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At least 235 records · Page 13

Experimental and Numerical Investigations on Dynamic Mechanical Properties of TPMS Structures

Triply Periodic Minimal Surface (TPMS) lattice structures have been of increasing interest due to their light weighting, enhanced mechanical properties, and energy absorption characteristics for automotive and biomedical applications. With the advent of additive manufacturing and geometric modeling software, TPMS lattices with complex geometries can be realized. In this work, TPMS lattice structures were fabricated with PLA using fused filament fabrication (FFF) and their dynamic properties are characterized through drop tower experiments. Although lightweight TPMS lattices are beneficial for their impact absorption capability, most of the existing works are limited to quasi-static compression and dynamic impact tests are rarely performed. The current study investigates the stress-strain and energy absorption characteristics of TPMS lattices through drop tower testing and numerical modeling. Finite element modeling for TPMS lattices is carried out to validate the experimental responses. The mechanical properties, deformation, and failure mechanisms of TPMS lattices under dynamic impact are summarized for potential future applications.

Pokkalla, Deepak↗

Ab Initio Direct Dynamics

The reactivity and dynamics of molecular systems can be explored computationally by classical trajectory calculations. The traditional approach involves fitting a functional form of a potential energy surface (PES) to the energies from a large number of electronic structure calculations and then integrating numerous trajectories on this fitted PES to model the molecular dynamics. The ever-decreasing cost of computing and continuing advances in computational chemistry software have made it possible to use electronic structure calculations directly in molecular dynamics simulations without first having to construct a fitted PES. In this “on-the-fly” approach, every time the energy and its derivatives are needed for the integration of the equations of motion, they are obtained directly from quantum chemical calculations. This approach started to become practical in the mid-1990s as a result of increased availability of inexpensive computer resources and improved computational chemistry software. The application of direct dynamics calculations has grown rapidly over the last 25 years and would require a lengthy review article. The present Account is limited to some of our contributions to methods development and various applications. To improve the efficiency of direct dynamics calculations, we developed a Hessian-based predictor-corrector algorithm for integrating classical trajectories. Hessian updating made this even more efficient. Furthermore, this approach was also used to improve algorithms for following the steepest descent reaction paths. For larger molecular systems, we developed an extended Lagrangian approach in which the electronic structure is propagated along with the molecular structure. Strong field chemistry is a rapidly growing area, and to improve the accuracy of molecular dynamics in intense laser fields, we included the time-varying electric field in a novel predictor-corrector trajectory integration algorithm. Since intense laser fields can excite and ionize molecules, we extended our studies to include electron dynamics. Specifically, we developed code for time-dependent configuration interaction electron dynamics to simulate strong field ionization by intense laser pulses. Our initial application of ab initio direct dynamics in 1994 was to CH 2 O → H 2 + CO; the calculated vibrational distributions in the products were in very good agreement with experiment. In the intervening years, we have used direct dynamics to explore energy partitioning in various dissociation reactions, unimolecular dissociations yielding three fragments, reactions with branching after the transition state, nonstatistical dynamics of chemically activated molecules, dynamics of molecular fragmentation by intense infrared laser pulses, selective activation of specific dissociation channels by aligned intense infrared laser fields, angular dependence of strong field ionization, and simulation of sequential double ionization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development of a Physics-Based Combustion Model for Engine Knock Prediction

The objective of this project is to improve the prediction of engine knock by developing a new combustion modeling framework. Engine knock is a limiting factor to constrain the increase of fuel efficiency for spark ignition (SI) engines in most passenger cars. Efforts to increase fuel efficiency, increasing the compression ratio or downsizing, lead to the increase in the tendency of the knock occurrence. The knock is an undesired ignition of the end-gas, unburned fuel/air mixture ahead of the spark-ignited premixed flame, resulting in rapid in-cylinder pressure rises and engine damages. The combustion modeling framework developed in this project can consider turbulence-chemistry interactions during end-gas ignition, while using a reasonably detailed chemical mechanism developed for ignition and combustion reactions under engine relevant conditions, and the subtle characteristics of spark-ignited flame propagation. It is developed in the context of large eddy simulation (LES), which can capture stochastic in-cylinder processes. The developed model is incorporated into a commercial software for engine simulation, CONVERGE CFD, as a user defined function, and validated. Engine knock and knock-free experiments as well as direct numerical simulation (DNS) of end-gas ignition in homogeneous turbulence are performed to help model development and provide data sets for model validation. With further validation, the developed model is expected to advance the predictive capability for engine knock simulations and thus contribute to improving the fuel efficiency.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

