Results for “Computer Algebra” — Page 20

DOE OSTI2026

Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1993

A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.

Radhadrishnan, Krishnan↗

NASA NTRS1987

Simplified algebraic grid generation in patched mesh systems

Some computational tools and techniques are described that are integrated into a simplified algebraic grid generation procedure. Major steps of such a procedure are also outlined. Grids generated via this approach for several complex geometries are shown to demonstrate the potential for wide application.

Luh, Raymond Ching-Chung↗

NASA NTRS1990

Flow field analysis for a class of waverider configurations

A package of computer codes for analysis of flow fields for waverider configurations is described. The package consists of a surface/volume grid generator and a finite-volume flow solver. The grid generator defines body geometries and computational grids by an algebraic homotopy procedure. The algebraic procedure is versatile in its application and can readily generate configurations in the class of blended wing-body geometries. This code has the ability to produce a wide variety of geometries in the given class with varying geometrical attributes. The flow solver employs a finite-volume formation and solves the explicit, Runge-Kutta integration technique. The method or flow simulation incorporates several techniques for acceleration of the convergence of the interaction process and an entropy corrected enthalpy damping procedure for efficient computation of high Mach number flows.

Moitra, Anutosh↗

DOE OSTI2022

Performance of an Astrophysical Radiation Hydrodynamics Code under Scalable Vector Extension Optimization

We present results of a performance study of an astrophysical radiation hydrodynamics code, V2D, on the Arm-based A64FX processor developed by Fujitsu. The code solves sparse linear systems, a task for which the A64FX architecture should be well suited. Here, we performed the performance analysis study on Ookami, an Apollo 80 platform utilizing the A64FX processor. We explored several compilers and performance anal-ysis packages and found the code did not perform as expected under scalable vector extension optimization, suggesting that a “deeper dive” into analyzing the code is worthwhile. However, a simple driver program that exercised basic sparse linear algebra routines used by V2D did show significant speedup with the use of the scalable vector extension optimization. We present the initial results from the study which used V2D on a relatively simple test problem that emphasized the repeated solution of sparse linear systems.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Xyce parallel electronic simulator users guide, version 6.0.

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia s needs, including some radiationaware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase a message passing parallel implementation which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows.

Keiter, Eric R↗

DOE OSTI2014

Xyce parallel electronic simulator users' guide, Version 6.0.1.

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia s needs, including some radiationaware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase a message passing parallel implementation which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows.

Keiter, Eric R↗

DOE OSTI2014

Xyce Parallel Electronic Simulator Users Guide Version 6.2.

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been de- signed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel com- puting platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia's needs, including some radiation- aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase -- a message passing parallel implementation -- which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. Trademarks The information herein is subject to change without notice. Copyright c 2002-2014 Sandia Corporation. All rights reserved. Xyce TM Electronic Simulator and Xyce TM are trademarks of Sandia Corporation. Portions of the Xyce TM code are: Copyright c 2002, The Regents of the University of California. Produced at the Lawrence Livermore National Laboratory. Written by Alan Hindmarsh, Allan Taylor, Radu Serban. UCRL-CODE-2002-59 All rights reserved. Orcad, Orcad Capture, PSpice and Probe are registered trademarks of Cadence Design Systems, Inc. Microsoft, Windows and Windows 7 are registered trademarks of Microsoft Corporation. Medici, DaVinci and Taurus are registered trademarks of Synopsys Corporation. Amtec and TecPlot are trademarks of Amtec Engineering, Inc. Xyce 's expression library is based on that inside Spice 3F5 developed by the EECS Department at the University of California. The EKV3 MOSFET model was developed by the EKV Team of the Electronics Laboratory-TUC of the Technical University of Crete. All other trademarks are property of their respective owners. Contacts Bug Reports (Sandia only) http://joseki.sandia.gov/bugzilla http://charleston.sandia.gov/bugzilla World Wide Web http://xyce.sandia.gov http://charleston.sandia.gov/xyce (Sandia only) Email xyce@sandia.gov (outside Sandia) xyce-sandia@sandia.gov (Sandia only)

