#### Motivating Applications & Software

Technologies developed by the CCR are closely aligned to Sandia's broader set of mission strategies. These technologies have applications in numerous areas including, but not limited to, nuclear weapons, cyber security, climate modeling, alternative energy, and improvements to the power grid.

#### Focus Areas

### Climate Science

Our emphasis is on developing high-order accurate numerical methods for climate modeling such as the spectral-element atmospheric dynamical-core and in leveraging our capabilities in scientific software engineering and uncertainty quantification to improve the rigor and predictivity of global climate models.

**Contact:** Collis, Samuel Scott, sscoll@sandia.gov.

**Projects:**

### Computational Geoscience

We apply our expertise in large-scale optimization and uncertainty quantification as well as scientific software design to geoscience problems including porous media flow, seismic imaging, and hydraulic fracture.

**Contact:** Collis, Samuel Scott, sscoll@sandia.gov.

**Projects:**

### Computational Materials

Modern materials science relies upon computational tools involving theory, modeling, and simulation to work in tandem with experimental measurements. We develop and apply computational methods and tools for materials science, including molecular dynamics, peridynamics, and density functional theory. Computational materials science plays a key role in enabling Sandia’s many mission areas that rely on fundamental understanding of materials behavior.

**Contact:** Crozier, Paul, pscrozi@sandia.gov.

**Projects:**

### Cyber Security

Our cybersecurity research is focused on developing cross-cutting enabling capabilities that can impact a wide range of cybersecurity challenges. This includes research in streaming algorithms to quickly process large cyber data streams, algorithms to find patterns in large graphs and machine learning techniques to detect adversarial behavior (e.g. phishing emails). Our researchers are part of the Cybersecurity Engineering Research Institute (CERI), which provides a conduit for collaboration with industry and academia.

**Contact:** Miller, Leann Adams, lamille@sandia.gov.

**Projects:**

### Defense Applications

We develop and apply multiphysics analysis tools that address various issues important to the DOE, DoD, DHS, and other U.S. Government agencies, and support production use of our codes by our principal customers. Our ALEGRA multiphysics code (http://www.cs.sandia.gov/ALEGRA/Alegra_Home.html), employs an Arbitrary Lagrangian-Eulerian (ALE) methodology targeted at the simulation of high strain rate, magnetohydrodynamic, electromechanic and high energy density physics phenomena. It is a C++ multi-material finite element code based on a large displacement fomulation designed to accurately model strong shock behavior.

**Contact:** Hansen, Glen, gahanse@sandia.gov.

**Projects:**

### Density Functional Theory

Our research in electronic structure methods, particularly density functional theory (DFT), spans investigations of improved physical approximations (new functionals, time-dependent DFT), development of high-performance quantum simulation codes (SeqQuest), and applications focused on probing microscopic materials chemistry underlying challenging materials problems. The research encompasses the pursuit for predictive simulations of materials behavior to inform engineering scale assessments: the search for new methods to quantify the role of electronic excitations and charge transport for energy storage, characterize states of matter far from equilibrium (energetic materials, shock wave physics, and equation of state), for aging and radiation response; researching high-performance implementations of these methods for practical applications; and deploying these advanced capabilities for problems of mission relevance. DFT is also used as the quantitative foundation for adding high-fidelity to dynamical simulations, training new molecular dynamics interatomic potentials and related coarser scale modeling methods.

**Contact:** Crozier, Paul, pscrozi@sandia.gov.

**Projects:**

### Magneto-Hydro Dynamics

The magnetohydrodynamics (MHD) model describes the dynamics of charged fluids in the presence of electromagnetic fields. MHD models are used to describe important phenomena in the natural world (e.g., solar flares, astrophysical magnetic field generation, Earth's magnetosphere interaction with the solar wind) and in technological applications (e.g., spacecraft propulsion, magnetically confined plasma for fusion energy devices such as tokamak reactors (e.g. ITER), and plasma dynamics in pulsed reactors such as Sandia’s Z-pinch device). We have an active research program to develop advanced computational formulations and solution methods for multiphysics MHD, and we deploy the results of this research in our large-scale massively parallel MHD simulation codes.

The mathematical basis for the continuum modeling of MHD systems is the solution of the governing partial differential equations (PDEs) describing conservation of mass, momentum, and energy, augmented by Maxwell's equations for the electric and magnetic field. This system of PDEs is non-self adjoint, strongly coupled, highly nonlinear, and characterized by multiple physical phenomena that span a very large range of length- and time-scales. These interacting, nonlinear multiple time-scale physical mechanisms can balance to produce steady-state behavior, nearly balance to evolve a solution on a dynamical time scale that is long relative to the component time-scales, or can be dominated by just a few fast modes. These characteristics make the scalable, robust, accurate, and efficient computational solution of these systems over relevant dynamical time scales of interest extremely challenging.

