Search NASA⌕ Search

SEARCH · Search NASA

Results for “blocked algorithm”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Theoretical framework for new magnetic materials for quantum computing and information storage. Final report for the Award No. DE-SC0018910

The focus of this grant was on molecular magnetic materials for information storage and quantum computing. We have been developing robust, first-principle methods for computing relevant electronic and magnetic properties of molecular building blocks (SMMs) of novel magnetic materials and quantum computers. These tools enable theoretical modeling of SMMs’ behavior, facilitating the interpretation of experimental studies and aiding the design of novel magnetic materials. Our strategy is based on the spin-flip (SF) approach, which extends the hierarchy of black-box single-reference methods to strongly correlated systems. Specifically, we developed general scalable algorithms and computer codes for calculating molecular properties, with an emphasis on spin-related properties, such as zero-field splittings, hyperfine couplings, and g-tensors. While our primary focus was on SF wave functions and SF-TDDFT, the underlying theory and computer codes were formulated using reduced density matrices, such that these tools are applicable to a broader class of methods. To extend the scope of applicability of wave-function-based SF methods to larger systems, we developed reduced-scaling approaches for the equation-of-motion coupled-cluster (EOM-CC) methods and continue developing libtensor (our open-source general tensor contraction library for many-body methods). We carried out extensive benchmarks and also carried out several applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Large-Scale Optimization with Linear Equality Constraints Using Reduced Compact Representation

For optimization problems with linear equality constraints, we prove that the (1,1) block of the inverse KKT matrix remains unchanged when projected onto the nullspace of the constraint matrix. In this work, we develop reduced compact representations of the limited-memory inverse BFGS Hessian to compute search directions efficiently when the constraint Jacobian is sparse. Orthogonal projections are implemented by a sparse QR factorization or a preconditioned LSQR iteration. In numerical experiments two proposed trust-region algorithms improve in computation times, often significantly, compared to previous implementations of related algorithms and compared to IPOPT.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Evaluation of the first version of the new RFPI system dedicated to PIP-II project accelerator

The Low-Level Radio Frequency (LLRF) control system is one of the most critical superconducting linac infrastructures responsible for the parameters of the beam acceleration. The LLRF system mainly focuses on the electromagnetic field parameters inside the cavity. While it incorporates fast feedback algorithms to optimize energy transfer to the passing particle beam it does not follow other cryomodule or cavity parameter changes. The Radio Frequency Protection Interlock (RFPI) system closely monitors various factors (like cryomodule vacuum, beamline vacuum, field emission probe current level, temperature, RF signal leakage, etc). Its simple but reliable logic has to provide an instant decision about the LLRF system or high-power amplifier output signal blocking in case of safety region excitation. This contribution presents a new version of the RFPI system which logic is implemented in the FPGA chip. The initial work on the prototype of the new system design resulted in the PoC (Proof of Concept) device. The PoC offers the possibility of various protection logic configurations, input signals parameters evaluation, and modularity aspects verification. The structure and test results from the device evaluation are summarized and discussed in this contribution.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Optimizing cloud motion estimation on the edge with phase correlation and optical flow

Abstract. Phase correlation (PC) is a well-known method for estimating cloud motion vectors (CMVs) from infrared and visible spectrum images. Commonly, phase shift is computed in the small blocks of the images using the fast Fourier transform. In this study, we investigate the performance and the stability of the blockwise PC method by changing the block size, the frame interval, and combinations of red, green, and blue (RGB) channels from the total sky imager (TSI) at the United States Atmospheric Radiation Measurement user facility's Southern Great Plains site. We find that shorter frame intervals, followed by larger block sizes, are responsible for stable estimates of the CMV, as suggested by the higher autocorrelations. The choice of RGB channels has a limited effect on the quality of CMVs, and the red and the grayscale images are marginally more reliable than the other combinations during rapidly evolving low-level clouds. The stability of CMVs was tested at different image resolutions with an implementation of the optimized algorithm on the Sage cyberinfrastructure test bed. We find that doubling the frame rate outperforms quadrupling the image resolution in achieving CMV stability. The correlations of CMVs with the wind data are significant in the range of 0.38–0.59 with a 95 % confidence interval, despite the uncertainties and limitations of both datasets. A comparison of the PC method with constructed data and the optical flow method suggests that the post-processing of the vector field has a significant effect on the quality of the CMV. The raindrop-contaminated images can be identified by the rotation of the TSI mirror in the motion field. The results of this study are critical to optimizing algorithms for edge-computing sensor systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Performance Study of Distance-Weighting Approach with Loopy Sum-Product Algorithm for Multi-Object Tracking in Clutter

