ridzal, Denis R.; Su, Mehmet F.; Fitzpatrick, David F.; Chilton, Ryan C.

Abstract not provided.

Walsh, Timothy W.; Aquino, Wilkins A.; Ridzal, Denis R.; Kouri, Drew P.; van Bloemen Waanders, Bart G.

Abstract not provided.

Atmospheric Chemistry and Physics

Ray, Jaideep R.; van Bloemen Waanders, Bart G.

Abstract not provided.

Ray, Jaideep R.; Lee, Jina L.; Lefantzi, Sophia L.; van Bloemen Waanders, Bart G.

The estimation of fossil-fuel CO2 emissions (ffCO2) from limited ground-based and satellite measurements of CO2 concentrations will form a key component of the monitoring of treaties aimed at the abatement of greenhouse gas emissions. To that end, we construct a multiresolution spatial parametrization for fossil-fuel CO2 emissions (ffCO2), to be used in atmospheric inversions. Such a parametrization does not currently exist. The parametrization uses wavelets to accurately capture the multiscale, nonstationary nature of ffCO2 emissions and employs proxies of human habitation, e.g., images of lights at night and maps of built-up areas to reduce the dimensionality of the multiresolution parametrization. The parametrization is used in a synthetic data inversion to test its suitability for use in atmospheric inverse problem. This linear inverse problem is predicated on observations of ffCO2 concentrations collected at measurement towers. We adapt a convex optimization technique, commonly used in the reconstruction of compressively sensed images, to perform sparse reconstruction of the time-variant ffCO2 emission field. We also borrow concepts from compressive sensing to impose boundary conditions i.e., to limit ffCO2 emissions within an irregularly shaped region (the United States, in our case). We find that the optimization algorithm performs a data-driven sparsification of the spatial parametrization and retains only of those wavelets whose weights could be estimated from the observations. Further, our method for the imposition of boundary conditions leads to a 10computational saving over conventional means of doing so. We conclude with a discussion of the accuracy of the estimated emissions and the suitability of the spatial parametrization for use in inverse problems with a significant degree of regularization.

Geoscientific Model Development

Ray, J.; Lee, Jina L.; Yadav, V.; Lefantzi, Sophia L.; Michalak, A.M.; van Bloemen Waanders, Bart G.

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) and fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO2 (ffCO2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO2 emissions and synthetic observations of ffCO2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.

Proposed for publication in SIAM Journal on Scientific Computing (SISC).

Ridzal, Denis R.; van Bloemen Waanders, Bart G.

Abstract not provided.

Wildey, Timothy M.; van Bloemen Waanders, Bart G.; Seidl, Daniel T.

Abstract not provided.

Computational Mechanics

Salloum, Maher S.; Johnson, Kyle J.; Bishop, Joseph E.; Aytac, Jon M.; Dagel, Daryl D.; van Bloemen Waanders, Bart G.

New manufacturing technologies such as additive manufacturing require research and development to minimize the uncertainties in the produced parts. The research involves experimental measurements and large simulations, which result in huge quantities of data to store and analyze. We address this challenge by alleviating the data storage requirements using lossy data compression. We select wavelet bases as the mathematical tool for compression. Unlike images, additive manufacturing data is often represented on irregular geometries and unstructured meshes. Thus, we use Alpert tree-wavelets as bases for our data compression method. We first analyze different basis functions for the wavelets and find the one that results in maximal compression and miminal error in the reconstructed data. We then devise a new adaptive thresholding method that is data-agnostic and allows a priori estimation of the reconstruction error. Finally, we propose metrics to quantify the global and local errors in the reconstructed data. One of the error metrics addresses the preservation of physical constraints in reconstructed data fields, such as divergence-free stress field in structural simulations. While our compression and decompression method is general, we apply it to both experimental and computational data obtained from measurements and thermal/structural modeling of the sintering of a hollow cylinder from metal powders using a Laser Engineered Net Shape process. The results show that monomials achieve optimal compression performance when used as wavelet bases. The new thresholding method results in compression ratios that are two to seven times larger than the ones obtained with commonly used thresholds. Overall, adaptive Alpert tree-wavelets can achieve compression ratios between one and three orders of magnitude depending on the features in the data that are required to preserve. These results show that Alpert tree-wavelet compression is a viable and promising technique to reduce the size of large data structures found in both experiments and simulations.

van Bloemen Waanders, Bart G.