CFD Analysis of RLUOB Zone 1 HEPA Filter Plenum and Testing Manifolds

The purpose of this computational fluid dynamics (CFD) analysis is to ensure that Camfil Farr’s upstream and downstream injection and sampling manifolds can meet or exceed the requirements outlined in the ASME AG-1 1997 a(2000) Code on Nuclear Air and Gas Treatment for the testing of HEPA and adsorbent filters. This paper will present a numerical simulation of airflow in the Radiological Laboratory Utility Office Building (RLUOB) zone 1 HEPA filter plenum and testing manifolds using the commercial CFD software ANSYS FLUENT 2020R1. The CFD analysis focuses on the investigation of the air flow distribution and air-aerosol mixing uniformity. The evaluation was done for all steps of the modeling process: grid generation, physics setup, simulation, and post-processing. The mass flow rate in each section of the zone 1 injection and sampling manifolds is also reported.

42 ENGINEERING↗

Insert Modeling in UNF ST&DARDS

The Used Nuclear Fuel-Storage, Transportation & Disposal Analysis Resource and Data System (UNF-ST&DARDS) is a software tool that integrates a used nuclear fuel (UNF) or spent nuclear fuel (SNF) relational database and key analysis capabilities to simplify and automate numerous UNF management and fuel cycle–related activities. UNF-ST&DARDS is being developed for the US Department of Energy’s Office of Nuclear Energy Spent Fuel and Waste Disposition program. UNF-ST&DARDS provides an integrated framework that uses advanced modeling and simulation to predict the behavior of SNF over the timescales associated with permanent disposal in a geologic repository. After leaving the spent fuel pool, SNF is transferred to dry storage in a dual-purpose canister (DPC). DPCs are considered “dual purpose” because they are designed for both storage and transportation, removing the need to transfer the fuel to a separate transportation cask. However, much research has been conducted investigating the feasibility of directly disposing of DPCs in geologic repositories. Direct disposal of DPCs could reduce worker exposure during repackaging, reducing the amount of low-level waste from the discarded DPCs and potentially saving billions of dollars. Therefore, direct disposal of as-loaded DPCs is desirable if it can be done safely.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Accurate and Efficient Parametric Model-Order Reduction for Turbulent Thermal Transport

This project produced new algorithms and software for low-cost exploration of turbulent thermal-fluids behavior under parametric variation by using reduced-order models (ROMs). The ROMs numerically solve the governing equations for fluid motion by using a small set of basis functions (typically, N=20-200 modes) to represent the solution. The base modes are computed as optimal combinations of solutions from expensive high-fidelity "anchor-point" solutions involving millions of unknowns, which are typically generated by solving the full Navier-Stokes equations on a supercomputer. The ROM solution is itself a combination of the base modes, where the basis coefficients are determined by evolving an NxN system of nonlinear equations. The overarching idea is to use the inexpensive ROM to predict solutions under conditions where the parameters differ from the anchor-point conditions. Several ingredients are required to make ROMs useful for thermal hydraulics analysis. These include: a stable and accurate ROM that is capable of reproducing the large-scale dynamics of turbulent flow, error indicators than can guide the choice of anchor points, and low-cost mechanisms for evaluating nonlinear terms in the reduced equations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Preliminary Thermal-Hydraulic Analysis of the UTA–2 Subcritical Linear Accelerator–Driven System