In this paper, we explore the performance of the distance-weighting probabilistic data association (DWPDA) approach in conjunction with the loopy sum-product algorithm (LSPA) for tracking multiple objects in clutter. First, we discuss the problem of data association (DA), which is to infer the correspondence between targets and measurements. DA plays an important role when tracking multiple targets using measurements of uncertain origin. Second, we describe three methods of data association: probabilistic data association (PDA), joint probabilistic data association (JPDA), and LSPA. We then apply these three DA methods for tracking multiple crossing targets in cluttered environments, e.g., radar detection with false alarms and missed detections. We are interested in two performance metrics: tracking accuracy and computation time. LSPA is known to be superior to PDA in terms of the former and to dominate JPDA in terms of the latter. Last, we consider an additional DA method that is a modification of PDA by incorporating a weighting scheme based on distances between position estimates and measurements. This distance-weighting approach, when combined with PDA, has been shown to enhance the tracking accuracy of PDA without significant change in the computation burden. Since PDA constitutes a crucial building block of LSPA, we hypothesize that DWPDA, when integrated with LSPA, would perform better under the two performance metrics above. Contrary to expectations, the distance-weighting approach does not enhance the performance of LSPA, whether in terms of tracking accuracy or computation time.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Networked Microgrid Topology Reconfiguration to Promote Fairness in Proactive Load Shedding

Increasing occurrences of natural disasters and grid emergency events consistently challenge the safe and reliable operations of power systems. During such emergency situations, system operators may proactively shed load to mitigate risks. However, uncoordinated implementation of load shedding may disrupt electricity supply and even lead to cascading failures. Meanwhile, it is crucial to address potential biases affecting different customers when executing load shedding. This paper addresses the dynamic topology reconfiguration problem for networked microgrids with distributed energy resources under emergency conditions. Specifically, we propose a novel rolling-horizon optimization model that integrates fairness-aware constraints into the networked microgrid topology reconfiguration. Unlike existing approaches that focus solely on efficiency or apply fairness considerations in static settings, our method explicitly incorporates temporal fairness constraints to restrict repeated or excessive load curtailment for load blocks. Moreover, the fairness-aware constraints are specifically developed for the context of dynamic networked microgrid topology reconfiguration, and are designed to be convex or amenable to linear reformulations, which offers a more tractable alternative to traditional models with non-convex formulations. Numerical studies on a modified IEEE 13-bus system and a larger-sized SMART-DS networked microgrid system demonstrate the performance of the proposed algorithm towards more fairness-aware networked microgrid topology reconfiguration decision-making.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Understanding kinetics of defect annihilation in chemoepitaxy-directed self-assembly.

Directed self-assembly (DSA) of block copolymers (BCP) has attracted considerable interest from the semiconductor industry because it can achieve semiconductor-relevant structures with a relatively simple process and low cost. However, the self-assembling structures can become kinetically trapped into defective states, which greatly impedes the implementation of DSA in high-volume manufacturing. Understanding the kinetics of defect annihilation is crucial to optimizing the process and eventually eliminating defects in DSA. Such kinetic experiments, however, are not commonly available in academic laboratories. To address this challenge, we perform a kinetic study of chemoepitaxy DSA in a 300 mm wafer fab, where the complete defectivity information at various annealing conditions can be readily captured. Through extensive statistical analysis, we reveal the statistical model of defect annihilation in DSA for the first time. The annihilation kinetics can be well described by a power law model, indicating that all dislocations can be removed by sufficiently long annealing time. We further develop image analysis algorithms to analyze the distribution of dislocation size and configurations and discover that the distribution stays relatively constant over time. The defect distribution is determined by the role of the guiding stripe, which is found to stabilize the defects. Although this study is based on polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA), we anticipate that these findings can be readily applied to other BCP platforms as well.

