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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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PyTrilinos is a Python interface to selected Trilinos packages. This makes Trilinos linear algebra classes, linear solvers, preconditioners, nonlinear solvers, eigensolvers, and tools available to Python programmers. This broadens the user base of Trilinos, and facilitates rapid prototyping of scientific codes and interactive manipulation of large, distributed data sets.
PyTrilinos is a Python interface to selected Trilinos packages. This makes Trilinos linear algebra classes, linear solvers, preconditioners, nonlinear solvers, eigensolvers, and tools available to Python programmers. This broadens the user base of Trilinos, and facilitates rapid prototyping of scientific codes and interactive manipulation of large, distributed data sets.
KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].
KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].
The goals of CRADA 350 were achieved in this Phase I SBIR work. Specifically, a software environment was developed which included a nonlinear solver, OASIS. During the Phase I work, we applied the algorithm to a number of nonlinear-solver benchmark problems, including SLAC accelerator problems. By searching over only two optimization-control parameters, this Phase I work has enabled the development of a systematic procedure to facilitate the finding of a “best-guessed” global minimum solution for various types of non-linear problems with different size and complexity. This set of rules was codified and led to a versatile nonlinear program, IMIGO.
SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this insight, we introduce a unifying framework with eight building blocks that abstracts the workflows of Lagrange-Newton methods. We then present Uno, a modular C++ solver that implements our unifying framework and allows the automatic combination of a wide range of strategies with no programming effort from the user. Uno is meant to (1) organize mathematical optimization strategies into a coherent hierarchy; (2) offer a wide range of efficient and robust methods that can be compared for a given instance; (3) enable researchers to experiment with novel optimization strategies; and (4) reduce the cost of development and maintenance of multiple optimization solvers. Uno’s software design allows user to compose new customized solvers for emerging optimization areas such as robust optimization or optimization problems with complementarity constraints, while building on reliable nonlinear optimization techniques. We demonstrate that Uno is highly competitive against state-of-the-art solvers filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO, and CONOPT on a subset of 429 small problems from the CUTE collection. Uno is available as open-source software under the MIT license at https://github.com/cvanaret/Uno and via its C, Julia, Python, Fortran, and AMPL interfaces.
Here recently, an asymptotic-preserving (AP) particle orbit integrator has been proposed with remarkable properties including exact energy conservation, the ability to capture of all first-order drifts (including the ∇B-drift), the ability to capture trapped-passing boundaries with parallel velocity extremely close to the critical velocity, and the ability to transition from strongly to weakly magnetized spatial regions. The new AP orbit integrator is implicit, employing a Crank-Nicolson (CN) temporal discretization to ensure exact energy conservation. This, in turn, requires a local nonlinear iteration involving particle velocities and positions, and the local electromagnetic fields, to obtain the new-time solution. Ref. [1] did not attempt to provide an efficient solver for this system, and employed a brute-force GMRES-driven Jacobian-free Newton-Krylov (JFNK) solver to invert the particle orbit equations at every timestep for expediency. While JFNK is robust and reliable, it is also expensive and very intrusive for practical implementations of the method (it requires having the JFNK machinery available and solving a 6 x 6 Jacobian system iteratively once per iteration per particle).
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SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This article overviews several significant improvements and new features added over the last 3 years to support scientific simulations run on high-performance computing systems. Notably, three new classes of one-step methods have been implemented: low storage Runge–Kutta, symplectic partitioned Runge–Kutta, and operator splitting. In addition, we describe new timestep adaptivity support for multirate methods, adjoint sensitivity analysis capabilities for explicit Runge–Kutta methods, additional options for Anderson acceleration in nonlinear solvers, and improved error handling and logging.
We approach the problem of parallelizing state-of-the-art nonlinear programming optimization algorithms.Specifically, we focus on parallelizing quasi-Newton interior-point methods that use limited-memory secant Hessian approximations. Such interior-point methods are known to have better convergence properties and to be more effective on large-scale problems than gradient-based and derivative-free optimization algorithms. We target nonlinear and potentially nonconvex optimization problems with an arbitrary number of bound constraints and a small number of general equality and inequality constraints on the optimization variables. These problems occur for example in the form of optimal control, optimal design, and inverse problems governed by ordinary or partial differential equations, whenever they are expressed in a “reduced-space” optimization approach. We introduce and analyze the time and space complexity of a decomposition method for solving the quasi-Newton linear systems that leverages the fact that the quasi-Newton Hessian matrix has a small number of dense blocks that border a low-rank update of a diagonal matrix. This enables an efficient parallelization on memory-distributed computers of the iterations of the optimization algorithm, a state-of-the-art filter line-search interior-point algorithm by Wächter et. al. We illustrate the efficiency of the proposed method by solving structural topology optimization problems on up to 4608 cores on a parallel machine.
Here in this paper, we present a new Monte Carlo method for solving the thermal radiative transfer (TRT) equations via the method of nonlinear elimination (NLEM). This method is inspired by the previous application of NLEM to thermal radiation diffusion. Our approach, called diffusion accelerated Implicit Monte Carlo (DAIMC), is a hybrid technique which combines a Monte Carlo method for solving a purely-absorbing transport equation and a diffusion solution that accounts for effective scattering, or absorption–reemission. The method aims to improve the implicitness of the traditional implicit Monte Carlo (IMC) method. We derive DAIMC generally for 3D Cartesian geometries, but in this paper, we present results and analysis in 1D slab geometry. These preliminary results indicate that DAIMC implementations may provide more accurate and robust TRT solutions than IMC in certain test problems.