The National Nuclear Security Administration’s mission includes establishing a reliable supply of 99 Mo without highly enriched uranium. Oak Ridge National Laboratory (ORNL) supports this objective through collaborative research and development with industrial partners. Niowave Inc., a current partner, is currently designing a subcritical linear accelerator-driven system (ADS) and preparing for the US Nuclear Regulatory Commission’s licensing process. Niowave’s system has the potential to efficiently supply medical radioisotopes. The technology includes a superconducting electron accelerator and a pile of both natural and low-enriched uranium (LEU) targets. The process fissions uranium and many valuable isotopes can then be extracted from the targets. Niowave is currently iterating through conceptual and detailed design processes for several system sizes. This report discusses UTA–2, which is at the demonstration stage. UTA–2 will validate numerical modeling results with experimental measurements before progressing to the detailed design of UTA–3, the commercial-sized ADS. The thermal-hydraulic behavior of the UTA–2 core design was numerically investigated using STAR-CCM+, as described in this report. STAR-CCM+, a state-of-the-art computational fluid dynamics (CFD) software that was commercially developed by Siemens, has an extensive user base and a set of validation studies. It is also compliant with the American Society of Mechanical Engineers’ Nuclear Quality Assurance 1 standard. Three cases are investigated in this report. Case 1 quantified the temperature field within the UTA–2 assembly and water tank using only conduction as the method of thermal energy transport. This simplified approach was overly conservative and yielded wetted cladding temperatures above the coolant saturation temperature. In this case, the maximum temperature of the wetted cladding surface of the highest power rod exceeded the saturation temperature of water by 63.8°C. Because of the overly conservative approach taken in Case 1 and its negative subcooled margin, buoyancy-driven natural circulation flow physics were implemented in Case 2. Adding coolant motion significantly distributed the thermal energy of the system through convective heat transfer. This relatively small amount of convective heat transfer significantly reduced system temperatures and increased the subcooled margin from –63.8 to 61.3°C. This margin confirmed that no boiling was expected during normal operation of UTA–2 at 230 W. Case 3 had no additional physics models but considered an overpower event during which the power of each LEU and natural uranium rod was at its respective peak values. This resulted in a study with the total assembly power equal to 176% of the nominal power of 230 W considered in Cases 1 and 2. The resulting natural circulation flows were slightly enhanced. The subcooled margin decreased slightly to 46.3°C, which is still a significant margin to local boiling of the water within the tank. This margin confirmed that no boiling was expected during an abnormal operation of UTA–2 at 406 W.

07 ISOTOPE AND RADIATION SOURCES↗

Modeling the U.S. Western Electric Interconnection to Understand the Consequences of Hydrometeorological Extremes and Options for Risk Mitigation

Electricity grid operators around the world face a dual challenge; withstanding increasingly severe weather and the longer term impacts of climate change, while simultaneously decarbonizing. Extreme weather events such as heat waves and droughts are rising in both severity and frequency, which is threatening the reliability of electricity grids through increased demand, generation capacity losses, and equipment failures. Consequently, incorporating hydrometeorological stressors into computational power systems analysis is becoming an even more critical tool in long term planning and short term operations. However, there is a general lack of open-source customizable grid simulation software capable of exhaustively stress testing the grid under hydrometeorological uncertainty, and/or examining potential risk mitigation pathways. A related, persistent challenge for power system modelers is striking an appropriate balance between model fidelity (e.g. spatial scale and time resolution) and computational tractability (wall clock run-time). In this study, we are proposing a solution to this problem with open-source software that allows users to seamlessly customize the scale and track the accuracy of grid operations models. Our approach allows users to search over numerous model parameters (network topology, mathematical formulation, economic hurdle rates, and transmission line scaling) to identify model instantiations that accommodate experimental design. Further, we use this approach to demonstrate the importance of including extreme weather events in model validation and model selection. Focusing on the occurrence of heatwaves and droughts in the U.S. Western Interconnection, we examine role of extreme events in balancing tradeoffs between model fidelity and run-time at the model design stage.