block copolymer↗
DOE OSTI2022

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Additionally, therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in Chacón et al. (2002) to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime (≥ 10 7 ) with the successful resolution of plasmoid instabilities and thin current sheets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic framework for solving the nonlinear equations that arise from IRK methods (and discontinuous Galerkin discretizations in time) applied to nonlinear numerical PDEs, including PDEs with algebraic constraints. Several new linearizations of the nonlinear IRK equations are developed, offering faster and more robust convergence than the often-considered simplified Newton, as well as an effective preconditioner for the true Jacobian if exact Newton iterations are desired. Inverting these linearizations requires solving a set of block 2 x 2 systems. Under quite general assumptions, it is proven that the preconditioned 2 x 2 operator's condition number is bounded by a small constant close to one, independent of the spatial discretization, spatial mesh, and time step, and with only weak dependence on the number of stages or integration accuracy. Moreover, the new method is built using the same preconditioners needed for backward Euler-type time stepping schemes, so can be readily added to existing codes. The new methods are applied to several challenging fluid flow problems, including the compressible Euler and Navier--Stokes equations, and the vorticity-streamfunction formulation of the incompressible Euler and Navier--Stokes equations. Up to 10th-order accuracy is demonstrated using Gauss IRK, while in all cases fourth-order Gauss IRK requires roughly half the number of preconditioner applications as required by standard Singly diagonally implicit Runge--Kutta methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Performance and Cost Potential for Direct-Fired Supercritical CO2 Natural Gas Power Plants

Direct-fired supercritical CO2 (sCO2) power cycles are being explored as an attractive alternative to natural gas combined cycle (NGCC) plants with carbon capture and storage (CCS). Therefore, understanding their performance and cost potential is important for the commercialization of the technology. This study presents the techno-economic optimization results of natural gas-fired, utility-scale power plants based on the direct sCO2 power cycle, which are lacking in public literature. To identify the optimum plant configuration, the study considered multiple cases with varying levels of thermal integration with the plant air separation unit (ASU). Several design variables for each power cycle configuration were identified and optimized to minimize the levelized cost of electricity (LCOE) for each case. The optimization design variables include the sCO2 cooler outlet temperatures, recuperator approach temperatures, and pressure drops. High fidelity models for recuperators, coolers, and turbines were developed and used to capture the impact of design variables on plant efficiency and capital costs. The optimization was conducted using a combination of manual sensitivity analyses and automated derivative-free optimization algorithms available under NETL’s Framework for Optimization and Quantification of Uncertainty and Sensitivity platform. The optimized direct sCO2 power plants offered similar or slightly higher plant efficiencies than the reference NGCC plants based on the F-class gas turbine with CCS. The LCOE of the optimized direct sCO2 plants is 13 to 17% higher than the reference NGCC plants with CCS due to high capital costs associated with the ASU and sCO2 power block, though there is significant room for improvement due to the high uncertainty in component capital costs for these new plants. Recuperators make up over 50% of the sCO2 power block costs. Consequently, any research and development efforts to reduce the recuperator capital costs will benefit the technology’s commercialization. The study also presents preliminary results showing the impact of co-firing landfill gas and natural gas on plant efficiency, LCOE, and CO2 emissions.

Pidaparti, Sandeep↗
DOE OSTI2023

Performance and Cost Potential for Direct-Fired Supercritical CO2 Natural Gas Power Plants

Direct-fired supercritical CO2 (sCO2) power cycles are being explored as an attractive alternative to natural gas combined cycle (NGCC) plants with carbon capture and storage (CCS). Therefore, understanding their performance and cost potential is important for the commercialization of the technology. This study presents the techno-economic optimization results of natural gas-fired, utility-scale power plants based on the direct sCO2 power cycle, which are lacking in public literature. To identify the optimum plant configuration, the study considered multiple cases with varying levels of thermal integration with the plant air separation unit (ASU). Several design variables for each power cycle configuration were identified and optimized to minimize the levelized cost of electricity (LCOE) for each case. The optimization design variables include the sCO2 cooler outlet temperatures, recuperator approach temperatures, and pressure drops. High fidelity models for recuperators, coolers, and turbines were developed and used to capture the impact of design variables on plant efficiency and capital costs. The optimization was conducted using a combination of manual sensitivity analyses and automated derivative-free optimization algorithms available under NETL’s Framework for Optimization and Quantification of Uncertainty and Sensitivity platform. The optimized direct sCO2 power plants offered similar or slightly higher plant efficiencies than the reference NGCC plants based on the F-class gas turbine with CCS. The LCOE of the optimized direct sCO2 plants is 13 to 17% higher than the reference NGCC plants with CCS due to high capital costs associated with the ASU and sCO2 power block, though there is significant room for improvement due to the high uncertainty in component capital costs for these new plants. Recuperators make up over 50% of the sCO2 power block costs. Consequently, any research and development efforts to reduce the recuperator capital costs will benefit the technology’s commercialization. The study also presents preliminary results showing the impact of co-firing landfill gas and natural gas on plant efficiency, LCOE, and CO2 emissions.