Abstract not provided.

Lefantzi, Sophia L.; Arunajatesan, Srinivasan A.; DeChant, Lawrence J.; Lee, Jina L.; van Bloemen Waanders, Bart G.

Abstract not provided.

Ridzal, Denis R.; Cyr, Eric C.; van Bloemen Waanders, Bart G.

Abstract not provided.

van Bloemen Waanders, Bart G.

Chemical/Biological/Radiological (CBR) contamination events pose a considerable threat to our nation's infrastructure, especially in large internal facilities, external flows, and water distribution systems. Because physical security can only be enforced to a limited degree, deployment of early warning systems is being considered. However to achieve reliable and efficient functionality, several complex questions must be answered: (1) where should sensors be placed, (2) how can sparse sensor information be efficiently used to determine the location of the original intrusion, (3) what are the model and data uncertainties, (4) how should these uncertainties be handled, and (5) how can our algorithms and forward simulations be sufficiently improved to achieve real time performance? This report presents the results of a three year algorithmic and application development to support the identification, mitigation, and risk assessment of CBR contamination events. The main thrust of this investigation was to develop (1) computationally efficient algorithms for strategically placing sensors, (2) identification process of contamination events by using sparse observations, (3) characterization of uncertainty through developing accurate demands forecasts and through investigating uncertain simulation model parameters, (4) risk assessment capabilities, and (5) reduced order modeling methods. The development effort was focused on water distribution systems, large internal facilities, and outdoor areas.

Salloum, Maher S.; Johnson, Kyle J.; Bishop, Joseph E.; van Bloemen Waanders, Bart G.; Karlson, Kyle N.; Beresh, Steven J.

Abstract not provided.

Cooper, Scott P.; Elbring, Gregory J.; Jakaboski, Blake E.; Lorenz, John C.; Mani, Seethambal S.; Normann, Randy A.; Rightley, Michael J.; van Bloemen Waanders, Bart G.; Weiss, Chester J.

The project objective was to detail better ways to assess and exploit intelligent oil and gas field information through improved modeling, sensor technology, and process control to increase ultimate recovery of domestic hydrocarbons. To meet this objective we investigated the use of permanent downhole sensors systems (Smart Wells) whose data is fed real-time into computational reservoir models that are integrated with optimized production control systems. The project utilized a three-pronged approach (1) a value of information analysis to address the economic advantages, (2) reservoir simulation modeling and control optimization to prove the capability, and (3) evaluation of new generation sensor packaging to survive the borehole environment for long periods of time. The Value of Information (VOI) decision tree method was developed and used to assess the economic advantage of using the proposed technology; the VOI demonstrated the increased subsurface resolution through additional sensor data. Our findings show that the VOI studies are a practical means of ascertaining the value associated with a technology, in this case application of sensors to production. The procedure acknowledges the uncertainty in predictions but nevertheless assigns monetary value to the predictions. The best aspect of the procedure is that it builds consensus within interdisciplinary teams The reservoir simulation and modeling aspect of the project was developed to show the capability of exploiting sensor information both for reservoir characterization and to optimize control of the production system. Our findings indicate history matching is improved as more information is added to the objective function, clearly indicating that sensor information can help in reducing the uncertainty associated with reservoir characterization. Additional findings and approaches used are described in detail within the report. The next generation sensors aspect of the project evaluated sensors and packaging survivability issues. Our findings indicate that packaging represents the most significant technical challenge associated with application of sensors in the downhole environment for long periods (5+ years) of time. These issues are described in detail within the report. The impact of successful reservoir monitoring programs and coincident improved reservoir management is measured by the production of additional oil and gas volumes from existing reservoirs, revitalization of nearly depleted reservoirs, possible re-establishment of already abandoned reservoirs, and improved economics for all cases. Smart Well monitoring provides the means to understand how a reservoir process is developing and to provide active reservoir management. At the same time it also provides data for developing high-fidelity simulation models. This work has been a joint effort with Sandia National Laboratories and UT-Austin's Bureau of Economic Geology, Department of Petroleum and Geosystems Engineering, and the Institute of Computational and Engineering Mathematics.