Keiter, Eric R.↗

DOE OSTI2015

Xyce Parallel Electronic Simulator Users Guide Version 6.4

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been de- signed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel com- puting platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia's needs, including some radiation- aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase -- a message passing parallel implementation -- which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. Trademarks The information herein is subject to change without notice. Copyright c 2002-2015 Sandia Corporation. All rights reserved. Xyce TM Electronic Simulator and Xyce TM are trademarks of Sandia Corporation. Portions of the Xyce TM code are: Copyright c 2002, The Regents of the University of California. Produced at the Lawrence Livermore National Laboratory. Written by Alan Hindmarsh, Allan Taylor, Radu Serban. UCRL-CODE-2002-59 All rights reserved. Orcad, Orcad Capture, PSpice and Probe are registered trademarks of Cadence Design Systems, Inc. Microsoft, Windows and Windows 7 are registered trademarks of Microsoft Corporation. Medici, DaVinci and Taurus are registered trademarks of Synopsys Corporation. Amtec and TecPlot are trademarks of Amtec Engineering, Inc. Xyce 's expression library is based on that inside Spice 3F5 developed by the EECS Department at the University of California. The EKV3 MOSFET model was developed by the EKV Team of the Electronics Laboratory-TUC of the Technical University of Crete. All other trademarks are property of their respective owners. Contacts Bug Reports (Sandia only) http://joseki.sandia.gov/bugzilla http://charleston.sandia.gov/bugzilla World Wide Web http://xyce.sandia.gov http://charleston.sandia.gov/xyce (Sandia only) Email xyce@sandia.gov (outside Sandia) xyce-sandia@sandia.gov (Sandia only)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Xyce™ Parallel Electronic Simulator Users' Guide, Version 6.5.

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia's needs, including some radiation- aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase -- a message passing parallel implementation -- which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. The information herein is subject to change without notice. Copyright © 2002-2016 Sandia Corporation. All rights reserved.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

An advanced joint inversion system for CO 2 storage modeling with large date sets for characterization and real-time monitoring-enhancing storage performance and reducing failure risks under uncertainties

As large-scale, commercial storage projects become operational, the problem of utilizing information from diverse sources becomes more critically important. In this project, we developed, tested, and applied an advanced joint data inversion system for CO 2 storage modeling with large data sets for use in site characterization and real-time monitoring. Emphasis was on the development of advanced and efficient computational algorithms for joint inversion of hydro-geophysical data, coupled with state-of-the-art forward process simulations. The developed system consists of (1) inversion tools using characterization data, such as 3D seismic survey (amplitude images), borehole log and core data, as well as hydraulic, tracer and thermal tests before CO 2 injection, (2) joint inversion tools for updating the geologic model with the distribution of rock properties, thus reducing uncertainty, using hydro-geophysical monitoring data, and (3) highly efficient algorithms for directly solving the dense or sparse linear algebra systems derived from the joint inversion. The system combines methods from stochastic analysis, fast linear algebra, and high performance computing. The developed joint inversion tools have been tested through synthetic CO 2 storage examples.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2016

Xyce Parallel Electronic Simulator Users' Guide Version 6.6.

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been de- signed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel com- puting platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia's needs, including some radiation- aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase -- a message passing parallel implementation -- which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. The information herein is subject to change without notice. Copyright c 2002-2016 Sandia Corporation. All rights reserved. Acknowledgements The BSIM Group at the University of California, Berkeley developed the BSIM3, BSIM4, BSIM6, BSIM-CMG and BSIM-SOI models. The BSIM3 is Copyright c 1999, Regents of the University of California. The BSIM4 is Copyright c 2006, Regents of the University of California. The BSIM6 is Copyright c 2015, Regents of the University of California. The BSIM-CMG is Copyright c 2012 and 2016, Regents of the University of California. The BSIM-SOI is Copyright c 1990, Regents of the University of California. All rights reserved. The Mextram model has been developed by NXP Semiconductors until 2007, Delft University of Technology from 2007 to 2014, and Auburn University since April 2015. Copyrights c of Mextram are with Delft University of Technology, NXP Semiconductors and Auburn University. The MIT VS Model Research Group developed the MIT Virtual Source (MVS) model. Copyright c 2013 Massachusetts Institute of Technology (MIT). The EKV3 MOSFET model was developed by the EKV Team of the Electronics Laboratory-TUC of the Technical University of Crete. Trademarks Xyce TM Electronic Simulator and Xyce TM are trademarks of Sandia Corporation. Orcad, Orcad Capture, PSpice and Probe are registered trademarks of Cadence Design Systems, Inc. Microsoft, Windows and Windows 7 are registered trademarks of Microsoft Corporation. Medici, DaVinci and Taurus are registered trademarks of Synopsys Corporation. Amtec and TecPlot are trademarks of Amtec Engineering, Inc. All other trademarks are property of their respective owners. Contacts World Wide Web http://xyce.sandia.gov https://info.sandia.gov/xyce (Sandia only) Email xyce@sandia.gov (outside Sandia) xyce-sandia@sandia.gov (Sandia only) Bug Reports (Sandia only) http://joseki-vm.sandia.gov/bugzilla http://morannon.sandia.gov/bugzilla

