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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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DOE OSTI2026

A fractional calculus framework for open quantum dynamics: From Liouville to Lindblad to memory kernels

Open quantum systems exhibit dynamics ranging from unitary evolution to irreversible dissipation. While the Gorini–Kossakowski–Sudarshan–Lindblad equation uniquely characterizes Markovian completely positive and trace-preserving (CPTP) evolution, many physical platforms display non-Markovian features such as algebraic relaxation and coherence backflow. Fractional calculus provides a natural way to model such long-memory behavior through power-law temporal kernels introduced by fractional time derivatives. Here, we develop a unified framework that embeds fractional master equations within the broader hierarchy of open-system formalisms. The fractional equation forms a structured subclass of memory-kernel models, reduces to the Lindblad form at unit order, and, through Bochner–Phillips subordination, admits a CPTP representation as an average over Lindblad semigroups. Its resolvent structure further connects fractional dynamics to established non-Markovian approaches, including Nakajima–Zwanzig kernels and hierarchical equations of motion, providing a compact surrogate for long-memory effects. This formulation positions fractional calculus as a rigorous and practical language for modeling non-Markovian quantum dynamics in chemical physics and physical chemistry, providing a CPTP-preserving, computationally efficient surrogate for structured condensed-phase environments where long-time memory and dissipation play a central role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Preconditioning a Newton-Krylov solver for all-speed melt pool flow physics

n this paper, we introduce a multigrid block-based preconditioner for solving linear systems arising from a Discontinuous Galerkin discretization of the all-speed Navier-Stokes equations with phase change. The equations are discretized in conservative form with a reconstructed Discontinuous Galerkin (rDG) method and integrated with fully-implicit time discretization schemes. To robustly converge the numerically stiff systems, we use the Newton-Krylov framework with a primitive-variable formulation (pressure, velocity, and temperature), which is better conditioned than the conservative-variable form at low-Mach number. In the limit of large acoustic CFL number and viscous Fourier number, there is a strong coupling between the velocity-pressure system and the linear systems become non-diagonally dominant. To effectively solve these ill-conditioned systems, an approximate block factorization preconditioner is developed, which uses the Schur complement to reduce a 3 x 3 block system into a sequence of two 2 x 2 block systems: velocity-pressure,v P , and velocity-temperature, v T . We compare the performance of the v P -v T Schur complement preconditioner to classic preconditioning strategies: monolithic algebraic multigrid (AMG), element-block SOR, and primitive variable block Gauss-Seidel. The performance of the preconditioned solver is investigated in the limit of large CFL and Fourier numbers for low-Mach lid-driven cavity flow, Rayleigh-Bénard melt convection, compressible internally heated convection, and 3D laser-induced melt pool flow. Here, numerical results demonstrate that the v P -v T Schur complement preconditioned solver scales well both algorithmically and in parallel, and is robust for highly ill-conditioned systems, for all tested rDG discretization schemes (up to 4th-order).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

FEM-BEM coupling methods for Tokamak plasma axisymmetric free-boundary equilibrium computations in unbounded domains

Incorporating boundary conditions at infinity into simulations on bounded computational domains is a repeatedly occurring problem in scientific computing. The combination of finite element methods (FEM) and boundary element methods (BEM) is the obvious instrument, and we adapt here for the first time the two standard FEM-BEM coupling approaches to the free-boundary equilibrium problem: the Johnson–Nédélec coupling and the Bielak–MacCamy coupling. We recall also the classical approach for fusion applications, dubbed according to its first appearance von-Hagenow–Lackner coupling and present the less used alternative introduced by Albanese, Blum and de Barbieri in . We show that the von-Hagenow–Lackner coupling suffers from undesirable non-optimal convergence properties, that suggest that other coupling schemes, in particular Johnson–Nédélec or Albanese–Blum–de Barbieri are more appropriate for non-linear equilibrium problems. Moreover, we show that any of such coupling methods requires Newton-like iteration schemes for solving the corresponding non-linear discrete algebraic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Matrix-Free High-Performance Saddle-Point Solvers for High-Order Problems in \(\boldsymbol{H}(\operatorname{\textbf{div}})\)