Pidaparti, Sandeep↗
DOE OSTI2021

An accurate, non-empirical method for incorporating decoherence into Ehrenfest dynamics

In mixed quantum-classical nonadiabatic molecular dynamics methods, the anchoring of the electronic wave function to a single nuclear geometry results in both quantitative and qualitative errors in the dynamics. In the context of both Ehrenfest and trajectory surface hopping methods, methods for incorporating decoherence are widely used to eliminate these errors. However, the accuracy of these methods often depends strongly on the parameterization of the decoherence time and/or other related quantities. Here, we present a refinement of the recently introduced collapse to a block (TAB) scheme for incorporating decoherence into Ehrenfest dynamics. The proposed approach incorporates an approximation to the history of the population dynamics and treats the coherence decay as Gaussian, rather than exponential. This method uses parameters that can be obtained from first principles, rather than empirical fitting. Application to one-dimensional models indicates excellent agreement with numerically exact simulations. We also introduce a second refinement to the TAB method: a robust linear least-squares algorithm for determining collapse probabilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

An Algorithm for Atom-Centered Lossy Compression of the Atomic Orbital Basis in Density Functional Theory Calculations

Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-ζ (QZ) size are required to adequately converge Kohn–Sham density functional theory (DFT) calculations toward the complete basis set limit. However, incrementing the cardinal number by one nearly doubles the AO basis dimension, and the computational cost scales as the cube of the AO dimension, so this is very computationally demanding. Here, in this work, we develop and test a threshold-based natural atomic orbital (NAO) scheme in which ϵ-NAOs are obtained as eigenfunctions of atomic blocks of the density matrix in a one-center orthogonalized representation. This enables compression of the AO basis that is optimal for a given threshold, 10 –ϵ , by discarding NAOs with occupation numbers below that threshold. Extensive pilot test calculations using the Hartree–Fock functional and taking the converged density matrix as input suggest that a threshold of 10 –5 can yield a compression factor (ratio of AO to compressed ϵ-NAO dimension) between 2.5 and 4.5 for the QZ pc-3 basis. The errors in relative energies are typically less than 0.1 kcal/mol when the compressed basis is used instead of the uncompressed basis. Between 10 and 100 times smaller errors (i.e., usually less than 0.01 kcal/mol) can be obtained with a threshold 10 –7 , while the compression factor is typically between 2 and 2.5.

basis sets↗
DOE OSTI2020

Development of Control System Functional Capabilities within the IES Plug-and-Play Simulation Environment

The concept of an Integrated Energy System (IES) is meant to combine different energy technologies in synergistic ways to achieve a more secure and economical energy supply. The RAVEN-based HYBRID framework is used to find the optimal installed capacity and the optimal economical dispatch of each component of the IES. A new RAVEN (Risk Analysis Virtual ENvironment) plugin for grid and capacity optimization (HERON) has been developed for optimizing the production variables of the IES given the demand profile. Currently, only the limits that affect the production variables and their corresponding time rates of change are considered (explicit constraints). However, other variables are additionally subject to constraints, but the associated limits are not accounted for (implicit constraints). In particular, for the power dispatch problem, the optimization algorithm takes into account the limits on the electrical power output and the corresponding hourly power variations but does not consider other constraints on process variables whose response effects the service life of the IES. This report describes a scheme that allows accounting for implicit constraints without increasing the size of the optimization problem. The Reference Governor (RG) algorithm is traditionally used for enforcing state and control constraints by modifying the set-point trajectories supplied to the feedback regulators. In our application, the RG is coupled within an iterative loop with the HERON-power dispatcher to generate optimal trajectories that ensure the operational constraints are met. A data-driven procedure to derive a representation of the dynamics of the controlled system was developed. First, the variables that represented the state of the system are selected (PCA-based approach), and then state-space representation matrices are derived from the collected measurements (DMDc algorithm). A preliminary version of the developed workflow based on Linear Time Invariant matrices was assessed by adopting a two-unit test case. More sophisticated versions of this workflow foreseeing the on-line derivation of system matrices will be deployed in FY 2021. Finally, a “plug-and-play” library of controllers and state observers was developed in Dymola. Some aspects of the current configuration of the IES unit components, e.g., the encapsulation of the control schemes into dedicated blocks, are consistent with the “plug-and-play” philosophy. Other features, e.g., the system buses collecting the input and the output variables, are not. For this reason, once listed and described the limits of the current configuration, necessary modifications to the plant model interface are presented. As a test-case, the interfaces of the SES model in the RAVEN-based HYBRID framework were reworked accordingly, and two different control schemes were applied to the same plant model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Mesoflow: An Open-Source Reacting Flow Solver for Catalysis at Mesoscale

