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This note presents recursive algorithms that are rapidly convergent and more stable for finding the principal square root of a complex matrix. Also, the developed algorithms are utilized to derive the fast and stable matrix sign algorithms which are useful in developing applications to control system problems.
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Numerical modeling is essential to support natural resource management and environmental policy-making. In the context of CO 2 geological sequestration, these models are indispensible parts of risk assessment tools. However, because of increasing complexity, modern numerical models require a great computational effort, which in some cases may be infeasible. An increasingly popular approach to overcome computational limitations is the use of surrogate models. This paper presents a new surrogate modeling approach to reduce the computational cost of running a complex, high-fidelity model. The approach is based on the simplification the high-fidelity model into computationally efficient, lower-fidelity models and on linking them with a mathematical function (linking function) that addresses the discrepancies between outputs from models with different levels of fidelity. The resulting linking function model, which can be developed with small computational effort, can be efficiently used in numerical applications where multiple runs of the original high-fidelity model are required, such as for uncertainty quantification or sensitivity analysis. The proposed approach was then applied to the development of a reduced order model for the prediction of groundwater quality impacts from CO 2 and brine leakage for the National Risk Assessment Partnership (NRAP) project.
A method is described for generating unstructured meshes of triangles or tetrahedra for computational domains of complex geometrical shape. To illustrate the power of the approach, it is applied to the solution of flows past several complete aircraft configurations. The advocated approach allows for the natural incorporation of mesh adaptivity and this is demonstrated for both inviscid and viscous computations in two and three dimensions.
In probabilistic risk assessment (PRA), the likelihoods and consequences of basic events are combined to determine possible system level outcomes and the likelihood of each outcome given an initial event. Both the consequences and likelihoods of basic events may be informed by the use of mathematical models or experimental data regarding the phenomena of interest. In either case, the impact of uncertainties on the results need to be evaluated. If a model is used to predict the evolution of an initiating event, uncertainty quantification can be computationally challenging for complex phenomena with many epistemic (e.g., model) uncertainties. In this work, a reduced order model is introduced for the flooding analysis of a multi-room building at a nuclear power plant under uncertainties which can require long run times using high fidelity computer models. The reduced order model focuses on macro-level transfer of water between rooms and tracks the water level within each room. In order to verify the model's fidelity, its results for the phenomena involved in a scenario of interest are compared to those of a computational fluid dynamics (CFD) code, which are taken to represent reality. This work does not focus on the overall fidelity of the flooding model, as the goal of the project for which it was developed is to develop a methodology rather than to analyze a particular case. The focus instead is on the tunability and verifiability of the reduced order model for relevant physical measures. In analyzing a particular case, the model may be required to incorporate more realistic description of phenomena; however, the procedure described in this work may be used to verify its performance as well. (authors)
Fusing various sensing data sources can significantly improve the accuracy and reliability of building occupancy detection. Fusing environmental sensors and wireless network signals are seldom studied for its computational and technical complexity. Here, this study aims to propose an integrated adaptive lasso model that is able to extract critical data features for environmental and Wi-Fi probe dual sensing sources. Through rapid feature extraction and process simplification, the proposed method aims to improve the computational efficiency of occupancy detecting models. To validate the proposed model, an onsite experiment was conducted to examine two occupancy data resolutions, (real-time and four-level occupancy resolutions). The results suggested that, among all twelve features, eight features are most relevant. The mean absolute error of the real-time occupancy can be reduced to 2.18 and F1_accuracy is about 84.36% for the four-level occupancy.
Sandia National Laboratories’ California site is celebrating its 60th anniversary (1956 to 2016), and high performance computing has been a key enabler for its scientists and engineers throughout much of its history. Since its founding, Sandia California has helped pioneer the use of HPC platforms including hosting Sandia’s first Cray-1 supercomputer in the 1970s and supporting development of scalable cluster computing platforms to create a new paradigm for cost-effective supercomputing in the 1990s. Recent decades of investment in creation of scalable application frameworks for scientific computing have also enabled new generations of modeling and simulation codes. These resources have facilitated computational analysis of complex phenomena in diverse applications spanning national defense, energy, and homeland security. Today, Sandia California researchers work with partners in academia, industry, and national labs to evolve the state-of-the-art in HPC, modeling, and data analysis (including foundational capabilities for exascale computing platforms) and apply them in transformational ways. Research efforts include mitigating the effects of silent hardware failures that can jeopardize the results of large-scale computations, developing exascale-capable asynchronous task-parallel programming models and runtime systems, formulating new techniques to better explore and analyze extreme-scale data sets, and increasing our understanding of materials and chemical sciences which has applications spanning nuclear weapons stockpile stewardship to more efficient automobile engines. The following section highlights some of these research and applications projects and further illustrates the breadth of our HPC capabilities.