Here, this work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in H(div). The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have applications in radiation diffusion and porous media flow problems, among others. Using the interpolation–histopolation basis, efficient matrix-free preconditioners can be constructed for the (1, 1)-block and Schur complement of the block system. With these approximations, block-preconditioned MINRES converges in a number of iterations that is independent of the mesh size and polynomial degree. The approximate Schur complement takes the form of an M-matrix graph Laplacian and therefore can be well-preconditioned by highly scalable algebraic multigrid methods. High-performance GPU-accelerated algorithms for all components of the solution algorithm are developed, discussed, and benchmarked. Numerical results are presented on a number of challenging test cases, including the “crooked pipe” grad-div problem, the SPE10 reservoir modeling benchmark problem, and a nonlinear radiation diffusion test case.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equation and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Numerical Stiffness based Simulation of Mixed Transmission Systems

Inclusion of power electronics allows increased controllability and stability in power systems. The simulation of such systems on a large-scale is challenging due to the presence of a large number of switches and nonlinear devices. This paper presents an advanced simulation algorithm to solve the aforementioned problem. The algorithm considers separation of differential algebraic equations (DAEs) on the basis of numerical stiffness and applies hybrid discretization algorithms to simulate the DAEs. The DAEs, in this paper, represent the nonlinear nonautonomous switched system dynamics of power systems. Stability analysis is performed on a general class of nonlinear nonautonomous switched systems to show the constraints under which the proposed algorithm is stable. To show the validity of the proposed algorithm, two case studies are considered: single high-voltage direct current (HVdc) substation based on the modular multilevel converter (MMC); and an example three-terminal MMC-HVdc system. Furthermore, relaxation techniques are introduced to create a stable interface for the separated DAEs. The developed algorithms are also validated with PSCAD/EMTDC-detailed reference models.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Compare linear-system solver and preconditioner stacks with emphasis on GPU performance and propose phase-2 NGP solver development pathway

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind project are Nalu-Wind, which is an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, and OpenFAST, which is a whole-turbine simulation code. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. In this report we evaluated GPU-performance baselines for the linear solvers in the Trilinos and hypre solver stacks using two representative Nalu-Wind simulations: an atmospheric boundary layer precursor simulation on a structured mesh, and a fixed-wing simulation using unstructured overset meshes. Both strong-scaling and weak-scaling experiments were conducted on the OLCF supercomputer Summit and similar proxy clusters. We focused on the performance of multi-threaded Gauss-Seidel and two-stage Gauss-Seidel that are extensions of classical Gauss-Seidel; of one-reduce GMRES, a communication-reducing variant of the Krylov GMRES; and algebraic multigrid methods that incorporate the afore-mentioned methods. The team has established that AMG methods are capable of solving linear systems arising from the fixed-wing overset meshes on CPU, a critical intermediate result for ExaWind FY20 Q3 and Q4 milestones. For the fixed-wing strong-scaling study (model with 3M grid-points), the team identified that Nalu-Wind simulations with the new Trilinos and hypre solvers scale to modest GPU counts, maintaining above 70% efficiency up to 6 GPUs. However, there still remain significant bottlenecks to performance: matrix assembly (hypre), AMG setup (hypre and Trilinos) In the weak-scaling experiments (going from 0.4M to 211M gridpoints), it's shown that the solver apply phases are faster on GPUs, but that Nalu-Wind simulation times grow, primarily due to the multigrid-setup process. Finally, based on the report outcomes, we propose a linear solver path-forward for the remainder of the ExaWind project. Near term, the NREL team will continue their work on GPU-based linear-system assembly. They will also investigate how the use of alternatives to the NVIDIA UVM (unified virtual memory) paradigm affects performance. Longer term, the NREL team will evaluate algorithmic performance on other types of accelerators and merge their improvements back to the main hypre repository branch. Near term, the Trilinos team will address performance bottlenecks identified in this milestone, such as implementing a GPU-based segregated momentum solve and reusing matrix graphs across linear-system assembly phases. Longer term, the Trilinos team will do detailed analysis and optimization of multigrid setup.