Our production MHD capabilities are contained within a family of multiphysics codes known as ALEGRA*. The codes -- including ALEGRA, ALEGRA-MHD, ALEGRA-HEDP and ALEGRA-EMMA -- constitute an extensive set of physics modeling capabilities built on software in the Nevada framework and third-party libraries. They simulate large deformations and strong shock physics including solid dynamics in an Arbitrary Lagrangian-Eulerian methodology as well as magnetics, magnetohydrodynamics, electromechanics and a wide range of phenomena for high-energy physics applications. Our principal customers have applied these codes in a variety of Z-pinch physics experiment designs and applications, in the development of advanced armor concepts, and in numerous National Security programs. Research and development in advanced methods, including code frameworks, large scale inline meshing, multiscale lagrangian hydrodynamics, resistive magnetohydrodynamic methods, material interface reconstruction, and code verification and validation, keeps the software on the cutting edge of high performance computing.

We also conduct research and development of advanced computational formulations and solution methods for challenging multiple-time-scale multiphysics MHD systems. For multiple-time-scale systems, fully-implicit methods can be an attractive choice that can often provide unconditionally-stable time integration techniques. The stability of these methods, however, comes at a cost, as these techniques generate large and highly nonlinear sparse systems of equations that must be solved at each time step. In the context of MHD, the dominant computational solution strategy has been the use of explicit, semi-implicit, and operator-splitting time integration methods. With the exception of fully-explicit strategies, which are limited by severe stability restrictions to follow the fastest component time scale, all these temporal integration methods include some implicitness to enable a more efficient solution of MHD systems. Such implicitness is aimed at removing one or more sources of numerical stiffness in the problem, either from parabolic diffusion or from fast wave phenomena. While these types of techniques currently form the basis for most production-level resistive MHD simulation tools, a number of outstanding numerical and computational issues remain. These include conditional stability limits, operator-splitting-type errors, heuristic time-step-controls and limited temporal orders of accuracy.

In our DOE Advanced Scientific Computing Research Applied Math Program funded research** we are pursuing the development and evaluation of

(1) higher-order-accurate, scalable, and efficient fully-implicit formulations for resistive and extended MHD with coupled multiphysics effects (e.g. anisotropic transport, multiple temperatures, coupled radiation-diffusion models, etc.),

(2) stable and accurate spatial discretizations based on unstructured mesh FE approximations that allow efficient enforcement of physical constraints (e.g. conservation, positivity preservation, div B = 0, etc),

(3) strongly coupled Newton-Krylov nonlinear solver with new physics-based and approximate block factorization preconditioners that enable scalable multilevel sub-block solvers,

(4) new mathematical algorithms and computer science techniques to effectively utilize extreme-scale resources with very high-core counts and high-concurrency node architectures.

To enable the research described above SNL has developed a very flexible multiphysics MHD simulation code, Drekar::XMHD that enables the development of new multiphysics MHD models and allows the rapid prototyping of new computational formulations and solution methods on large-scale parallel machines. This code has been demonstrated to weak-scale on a Cray XK7 and an IBM BG/Q on up to 128K and 256K cores (respectively). Recently we have also carried out strong scaling studies on up to 500,000 cores of an IBM BG/Q for a fully-coupled Krylov/AMG V-cycle linear solver that is a critical kernel for scalable solution of MHD systems.

**Contact:** Parks, Michael L., mlparks@sandia.gov.

**Projects:**

### Mini-Applications

Application performance is determined by a combination of many choices: hardware, runtime environment, languages and compilers used, algorithm choice and implementation, and more. In this complicated environment, we find that the use of mini-applications, small self-contained proxies for real applications is an excellent approach for rapidly exploring the parameter space of all these choices. Furthermore, use of mini-applications enriches the interaction between application, library and computer system developers by providing explicit functioning software and concrete performance results that lead to detailed, focused discussions of design trade-offs, algorithm choices and runtime performance issues.

**Contact:** Hoekstra, Robert J., rjhoeks@sandia.gov.

**Projects:**

### Molecular Dynamics

We develop and use molecular dynamics and related simulation methodologies, especially those encompassed in our LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) molecular simulation package (http://lammps.sandia.gov). LAMMPS is a freely available, widely used software package that runs in serial or on high performance computing platforms, and includes potentials for sold-state materials, soft matter, and coarse-grained or mesoscopic systems.