The computation of flow over complex geometries, such as realistic aircraft configurations, poses difficult grid generation problems for computational aerodynamicists. The creation of a traditional, single-module grid of acceptable quality about an entire configuration may be impossible even with the most sophisticated of grid generation techniques. A zonal approach, wherein the flow field is partitioned into several regions within which grids are independently generated, is a practical alternative for treating complicated geometries. This technique not only alleviates the problems of discretizing a complex region, but also facilitates a block processing approach to computation thereby circumventing computer memory limitations. The use of such a zonal scheme, however, requires the development of an interfacing procedure that ensures a stable, accurate, and conservative calculation for the transfer of information across the zonal borders.
In this work, we explore the possibility of applying automated crystal structure prediction to reproduce the experimentally identified metastable porous polymorphs. Using our recently developed High-Throughput Organic Crystal Structure Prediction ( HTOCSP ) framework, we conducted a systematic study on five representative organic crystalline systems including hydrogen-bonded frameworks (HOFs), featured by the presence of significant porosity, in conjunction with different choices of energy models from classical, machine learning force fields, tight binding to density functional theory. Our results suggest that the current structure generation framework, with careful selection of symmetry conditions, is likely to generate rather complex and abundant metastable crystal candidates for porous crystals. In conjunction with the recent advance in universal machine learning force fields, it becomes possible to identify experimental structures as the energetically favorable candidates from a simple energy versus density analysis, thus paving the way for computational design of complex porous materials with the target systems prior to the experimental synthesis and characterization.
Structural determination of protein-protein complexes such as multidomain nuclear receptors has been challenging for high-resolution structural techniques. Here, we present a combined use of multiple biophysical methods, termed iSPOT, an integration of shape information from small-angle X-ray scattering (SAXS), protection factors probed by hydroxyl radical footprinting, and a large series of computationally docked conformations from rigid-body or molecular dynamics (MD) simulations. Specifically tested on two model systems, the power of iSPOT is demonstrated to accurately predict the structures of a large protein-protein complex (TGFβ-FKBP12) and a multidomain nuclear receptor homodimer (HNF-4α), based on the structures of individual components of the complexes. Although neither SAXS nor footprinting alone can yield an unambiguous picture for each complex, the combination of both, seamlessly integrated in iSPOT, narrows down the best-fit structures that are about 3.2 Å and 4.2 Å in RMSD from their corresponding crystal structures, respectively. Furthermore, this proof-of-principle study based on the data synthetically derived from available crystal structures shows that the iSPOT—using either rigid-body or MD-based flexible docking—is capable of overcoming the shortcomings of standalone computational methods, especially for HNF-4α. Here, by taking advantage of the integration of SAXS-based shape information and footprinting-based protection/accessibility as well as computational docking, this iSPOT platform is set to be a powerful approach towards accurate integrated modeling of many challenging multiprotein complexes.
We present a simple multi-dimensional exhaustive search method to obtain, in a reasonable time, the optimal solution of a nonlinear programming problem. It is more relevant in the present day non-mainframe computing scenario where an estimated 95% computing resources remains unutilized and computing speed touches petaflops. While the processor speed is doubling every 18 months, the band width is doubling every 12 months, and the hard disk space is doubling every 9 months. A randomized search algorithm or, equivalently, an evolutionary search method is often used instead of an exhaustive search algorithm. The reason is that a randomized approach is usually polynomial-time, i.e., fast while an exhaustive search method is exponential-time i.e., slow. We discuss the increasing importance of exhaustive search in optimization with the steady increase of computing power for solving many real-world problems of reasonable size. We also discuss the computational error and complexity of the search algorithm focusing on the fact that no measuring device can usually measure a quantity with an accuracy greater than 0.005%. We stress the fact that the quality of solution of the exhaustive search - a deterministic method - is better than that of randomized search. In 21 st century computing environment, exhaustive search cannot be left aside as an untouchable and it is not always exponential. We also describe a possible application of these algorithms in improving the efficiency of solar cells - a real hot topic - in the current energy crisis. These algorithms could be excellent tools in the hands of experimentalists and could save not only large amount of time needed for experiments but also could validate the theory against experimental results fast.