17 WIND ENERGY↗
DOE OSTI2025

MOSCATO Development and Integration in Fiscal Year 2025: Implementation of Multiphase, Multiphysics Modeling Capabilities for Molten Salt Systems

MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy corrosion for molten salt systems. In FY25, significant developments were made to the code package, enhancing its capabilities for modeling all relevant phenomena within operating moltens salt reactors (MSRs). The developments and activities in FY25 included: 1. Implementation of Level-Set methods to enable modeling of single-bubble behavior in molten salts. In FY25, the Level-Set two-phase flow modeling implementation was improved to simulate single bubble behavior with molten salt media. The large density and viscosity ratios between typical gases and molten salt liquids present challenges for these types of numerical solvers. With enhancements to the pressure projection method, MOSCATO’s Level-Set solver was able to be successfully validated to experiments related to helium bubble rise in stagnant molten salt. The simulated bubble rising velocity showed reasonable good agreement with experimental measurements. The bubble shape and dynamics were also visually compared with experimental snapshots, demonstrating a good qualitative match. 2. Generation of mass transfer correlations for multiphase flow systems. To enable calculations of the tritium transport across the interface between gas bubbles and salt, we modeled high- Schmidt-number mass transfer around a sphere across a broad range of Reynolds numbers. The mesh near the sphere surface was highly refined to resolve steep concentration gradients caused by the low diffusion coefficient. Literature-based mass transfer correlations were compared with the numerical results, and modifications were proposed to improve agreement, particularly at higher Schmidt numbers. These mass transfer correlations were subsequently provided to other national laboratories to help enable high quality mass transfer simulations using lower-order solvers under development within the NEAMS program. 3. Preliminary implementation of a bubbly flow solver. To model bubbly flow in molten salt, we implemented a bubbly flow solver for void fractions less than 5%. To do so, an algebraic relative velocity model that assumes small bubbles with rapid momentum equilibration was added to MOSCATO to compute bubble velocities. Preliminary comparisons with experimental data showed reasonable agreement, and further improvements are underway. 4. Generation of mass transfer correlations for MSRE subchannel The Molten-Salt Reactor Experiment (MSRE) was a landmark historical project that demonstrated the feasibility of molten-salt reactor technology. The MSRE campaign also generated a significant body of experimental data and reports that continue to support molten-salt–related research. In this report, the MSRE core subchannel was used as the reference geometry for a mass transfer study performed with MOSCATO. The geometry and computational mesh were adapted from a previous study, providing adequate resolution for the relatively low Reynolds number in this case. Additional mesh refinement was applied to reach higher Schmidt numbers, enabling the derivation of a reliable mass-transfer correlation for the present scenario. 5. Simulations of oxygen ingressions into molten salt. In the previous fiscal year, we initiated a study to simulate oxygen ingression in stagnant salt. As oxygen enters the salt through its surface, it reacts with Ce 3+ to form solid CeO 2 and other reaction products. To more fully capture the complex diffusion-convection-reaction mechanisms, capabilities for modeling natural convection in the salt vessel were added. These were needed as the flow of the ingressed gas induced flow in the salt caused by surface shear and non-isothermal effects. With these updated physics in place, we were able to successfully reproduce the experimental results for the rate of change of CeCl 3 concentrations versus time. 6. Flow corrosion model validation. In FY24, MOSCATO’s corrosion model was validated against static corrosion experiments. In FY25, this work was extended to a flow corrosion experiment, where FLiNaK salt was driven by natural convection, with initial salt impurities to initiate corrosion. Despite uncertainties in parameters such as elemental diffusion coefficients in the alloy and unknown H + concentrations, the simulations achieved good agreement with experimental results, especially in predicting sample mass losses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in Chacón et al. (2014) [18] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ $\ggg$ 1 (with $\mathcal{X}$∥, $ \mathcal{X}$⟂ the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. Further, the implicit algorithm is second-order accurate temporally and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the finite-dimensional linear operator compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as ~ (NΔt) 1/4 (with N the total mesh size and Δt the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ = 10 10 ) .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Cell-Edge Detection via Selective Cooperation and Generalized Canonical Correlation

Improving the uplink quality of service for users located around the boundaries between cells is a key challenge in cellular systems. Existing approaches relying on power control throttle the rates of cell-center users, while multi-user detection requires accurate channel estimates for the cell-edge users, which is another challenge due to their low received signal-to-noise ratio (SNR). Utilizing the fact that cell-edge user signals are weak but common (received at roughly equal power) at different base stations (BSs), this paper establishes a connection between cell-edge user detection and generalized canonical correlation analysis (GCCA). It puts forth a GCCA-based method that leverages selective BS cooperation to recover the cell-edge user signal subspace even at low SNR. The cell-edge user signals can then be extracted from the resulting mixture via algebraic signal processing techniques. The paper includes theoretical analysis showing why GCCA recovers the correct subspace containing the cell-edge user signals under mild conditions. The proposed method can also identify the number of cell-edge users in the system, i.e., the common subspace dimension. Simulations reveal significant performance improvement relative to various multiuser detection techniques. Cell-edge detection performance is further studied as a function of how many / which BSs are selected, and it is shown that using the closest three BS is always the best choice.

base station cooperation↗
DOE OSTI2023

Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers

Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ansätze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number n of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size 2 n − 2 can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such "complete" pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings.