**Contact:** Crozier, Paul, pscrozi@sandia.gov.

**Projects:**

### Multiscale Mathematics

In many physical applications of interest, events at very small length and time scales dictate the large scale response. Multiscale modeling and simulation has emerged as an important discipline to help us understand and control the behavior of processes across vastly different scales. Most classical modeling methods are either invalid or computationally infeasible outside their native spatial and temporal scales. Multiscale models must bridge disparate length and time scales to accurately represent the dominant physics at all scales, and effectively couple across them. Multiscale mathematics includes mathematical and computational tools and techniques for the development and analysis of multiscale models and their efficient and accurate solution.

- Formulation and analysis of optimization-based atomistic-to-continuum coupling methods
- Development of optimization-based algorithms for physics-compatible data transfers between models and across scales
- Development of optimization-based additive operator-splitting techniques

We also participate on the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4), led by George Karniadakis at Pacific Northwest National Laboratory. This project focuses on developing rigorous mathematical foundations for understanding and controlling fundamental mechanisms in mesoscale processes to enable scalable synthesis of complex materials, through the design of efficient modeling methods and corresponding scalable algorithms. This large multi-institution project is funded by the DOE Office of Advanced Scientific Computing Research (ASCR) as one of the Mathematical Multifaceted Integrated Capabilities Centers (MMICCs).

We have an active research effort in nonlocal multiscale modeling. Nonlocal models have length scales embedded within them. Their behavior changes relative to the length scale to which they are applied, making them suitable for multiscale modeling. In particular, we are interested in nonlocal models for multiscale modeling of solids, especially fracture modeling, as well as multiscale diffusion modeling.

**Contact:** Parks, Michael L., mlparks@sandia.gov.

**Projects:**

### Nuclear Energy

We develop and apply new coupled and integrated capabilities in support of nuclear energy, including reactor performance and safety and used nuclear fuel storage and disposal. We are a core partner in the Consortium for Advanced Simulation of Light Water Reactors (CASL) and are developing and deploying center capabilities that comprise the foundation of the Virtual Environment for Reactor Applications (VERA), recently released by CASL for use by its nuclear industry partners to address many of their most challenging operational and safety problems. We also support the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program through our Verification & Validation and Uncertainty Quantification capabilities and expertise.

**Contact:** Summers, Randall M., rmsumme@sandia.gov.

**Projects:**

### Nuclear Nonproliferation

### Peridynamics

The peridynamic theory of solid mechanics, developed at Sandia, is a nonlocal extension of classical continuum mechanics for discontinuities and long-range forces. It is a mathematical theory that unifies the mechanics of continuous media, cracks, and discrete particles. Our research in peridynamics span a number of interrelated areas, including mathematics, mechanics, constitutive-model development, scientific computing, and engineering. We apply peridynamics with a focus on pervasive material failure and fracture to meet the challenges of Sandia's national security missions. Our work is enriched through ongoing collaborations with academia and industry.

**Contact:** Crozier, Paul, pscrozi@sandia.gov.

**Projects:**

### Smart Grid

Electricity grid operators routinely solve optimization problems to address core decision processes at various time-scales, ranging from 5 minutes to multiple decades. Historically, these problems are addressed in terms of deterministic optimization, with resources kept in reserve to address any potential uncertainty regarding the future. In the context of daily operations, this approach is becoming increasingly costly and unreliable with the introduction of significant quantities of renewables generation units, e.g., wind and solar farms, for which the electricity generation levels are both variable and uncertain. For planning, increasing volatile weather leads to disruptions caused by events that were not anticipated, e.g., "100 year" floods occurring multiple times in a decade. Thus, stochastic optimization — the ability to perform optimization while directly addressing system and environmental uncertainties — is becoming a significant algorithm driver for utilities and national planning agencies. The development of efficient algorithms for stochastic optimization remains a significant challenge, however, due to the complexity of the associated decision problems. This research is being conducted in the context of Sandia's Coopr optimization package, through the modeling and solver functionality provided by the Pyomo and PySP libraries.

Beyond optimization, predictive simulation will likely play a significant role in the future electricity grid. Specifically, the ability to anticipate the consequences of and risk associated with specific control actions is critical in the operation of a resilient electricity grid. Examples of predictive simulation tools include advanced circuit simulators such as Xyce, which are capable of faster-than-real-time simulations of large-scale electricity networks. Similarly, network analysis tools can be leveraged to identify critical nodes in an electricity grid, which can inform both longer-term planning processes and shorter-term security concerns.

**Contact:** Hart, William E., wehart@sandia.gov.

**Projects:**