Economics↗

Development of a Physics-Based Combustion Model for Engine Knock Prediction

The objective of this project is to improve the prediction of engine knock by developing a new combustion modeling framework. Engine knock is a limiting factor to constrain the increase of fuel efficiency for spark ignition (SI) engines in most passenger cars. Efforts to increase fuel efficiency, increasing the compression ratio or downsizing, lead to the increase in the tendency of the knock occurrence. The knock is an undesired ignition of the end-gas, unburned fuel/air mixture ahead of the spark-ignited premixed flame, resulting in rapid in-cylinder pressure rises and engine damages. The combustion modeling framework developed in this project can consider turbulence-chemistry interactions during end-gas ignition, while using a reasonably detailed chemical mechanism developed for ignition and combustion reactions under engine relevant conditions, and the subtle characteristics of spark-ignited flame propagation. It is developed in the context of large eddy simulation (LES), which can capture stochastic in-cylinder processes. The developed model is incorporated into a commercial software for engine simulation, CONVERGE CFD, as a user defined function, and validated. Engine knock and knock-free experiments as well as direct numerical simulation (DNS) of end-gas ignition in homogeneous turbulence are performed to help model development and provide data sets for model validation. With further validation, the developed model is expected to advance the predictive capability for engine knock simulations and thus contribute to improving the fuel efficiency.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

VAST: the Void Analysis Software Toolkit

Voids are expansive regions in the universe containing significantly fewer galaxies than surrounding galaxy clusters and filaments. They are a fundamental feature of the cosmic web and provide important information about galaxy physics and cosmology. For example, correlations between voids and luminous tracers of large-scale structure improve constraints on the expansion of the universe as compared to using tracers alone, and numerous studies have shown that the void environment influences the evolution of galaxies. However, what constitutes a void is vague and formulating a concrete definition to use in a void-finding algorithm is not trivial. As a result, several different algorithms exist to identify these cosmic underdensities. Our Void Analysis Software Toolkit, or VAST, provides Python 3 implementations of two such algorithms: VoidFinder and V 2 . This consolidation of two popular void-finding algorithms allows the user to, for example, easily compare the results of their analysis using different void definitions.

97 MATHEMATICS AND COMPUTING↗

Numerical modeling of hydrogen mixing in a direct-injection engine fueled with gaseous hydrogen

Hydrogen is considered as one of the most promising options to achieve effective decarbonization of the energy and transportation sectors. As such, it has recently been receiving increasing attention because of its promising potential as an energy carrier for advanced energy and propulsion systems. With a focus on internal combustion engines, direct injection (DI) of gaseous hydrogen during the compression stroke offers great potential for high engine efficiency and specific power while reducing the risk of backfiring and pre-ignition issues. Therefore, many experimental and numerical efforts have recently been dedicated to understanding the physical and chemical behaviors of hydrogen in engine during mixing and combustion. This study focuses on computational fluid dynamics (CFD) modeling of the hydrogen DI process in a hydrogen optical research engine. Under the conditions studied, gaseous hydrogen is injected into the combustion chamber via a centrally located single-hole injector at a pressure of 100 bar. Two configurations, namely low-and high-tumble, are investigated to understand the impact of different in-cylinder flow patterns on the fuel-air mixture preparation. Simulations are carried out using the commercial CFD software CONVERGE. Here, the in-cylinder turbulence is modeled with an unsteady Reynolds-averaged Navier-Stokes (URANS) formulation closed by the renormalization group (RNG) k-ε model. Several numerical methods and model constants, including but not limited to turbulent Schmidt number, are evaluated. The numerical results are systematically compared against experimental measurements of velocity and hydrogen concentration fields on the vertical center plane to assess the performance of the CFD model, unveil the physics of hydrogen mixing, and establish best practices for modeling hydrogen DI under relatively high injection pressure conditions.

33 ADVANCED PROPULSION SYSTEMS↗

Rapid prototyping of arbitrary 2D and 3D wireframe DNA origami

Wireframe DNA origami assemblies can now be programmed automatically from the top-down using simple wireframe target geometries, or meshes, in 2D and 3D, using either rigid, six-helix bundle (6HB) or more compliant, two-helix bundle (DX) edges. While these assemblies have numerous applications in nanoscale materials fabrication due to their nanoscale spatial addressability and high degree of customization, no easy-to-use graphical user interface software yet exists to deploy these algorithmic approaches within a single, standalone interface. Further, top-down sequence design of 3D DX-based objects previously enabled by DAEDALUS was limited to discrete edge lengths and uniform vertex angles, limiting the scope of objects that can be designed. Here, we introduce the open-source software package ATHENA with a graphical user interface that automatically renders single-stranded DNA scaffold routing and staple strand sequences for any target wireframe DNA origami using DX or 6HB edges, including irregular, asymmetric DX-based polyhedra with variable edge lengths and vertices demonstrated experimentally, which significantly expands the set of possible 3D DNA-based assemblies that can be designed. ATHENA also enables external editing of sequences using caDNAno, demonstrated using asymmetric nanoscale positioning of gold nanoparticles, as well as providing atomic-level models for molecular dynamics, coarse-grained dynamics with oxDNA, and other computational chemistry simulation approaches.