Shkolnikov, V. O.↗
DOE OSTI2017

An algebraic multigrid method for Q 2 - Q 1 mixed discretizations of the Navier-Stokes equations: AMG for Q 2 - Q 1 discretization

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily colocated at mesh points. Specifically, we investigate a Q 2 -Q 1 mixed finite element discretization of the incompressible Navier–Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees of freedom (DOFs) are defined at spatial locations where there are no corresponding pressure DOFs. Thus, AMG approaches leveraging this colocated structure are not applicable. This article instead proposes an automatic AMG coarsening that mimics certain pressure/velocity DOF relationships of the Q 2 -Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity DOFs resembles that on the finest grid. To define coefficients within the intergrid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier–Stokes problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Batched Sparse Linear Algebra (Final Report for Subcontract B648960)

This report finalizes design specifications for developing batched kernels for small tensor operations for unassembled matrix-free iterative solvers, batched solvers for partially assembled operators, and batched solvers with support for various sparse formats. The outcome of the project milestones is a set of interfaces to Batched Sparse LA solvers running on hardware accelerators for use in ECP Libraries and Applications. It is part of the development of sparse batched kernels, solvers/preconditioners as well as creating interoperability in xSDK libraries with sparse and dense batched functions to benefit ECP applications. The participants included representatives from ECP libraries (not limited to the xSDK project), applications, and vendors (AMD, Intel, and NVIDIA). Batched sparse linear algebra solvers form the new frontier for algorithmic development and performance engineering. Many applications (ECP and non-ECP alike) require simultaneous solutions of small linear systems of equations that are structurally sparse. To move towards high hardware utilization, it is important to provide these applications with appropriate interfaces to efficient batched sparse solvers running on modern hardware accelerators. We present interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the software portable between the major hardware accelerators from AMD, Intel, and NVIDIA. The presented interface specifications includes batched band, sparse iterative, and sparse direct solvers. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, SUNDIALS, and SuperLU_dist.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

De Sitter space is sometimes not empty

Multiple lines of evidence suggest that the Hilbert space of an isolated de Sitter universe is one dimensional but can appear larger when probed by a gravitating observer. To test this idea, we compute the von Neumann entropy of a field theory in a two-dimensional de Sitter universe which is entangled in a thermal-like state with the same field theory on a disjoint, asymptotically anti-de Sitter (AdS) black hole. Previously, it was shown that the replica trick for computing the entropy of such entangled gravitating systems requires the inclusion of a non-perturbative effect in quantum gravity — novel wormholes connecting the two spaces. Here we show that: (a) the expected wormholes connecting de Sitter and AdS universes exist, avoiding a no-go theorem via the presence of sources on the AdS boundary; (b) the entanglement entropy vanishes if the nominal entropy of the de Sitter cosmological horizon (S ds = $A^{dS}_{horizon}$/4G N ) is less than the entropy of the AdS black hole horizon (S BH = $A^{AdS}_{horizon}$/4G N ), i.e., S dS < S BH ; (c) the entanglement entropy is finite when S dS > S BH . Thus, the de Sitter Hilbert space is effectively nontrivial only when S dS > S BH . The AdS black hole we introduce can be regarded as an “observer” for de Sitter space. In this sense, our result is a non-perturbative generalization of the recent perturbative argument that the algebra of observables on the de Sitter static patch becomes nontrivial in the presence of an observer.