47 OTHER INSTRUMENTATION↗

DOE OSTI2017

Xyce Parallel Electronic Simulator Users' Guide Version 6.7.

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel com- puting platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia's needs, including some radiation- aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase -- a message passing parallel implementation -- which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. The information herein is subject to change without notice. Copyright c 2002-2017 Sandia Corporation. All rights reserved. Trademarks Xyce TM Electronic Simulator and Xyce TM are trademarks of Sandia Corporation. Orcad, Orcad Capture, PSpice and Probe are registered trademarks of Cadence Design Systems, Inc. Microsoft, Windows and Windows 7 are registered trademarks of Microsoft Corporation. Medici, DaVinci and Taurus are registered trademarks of Synopsys Corporation. Amtec and TecPlot are trademarks of Amtec Engineering, Inc. All other trademarks are property of their respective owners. Contacts World Wide Web http://xyce.sandia.gov https://info.sandia.gov/xyce (Sandia only) Email xyce@sandia.gov (outside Sandia) xyce-sandia@sandia.gov (Sandia only) Bug Reports (Sandia only) http://joseki-vm.sandia.gov/bugzilla http://morannon.sandia.gov/bugzilla

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Xyce Parallel Electronic Simulator Users' Guide Version 6.8

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been de- signed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel com- puting platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia's needs, including some radiation- aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase$-$ a message passing parallel implementation $-$ which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Xyce Parallel Electronic Simulator Users' Guide Version 6.10

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia's needs, including some radiation- aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase -- a message passing parallel implementation -- which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Xyce Parallel Electronic Simulator Users' Guide (Version 7.2)

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandias needs, including some radiation-aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase - a message passing parallel implementation - which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows.

42 ENGINEERING↗

NASA NTRS1979

A general and computationally fast formulation for radiative transfer with scattering

A general formulation of monocromatic radiative transfer with scattering has been developed for plane-parallel geometry. The inhomogeneous and nonisothermal medium absorbs, emits, and anisotropically scatters radiation. Surfaces can emit and scatter radiation in any specified manner. The solution procedure uses the fact that phase incoherent scattering is linear in radiative sources. Certain basic scattering functions are then defined and calculated by an adding computer code using matrix algebra. These scattering functions are weighted by the temperature field and summed (superimposed) to obtain the solution for any specific problem. Numerical results for exiting intensities and one-sided heat fluxes from general media bound by one arbitrary surface are presented. These parametric studies demonstrate the effects of scattering particles and surfaces on radiative transfer from inhomogeneous and nonisothermal media. Application of the formulation to radiative equilibrium is also discussed. The conclusion is that all problems in plane-parallel radiative transfer with scattering can be solved by a common and computationally fast algorithm based on this formulation.

Cogley, A. C.↗

NASA NTRS1984

Efficient matrix partitioning for optical computing

Techniques for partitioning optical linear algebra problems to make them amenable to solution using optical processors programmed with simple algorithms are explored. Generalized methods for splitting a linear algebra matrix into a series of submatrices are reviewed, showing that simple forms can be pipelined smoothly and that parallel accumulation can be achieved by beam combining on detectors or by summing electronically. The techniques offer simplified bookkeeping, algorithmic independence, and high efficiency. The computational speed will depend on the number of multiplier-accumulators devoted to the task.

Caulfield, H. J.↗