59 BASIC BIOLOGICAL SCIENCES↗

Machine Learning-Driven Conservative-to-Primitive Conversion in Hybrid Piecewise Polytropic and Tabulated Equations of State

We present a novel machine learning (ML)-based method to accelerate conservative-to-primitive inversion, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding techniques are computationally expensive, particularly for large-scale relativistic hydrodynamics simulations. To address this, we employ feedforward neural networks (NNC2PS and NNC2PL), trained in PyTorch (2.0+) and optimized for GPU inference using NVIDIA TensorRT (8.4.1), achieving significant speedups with minimal accuracy loss. The NNC2PS model achieves 𝐿 1 and 𝐿 ∞ errors of 4.54 × 10 −7 and 3.44 × 10−6, respectively, while the NNC2PL model exhibits even lower error values. TensorRT optimization with mixed-precision deployment substantially accelerates performance compared to traditional root-finding methods. Specifically, the mixed-precision TensorRT engine for NNC2PS achieves inference speeds approximately 400 times faster than a traditional single-threaded CPU implementation for a dataset size of 1,000,000 points. Ideal parallelization across an entire compute node in the Delta supercomputer (dual AMD 64-core 2.45 GHz Milan processors and 8 NVIDIA A100 GPUs with 40 GB HBM2 RAM and NVLink) predicts a 25-fold speedup for TensorRT over an optimally parallelized numerical method when processing 8 million data points. Moreover, the ML method exhibits sub-linear scaling with increasing dataset sizes. We release the scientific software developed, enabling further validation and extension of our findings. By exploiting the underlying symmetries within the equation of state, these findings highlight the potential of ML, combined with GPU optimization and model quantization, to accelerate conservative-to-primitive inversion in relativistic hydrodynamics simulations.

conservative-to-primitive conversion↗

Climate Model Output Rewriter

The Climate Model Output Rewriter (CMOR) software was first developed by LLNL’s PCMDI program in early 2000s and was formally released with v1.0 (July 2006), v2.0 (January 2011), and v3.1(June 2016). CMOR is used to produce Climate and Forecast Convention (http://cfconventions.org/) CF-compliant netCDF files, in the standard format required to satisfy the World Climate Research Program (WCRP) Coupled Model Intercomparison Project (CMIP). The software has been used across multiple phases of the Earth System Modeling (ESM) project CMIP (CMIP3, CMIP5, CMIP6, and planned use in CMIP7) along with numerous parallel projects focused on preparation observations for use in model evaluation (obs4MIPs) and forcing datasets (input4MIPs) to guide ESM simulations to meet strict experimental protocols. More information can be obtained from the CMOR website and code repositories: https://cmor.llnl.gov/; https://github.com/pcmdi/cmor; https://github.com/PCMDI/cmor3_documentation The ESM variable definitions used as input for CMOR can also be viewed in code repositories: https://github.com/PCMDI/cmip3-cmor-tables/; https://github.com/PCMDI/cmip5-cmor-tables/; https://github.com/PCMDI/cmip6-cmor-tables/

Mauzey, ChristopherF↗

ThinCurr: An open-source 3D thin-wall eddy current modeling code for the analysis of large-scale systems of conducting structures