Computational mechanics is that discipline of applied science and engineering devoted to the study of physical phenomena by means of computational methods based on mathematical modeling and simulation, utilizing digital computers. The discipline combines theoretical and applied mechanics, approximation theory, numerical analysis, and computer science. Computational mechanics has had a major impact on engineering analysis and design. When applied to structural mechanics, the discipline is referred to herein as computational structural mechanics. Complex structures being considered by NASA for the 1990's include composite primary aircraft structures and the space station. These structures will be much more difficult to analyze than today's structures and necessitate a major upgrade in computerized structural analysis technology. NASA has initiated a research activity in structural analysis called Computational Structural Mechanics (CSM). The broad objective of the CSM activity is to develop advanced structural analysis technology that will exploit modern and emerging computers, such as those with vector and/or parallel processing capabilities. Here, the current research directions for the Methods and Application Studies Team of the Langley CSM activity are described.
The advent of exascale supercomputers heralds a new era of scientific discovery, yet it introduces significant architectural challenges that must be overcome for MPI applications to fully exploit its potential. Among these challenges is the adoption of heterogeneous architectures, particularly the integration of GPUs to accelerate computation. Additionally, the complexity of multithreaded programming models has also become a critical factor in achieving performance at scale. The efficient utilization of hardware acceleration for communication, provided by modern NICs, is also essential for achieving low latency and high throughput communication in such complex systems. In response to these challenges, the MPICH library, a high-performance and widely used Message Passing Interface (MPI) implementation, has undergone significant enhancements. Here, this paper presents four major contributions that prepare MPICH for the exascale transition. First, we describe a lightweight communication stack that leverages the advanced features of modern NICs to maximize hardware acceleration. Second, our work showcases a highly scalable multithreaded communication model that addresses the complexities of concurrent environments. Third, we introduce GPU-aware communication capabilities that optimize data movement in GPU-integrated systems. Finally, we present a new datatype engine aimed at accelerating the use of MPI derived datatypes on GPUs. These improvements in the MPICH library not only address the immediate needs of exascale computing architectures but also set a foundation for exploiting future innovations in high-performance computing. By embracing these new designs and approaches, MPICH-derived libraries from HPE Cray and Intel were able to achieve real exascale performance on OLCF Frontier and ALCF Aurora respectively.
Grid convergence of several high order methods for the computation of rapidly developing complex unsteady viscous compressible flows with a wide range of physical scales is studied. The recently developed adaptive numerical dissipation control high order methods referred to as the ACM and wavelet filter schemes are compared with a fifth-order weighted ENO (WENO) scheme. The two 2-D compressible full Navier-Stokes models considered do not possess known analytical and experimental data. Fine grid solutions from a standard second-order TVD scheme and a MUSCL scheme with limiters are used as reference solutions. The first model is a 2-D viscous analogue of a shock tube problem which involves complex shock/shear/boundary-layer interactions. The second model is a supersonic reactive flow concerning fuel breakup. The fuel mixing involves circular hydrogen bubbles in air interacting with a planar moving shock wave. Both models contain fine scale structures and are stiff in the sense that even though the unsteadiness of the flows are rapidly developing, extreme grid refinement and time step restrictions are needed to resolve all the flow scales as well as the chemical reaction scales.
Stability constants provide insight into ion complexation in water. While computational studies have been shown to model the energy of the complexation successfully using a thermodynamic cycle approach, it does not extend to calculating the stability constants for 1:1 lanthanide to ligand complexes in solution. Using B3LYP and 6-31+G* Pople basis with small core effective core potential (ECP) on the lanthanum ion, and a solvent model based on the full solute electron density (SMD) solvation model we computed and compared with previously published stability constants of the ligands: acetate, acetohydroximate, acetylacetonate, methanoate, tropolonate, hydroxide, catecholate, malonate, oxalate, phthalate, and sulfate. The best R 2 values for the thermodynamic cycle can only be determined by separating the mono and divalent ions to achieve an R 2 value of 0.86 and 0.74 for mono and divalent ions, respectively. We show that by optimizing the lanthanide-ligand structures in implicit solvent, we achieve an improved correlation between experimental and computed stability constants of R 2 value of 0.89 for the combined mono and divalent ions.
Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological summaries cannot and 2) to still be robust to perturbations in the dataset. The combination of these two properties, known respectively as stability and discriminativity, has led to theoretical distances which are either thought to be or shown to be computationally complex and thus their implementations have been scarce. In order to design similarity measures on merge trees which are computationally feasible for more complex merge trees, many researchers have elected to loosen the restrictions on at least one of these two properties. The question still remains, however, if there are practical situations where trading these desirable properties is necessary. Here we construct a distance between merge trees which is designed to retain both discriminativity and stability. While our approach can be expensive for large merge trees, we illustrate its use in a setting where the number of nodes is small. This setting can be made more practical since we also provide a proof that persistence simplification increases the outputted distance by at most half of the simplified value. As a result, we demonstrate our distance measure on applications in shape comparison and on detection of periodicity in the von Kármán vortex street.