2D gravity↗
DOE OSTI2016

Data-Driven Optimization for the Design and Control of Large-Scale Systems (LDRD Final Report)

Engineering decisions are often formulated as optimization problems such as the optimal design or control of physical systems. In these applications, the resulting optimization problems are constrained by large-scale simulations involving systems of partial differential equations (PDEs), ordinary differential equations (ODEs), and differential algebraic equations (DAEs). In addition, critical components of these systems are fraught with uncertainty, including unverifiable modeling assumptions, unknown boundary and initial conditions, and uncertain coefficients. Typically, these components are estimated using noisy and incomplete data from a variety of sources (e.g., physical experiments). The lack of knowledge of the true underlying probabilistic characterization of model inputs motivates the need for optimal solutions that are robust to this uncertainty. In this report, we introduce a framework for handling "distributional" uncertainties in the context of simulation-based optimization. This includes a novel measure discretization technique that will lead to an adaptive optimization algorithm tailored to exploit the structures inherent to simulation- based optimization.

42 ENGINEERING↗
DOE OSTI2020

Toward a scalable robust security-constrained optimal power flow using a proximal projection bundle method

Robust security-constrained optimal power flow (rSCOPF) aims to find the worst-case contingencies of alternating current optimal power flow (ACOPF) in power systems. With the rise of GPU architectures on the upcoming supercomputer architectures, optimization algorithms that rely on sparse linear algebra and indefinite linear systems are becoming increasingly hard to solve efficiently (e.g. interior-point method). To address this we revisit a maximin optimization formulation of the rSCOPF and the single-level mixed-integer semidefinite programming (MISDP) reformulation, which is obtained by taking the Lagrangian relaxation of the inner minimization ACOPF problem. In this paper, we focus on the development of a proximal projection bundle method (PPBM) for solving continuous relaxation node subproblems of the MISDP problem, based primarily on the well-known alternating direction method of multipliers. Cutting planes reminiscent of bundle method ideas are also applied in coordination with updates of the proximal parameter. The cutting-plane method can generate a large number of linear inequalities, leading to a large scale but decomposable quadratic programming (QP) subproblem that is amenable to GPUs. We present the numerical results on the IEEE 30, 57, 118, and 300-bus systems by using our PBMM method. We discuss the main computational bottleneck of our method, which is the time taken to solve each iteration of a QP subproblem instance of the PPBM, and how GPU architectures can accelerate this solution process.

bundle method↗
DOE OSTI2019

Chapter Six - Derivation, cross-validation, and comparison of analytic formulas for electrostatic deflector aberrations

Here, we derived first and second order analytic aberration formulas in the horizontal transverse plane for an electrostatic deflector specified by the reference orbit radius, the central angle spanning the deflector, and its inhomogeneity coefficients. The derivation was performed using an iterative order-by-order perturbation method in a Frenet–Serret beamline coordinate system. We produced a C program edabrt for calculation of the first and second order aberrations using the formulas that we derived. The electrostatic deflector aberration formulas from Wollnik (1965) disagree with COSY INFINITY and the aberration formulas that we derived here, and they also deviate from the first and second order symplecticity conditions. The reason for this discrepancy is that the aberration formulas from Wollnik (1965) consider only motion in the main field of the deflector and do not properly account for fringe field effects, in particular the necessarily occurring change of kinetic energy due to the change in potential. The code GIOS uses electrostatic aberration formulas from Wollnik (1965) and exhibits the same discrepancy. We performed a comparison of first and second order electrostatic deflector aberrations for (1) the analytic formulas derived in this work, (2) differential-algebraic (DA) numerical integration of the equations of motion using the code COSY INFINITY, (3) the aberration formulas from Wollnik (1965), (4) aberrations computed using the code GIOS, and (5) the aberration formulas from Wollnik (1965) adjusted to account for the occurring change in potential. An electrostatic spherical deflector and an electrostatic cylindrical deflector were used as test cases for this comparison. There is excellent agreement between methods (1), (2), and (5), and these three methods satisfy the first and second order symplecticity conditions.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Smoothers for Matrix-Free Algebraic Multigrid Preconditioning of High-Order Finite Elements

We investigate smoothers for use in matrix-free algebraic multigrid (AMG) preconditioning of high-order finite element problems. These AMG preconditioners are matrix-free in the sense that they are built from a related low-order refined finite element problem whose system matrix can be much more rapidly assembled than the high-order problem. Our proposed smoother, which we call distributive relaxation, is more robust to the anisotropy present in many low-order refined meshes which feature a clustering of nodes near the boundaries between high-order finite elements. For solving the low-order refined problem, we show that this new distributive relaxation smoother possesses significantly improved performance compared to more traditional smoothers.

97 MATHEMATICS AND COMPUTING↗