In this paper we present a new thin-wall eddy current modeling code, ThinCurr, for studying inductively-coupled currents in 3D conducting structures -- with primary application focused on the interaction between currents flowing in coils, plasma, and conducting structures of magnetically-confined plasma devices. The code utilizes a boundary finite element method on an unstructured, triangular grid to accurately capture device structures. The new code, part of the broader Open FUSION Toolkit, is open-source and designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. Scalability to large models is enabled through use of hierarchical off-diagonal low-rank compression of the inductance matrix, which is otherwise dense. Ease of handling large models of complicated geometry is further supported by automatic determination of supplemental elements through a greedy homology approach. Here, a detailed description of the numerical methods of the code and verification of the implementation of those methods using cross-code comparisons against the VALEN code and Ansys commercial analysis software is shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Non-Adiabatic Excited State Molecular Dynamics Methodologies: comparison and convergence

Direct atomistic simulation of nonadiabatic molecular dynamics is a challenging goal that allows important insights into fundamental physical phenomena. A variety of frameworks, ranging from fully quantum treatment of nuclei to semiclassical and mixed quantum–classical approaches, were developed. These algorithms are then coupled to specific electronic structure techniques. Such diversity and lack of standardized implementation make it difficult to compare the performance of different methodologies when treating realistic systems. Here, we compare three popular methods for large chromophores: Ehrenfest, surface hopping, and multiconfigurational Ehrenfest with ab initio multiple cloning (MCE-AIMC). These approaches are implemented in the NEXMD software, which features a common computational chemistry model. The resulting comparisons reveal the method performance for population relaxation and coherent vibronic dynamics. Finally, we study the numerical convergence of MCE-AIMC algorithms by considering the number of trajectories, cloning thresholds, and Gaussian wavepacket width. Our results provide helpful reference data for selecting an optimal methodology for simulating excited-state molecular dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A REDUCED ORDER MODELING APPROACH TO PROBABILISTIC CREEP-DAMAGE PREDICTIONS IN FINITE ELEMENT ANALYSIS

This paper introduces a computationally efficient Reduced Order Modeling (ROM) approach for the probabilistic prediction of creep-damage failure. Component-level probabilistic simulations are needed to assess the reliability and safety of high-temperature components. Full-scale probabilistic creep-damage modeling in finite element (FE) approach is computationally expensive requiring many hundreds of simulations to replicate the uncertainty of component failure. To that end, ROM is proposed to minimize the elevated computational cost while controlling the loss of accuracy. It is proposed that full-scale probabilistic simulations can be completed in 1D at a reduced cost, the extremum conditions extracted, and those conditions applied for lower-cost 2D/3D probabilistic simulations of components that capture the mean and uncertainty of failure. The probabilistic Sine-hyperbolic (Sinh) model is selected which in previous work was calibrated to alloy 304 stainless steel. The Sinh model includes probability density functions (pdfs) for test condition (stress and temperature), initial damage (i.e. microstructure), and material properties uncertainty. The Sinh model is programmed into ANSYS finite element software using the USERCREEP.F material subroutine. First, the Sinh model and FE code are subject to verification and validation to ensure the accuracy of the simulations. Numerous Monte Carlo simulations are executed in a 1D model to generate probabilistic creep deformation, damage, and rupture data. This data is analyzed and the probabilistic parameters corresponding to extreme creep response are extracted. The ROM concept is applied where only the extreme conditions are applied in the 2D probabilistic prediction of a component. The probabilistic predictions between the 1D and 2D geometry is compared to assess ROM for creep. The accuracy of the probabilistic prediction employing the ROM approach will potentially reduce the time and cost of simulating complex engineering systems. Future studies will introduce multi-stage Sinh, stochasticity, and spatial uncertainty for improved prediction.

36 MATERIALS SCIENCE↗

Replicated Computational Results (RCR) Report for "Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software''

In, a practical implementation of a novel adaptive precision block-Jacobi preconditioner is introduced. In particular, the authors present a heavily-tuned GPU implementation of the adaptive precision block-Jacobi preconditioner within the Ginkgo numerical linear algebra library. The performance of the methodology and implementation is demonstrated using the proposed preconditioning scheme within Ginkgo’s high-performance Conjugate Gradient (CG) implementation on an NVIDIA Volta GPU. In this report, we replicate a subset of the computational results presented in. The focus is generating results from Fig. 9 to evaluate the performance of using Ginkgo’s CG solver integrated with either the full or the adaptive precision block-Jacobi preconditioner applied to a variety of test cases

97 MATHEMATICS AND COMPUTING↗