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In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have adhered to specific guiding principles that minimized the impact to current users while providing maximum flexibility for later evolution of solvers and data structures. The redesign was done through the addition of new linear and nonlinear solvers classes, enhancements to the vector class, and the creation of modern Fortran interfaces. The vast majority of this work has been performed “behind-the-scenes,” with minimal changes to the user interface and no reduction in solver capabilities or performance. These changes allow SUNDIALS users to more easily utilize external solver libraries and create highly customized solvers, enabling greater flexibility on extreme-scale, heterogeneous computational architectures.
In this study, explicit Runge–Kutta methods and implicit multistep methods utilizing a Newton–Krylov nonlinear solver are evaluated for a range of configurations of the shallow-water dynamical core of the spectral element community atmosphere model to evaluate their computational performance. These configurations are designed to explore the attributes of each method under different but relevant model usage scenarios including varied spectral order within an element, static regional refinement, and scaling to the largest problem sizes. This analysis is performed within the shallow-water dynamical core option of a full climate model code base to enable a wealth of simulations for study, with the aim of informing solver development within the more complete hydrostatic dynamical core used for climate research. The limitations and benefits to using explicit versus implicit methods, with different parameters and settings, are discussed in light of the trade-offs with Message Passing Interface (MPI) communication and memory and their inherent efficiency bottlenecks. Given the performance behavior across the configurations analyzed here, the recommendation for future work using the implicit solvers is conditional based on scale separation and the stiffness of the problem. For the regionally refined configurations, the implicit method has about the same efficiency as the explicit method, without considering efficiency gains from a preconditioner. The potential for improvement using a preconditioner is greatest for higher spectral order configurations, where more work is shifted to the linear solver. Finally, initial simulations with OpenACC directives to utilize a Graphics Processing Unit (GPU) when performing function evaluations show improvements locally, and that overall gains are possible with adjustments to data exchanges.
In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a way of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.
The behavior of nuclear fuel in the reactor environment is affected by multiple physics, most notably heat conduction and solid mechanics, which can have a strong influence on each other. To provide credible solutions, a fuel performance simulation code must have the ability to obtain solutions for each of the physics, including coupling between them. Solution strategies for solving systems of coupled equations can be categorized as loosely-coupled, where the individual physics are solved separately, keeping the solutions for the other physics fixed at each iteration, or tightly coupled, where the nonlinear solver simultaneously drives down the residual for each physics, taking into account the coupling between the physics in each nonlinear iteration. In this paper, we compare the performance of loosely and tightly coupled solution algorithms for thermomechanical problems involving coupled thermal and mechanical contact, which is a primary source of interdependence between thermal and mechanical solutions in fuel performance models. The results indicate that loosely-coupled simulations require significantly more nonlinear iterations, and may lead to convergence trouble when the thermal conductivity of the gap is too small. We also apply the tightly coupled solution strategy to a nuclear fuel simulation of an experiment in a test reactor. Studying the results from these simulations indicates that perhaps convergence for either approach may be problem dependent, i.e., there may be problems for which a loose coupled approach converges, where tightly coupled won’t converge and vice versa.
The behavior of nuclear fuel in the reactor environment is affected by multiple physics, most notably heat conduction and solid mechanics, which can have a strong influence on each other. To provide credible solutions, a fuel performance simulation code must have the ability to obtain solutions for each of the physics, including coupling between them. Solution strategies for solving systems of coupled equations can be categorized as loosely-coupled, where the individual physics are solved separately, keeping the solutions for the other physics fixed at each iteration, or tightly coupled, where the nonlinear solver simultaneously drives down the residual for each physics, taking into account the coupling between the physics in each nonlinear iteration. In this paper, we compare the performance of loosely and tightly coupled solution algorithms for thermomechanical problems involving coupled thermal and mechanical contact, which is a primary source of interdependence between thermal and mechanical solutions in fuel performance models. The results indicate that loosely-coupled simulations require significantly more nonlinear iterations, and may lead to convergence trouble when the thermal conductivity of the gap is too small. We also apply the tightly coupled solution strategy to a nuclear fuel simulation of an experiment in a test reactor. Studying the results from these simulations indicates that perhaps convergence for either approach may be problem dependent, i.e., there may be problems for which a loose coupled approach converges, where tightly coupled won't converge and vice versa. (authors)
Many enterprises invest on drone delivery research and development to drop off packages at consumers’ doorsteps in a matter of minutes. We study delivery drone route planning over a battery swapping network allowing farther reach by penetrating current battery capacity constraints. A mixed-integer nonlinear programming model is created to plan efficient drone routing over the swapping machines by minimizing the delivery lead time. We develop an exact solution method, evaluate its performance, and compare it with a straightforward nonlinear solver application. A case study highlights the applicability of the model. Data and source code to the solver are publicly shared.