Kalashnikova, Irina; Barone, Matthew F.; Fike, Jeffrey A.; Balajewicz, Maciej B.; Arunajatesan, Srinivasan A.; van Bloemen Waanders, Bart G.; Dowell, Earl D.

Abstract not provided.

Ivey, Mark D.; Robinson, David G.; Boslough, Mark B.; Backus, George A.; Peterson, Kara J.; van Bloemen Waanders, Bart G.; Swiler, Laura P.; Desilets, Darin M.; Reinert, Rhonda K.

This study began with a challenge from program area managers at Sandia National Laboratories to technical staff in the energy, climate, and infrastructure security areas: apply a systems-level perspective to existing science and technology program areas in order to determine technology gaps, identify new technical capabilities at Sandia that could be applied to these areas, and identify opportunities for innovation. The Arctic was selected as one of these areas for systems level analyses, and this report documents the results. In this study, an emphasis was placed on the arctic atmosphere since Sandia has been active in atmospheric research in the Arctic since 1997. This study begins with a discussion of the challenges and benefits of analyzing the Arctic as a system. It goes on to discuss current and future needs of the defense, scientific, energy, and intelligence communities for more comprehensive data products related to the Arctic; assess the current state of atmospheric measurement resources available for the Arctic; and explain how the capabilities at Sandia National Laboratories can be used to address the identified technological, data, and modeling needs of the defense, scientific, energy, and intelligence communities for Arctic support.

Mckenna, Sean A.; Vugrin, Eric D.; Hart, William E.; van Bloemen Waanders, Bart G.

Abstract not provided.

Lefantzi, Sophia L.; Klise, Katherine A.; Salazar, Luke S.; Mckenna, Sean A.; van Bloemen Waanders, Bart G.; Ray, Jaideep R.

We investigate Bayesian techniques that can be used to reconstruct field variables from partial observations. In particular, we target fields that exhibit spatial structures with a large spectrum of lengthscales. Contemporary methods typically describe the field on a grid and estimate structures which can be resolved by it. In contrast, we address the reconstruction of grid-resolved structures as well as estimation of statistical summaries of subgrid structures, which are smaller than the grid resolution. We perform this in two different ways (a) via a physical (phenomenological), parameterized subgrid model that summarizes the impact of the unresolved scales at the coarse level and (b) via multiscale finite elements, where specially designed prolongation and restriction operators establish the interscale link between the same problem defined on a coarse and fine mesh. The estimation problem is posed as a Bayesian inverse problem. Dimensionality reduction is performed by projecting the field to be inferred on a suitable orthogonal basis set, viz. the Karhunen-Loeve expansion of a multiGaussian. We first demonstrate our techniques on the reconstruction of a binary medium consisting of a matrix with embedded inclusions, which are too small to be grid-resolved. The reconstruction is performed using an adaptive Markov chain Monte Carlo method. We find that the posterior distributions of the inferred parameters are approximately Gaussian. We exploit this finding to reconstruct a permeability field with long, but narrow embedded fractures (which are too fine to be grid-resolved) using scalable ensemble Kalman filters; this also allows us to address larger grids. Ensemble Kalman filtering is then used to estimate the values of hydraulic conductivity and specific yield in a model of the High Plains Aquifer in Kansas. Strong conditioning of the spatial structure of the parameters and the non-linear aspects of the water table aquifer create difficulty for the ensemble Kalman filter. We conclude with a demonstration of the use of multiscale stochastic finite elements to reconstruct permeability fields. This method, though computationally intensive, is general and can be used for multiscale inference in cases where a subgrid model cannot be constructed.

Ray, Jaideep R.; Lefantzi, Sophia L.; Mckenna, Sean A.; van Bloemen Waanders, Bart G.

Abstract not provided.

Ray, Jaideep R.; Lefantzi, Sophia L.; Mckenna, Sean A.; van Bloemen Waanders, Bart G.

Abstract not provided.

Lefantzi, Sophia L.; Mckenna, Sean A.; Ray, Jaideep R.; van Bloemen Waanders, Bart G.

Abstract not provided.

Ray, Jaideep R.; Lefantzi, Sophia L.; van Bloemen Waanders, Bart G.

Abstract not provided.

Advances in Water Resources

Mckenna, Sean A.; van Bloemen Waanders, Bart G.; Ray, Jaideep R.

Abstract not provided.