We present the capabilities and software performance metrics of our open-source continuum solver for catalysis, Mesoflow, developed specifically for modeling transport and chemistry at the mesoscale. Our solver utilizes Cartesian block-structured adaptive mesh refinement to resolve complex catalyst surface morphologies directly obtained from X-ray tomography data. An immersed boundary based formulation enables rapid representation of complex geometries prevalent in most mesoporous catalyst interfaces. The solver is developed on top of open-source performance portable library, AMReX, providing parallel execution capabilities on current and upcoming high-performance-computing (HPC) architectures. Our flexible software framework enables integration of complex chemical mechanisms at heterogenous interfaces and time-split algorithms for circumventing highly disparate reaction and flow time-scales. Our current studies indicate a ten-fold performance gain by using graphics-processing-units (GPUs) compared to a single processor for representative problem sizes (2 million cell mesh). We will also present a brief introduction on how to build and use this software for application problems pertaining to catalytic upgrading and gas transport within porous catalyst particles.

adaptive meshing↗
DOE OSTI2022

Module-OT: A Turnkey Solution for Securing Energy Systems

The Modular Security Apparatus for Managing Distributed Cryptography for Command-and-Control Messages on Operational Technology Networks (Module-OT) is a flexible and lightweight solution for grid-edge devices focusing on end-to-end security. It is a bump- in- the-wire solution acting as a secure conduit for data between devices or systems across a network. It improves the cybersecurity posture of DER systems by providing authentication, authorization, and data integrity to secure DER communications. Additionally, it performs key management, provides data security through whitelisting Internet Protocol addresses and ports, blocks unauthorized connections, controls user access, and allows serial or Ethernet connections for added flexibility. The core software is portable to various Linux-based operating systems and is developed to be customized by the developer and researcher communities. Module-OT has been validated in the lab, has been demonstrated at a 500-KW PV-plus-storage site, and has been proven ready to secure operational technology devices. Its core functionality meets current standards, including validation procedures of the NIST Cryptographic Algorithm Validation Program (CAVP) and the Federal Information Processing Standard (FIPS 140-2). Because of its capability to provide an accessible and affordable option for stepping up security across modern energy systems, Module-OT can serve as an effective technological option to standardize cybersecurity moving forward.

cryptography↗
DOE OSTI2024

Self-Assembly of a Triblock Copolymer in the Presence of a Rigid Conjugated Polyelectrolyte

The properties of conducting polymers are strongly influenced by structural changes induced by long-range order, which can be achieved by using block copolymers that self-assemble into crystalline structures. These blends result in unique mesophases distinct from the pure components with self-assembly behavior modulated by solution conditions and polymer architectures. High-throughput small-angle X-ray scattering data of aqueous Pluronic P123 (PEO 20 –PPO 70 –PEO 20 ) and conjugated polyelectrolyte poly[3-(potassium-4-butanoate) thiophene-2,5-diyl] (PPBT) blends at various concentrations and temperatures were automatically classified into phase maps by autophasemap, an unsupervised statistical analysis algorithm. The outlined phase boundaries revealed that adding PPBT to high P123 concentrations induced a transition from cubicly ordered spherical micelles to hexagonally packed cylindrical micelles. Shear alignment via rheological small-angle neutron scattering of the blends produced monolithic oriented cubic and hexagonal crystal gels. Furthermore, these insights into the self-assembly of conductive polymer blends will aid in the design of soft materials with tunable structural and electronic properties.

36 MATERIALS SCIENCE↗
DOE OSTI2022

mesoflow [SWR-22-56]

Mesoflow is a continuum scale simulation tool developed specifically for modeling transport and chemistry at the mesoscale. Our solver utilizes Cartesian block-structured adaptive mesh refinement to resolve complex surface morphologies (of catalysts/biomass particles among others) directly obtained from X-ray tomography data. An immersed boundary based formulation enables rapid representation of complex geometries prevalent in most mesoporous interfaces. The solver is developed on top of open-source performance portable library, AMReX, providing parallel execution capabilities on current and upcoming high-performance-computing (HPC) architectures. Our flexible software framework enables integration of complex chemical mechanisms at heterogenous interfaces and time-split algorithms for circumventing highly disparate reaction and flow time-scales. Our current studies indicate a ten-fold performance gain by using graphics-processing-units (GPU) compared to a single processor for representative problem sizes (2 million cell mesh).

Sitaraman, Hariswaran↗