Results for “error vector” — Page 25

DOE OSTI2022

SIERRA Multimechanics Module: Aria User Manual (V.5.4)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

SIERRA Multimechanics Module: Aria User Manual (Version.5.2)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.2)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.4)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria User Manual (V.5.6)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( $Re$ < 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic $h$-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.6)

Aria is a Galerkin nite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

42 ENGINEERING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria User Manual - Version 5.8

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual - Version 5.8

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process ows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria User Manual (V.5.10)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ($Re$ < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic $h$-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.10)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ($Re$ < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic $h$-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

42 ENGINEERING↗

DOE OSTI2020

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.4.56)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h -adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Improved proton computed tomography by dual modality image reconstruction

Purpose: Proton computed tomography (CT) is a promising image modality for improving the stopping power estimates and dose calculations for particle therapy. However, the finite range of about 33 cm of water of most commercial proton therapy systems limits the sites that can be scanned from a full 360° rotation. In this paper the authors propose a method to overcome the problem using a dual modality reconstruction (DMR) combining the proton data with a cone-beam x-ray prior. Methods: A Catphan 600 phantom was scanned using a cone beam x-ray CT scanner. A digital replica of the phantom was created in the Monte Carlo code Geant4 and a 360° proton CT scan was simulated, storing the entrance and exit position and momentum vector of every proton. Proton CT images were reconstructed using a varying number of angles from the scan. The proton CT images were reconstructed using a constrained nonlinear conjugate gradient algorithm, minimizing total variation and the x-ray CT prior while remaining consistent with the proton projection data. The proton histories were reconstructed along curved cubic-spline paths. Results: The spatial resolution of the cone beam CT prior was retained for the fully sampled case and the 90° interval case, with the MTF = 0.5 (modulation transfer function) ranging from 5.22 to 5.65 linepairs/cm. In the 45° interval case, the MTF = 0.5 dropped to 3.91 linepairs/cm For the fully sampled DMR, the maximal root mean square (RMS) error was 0.006 in units of relative stopping power. For the limited angle cases the maximal RMS error was 0.18, an almost five-fold improvement over the cone beam CT estimate. Conclusions: Dual modality reconstruction yields the high spatial resolution of cone beam x-ray CT while maintaining the improved stopping power estimation of proton CT. In the case of limited angles, the use of prior image proton CT greatly improves the resolution and stopping power estimate, but does not fully achieve the quality of a 360° proton CT scan.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2019

SIERRA Multimechanics Module: Aria User Manual (V.4.54)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re %3C 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

SIERRA Multimechanics Module: Aria Thermal Theory Manual - Version 4.52

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re %3C 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

High order interpolation of magnetic fields with vector potential reconstruction for particle simulations

We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary differential equation (ODE) integrators, such as the Dormand-Prince method. The method provides C(m) continuity and achieves high-order accuracy, making it particularly suited for particle trajectory integration and Poincaré section analysis under optimal integration order and timestep adjustments. Through numerical experiments, we demonstrate that the Hermite interpolation method preserves volume and continuity, which are critical for conserving toroidal canonical momentum and magnetic moment in guiding center simulations, especially over long-term trajectory integration. Furthermore, we analyze the impact of insufficient derivative continuity on Runge-Kutta schemes and show how it degrades accuracy at low error tolerances, introducing discontinuity-induced truncation errors. Lastly, we demonstrate performant Poincaré section analysis in two relevant settings of field data collocated from finite element meshes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗

DOE OSTI2014

WE-G-18A-05: Cone-Beam CT Reconstruction with Deformed Prior Image

Purpose: Prior image can be incorporated into image reconstruction process to improve the quality of on-treatment cone-beam CT (CBCT) from sparseview or low-dose projections. However, the deformation between the prior image and on-treatment CBCT are not considered in current prior image based reconstructions (e.g., prior image constrained compressed sensing (PICCS)). The purpose of this work is to develop a deformed-prior-imagebased- reconstruction strategy (DPIR) to address the mismatch problem between the prior image and target image. Methods: The deformed prior image is obtained by a projection based registration approach. Specifically, the deformation vector fields (DVF) used to deform the prior image is estimated through matching the forward projection of the prior image and the measured on-treatment projection. The deformed prior image is then used as the prior image in the standard PICCS algorithm. Simulation studies on the XCAT phantom was conducted to evaluate the performance of the projection based registration procedure and the proposed DPIR strategy. Results: The deformed prior image matches the geometry of on-treatment CBCT closer as compared to the original prior image. Using the deformed prior image, the quality of the image reconstructed by DPIR from few-view projection data is greatly improved as compared to the standard PICCS algorithm. The relative image reconstruction error is reduced to 11.13% in the proposed DPIR from 17.57% in the original PICCS. Conclusion: The proposed DPIR approach can solve the mismatch problem between the prior image and target image, which overcomes the limitation of the original PICCS algorithm for CBCT reconstruction from sparse-view or low-dose projections.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

SU-E-J-237: Real-Time 3D Anatomy Estimation From Undersampled MR Acquisitions

Recent developments made MRI guided radiotherapy feasible. Performing simultaneous imaging during fractions can provide information about changing anatomy by means of deformable image registration for either immediate plan adaptations or accurate dose accumulation on the changing anatomy. In 3D MRI, however, acquisition time is considerable and scales with resolution. Furthermore, intra-scan motion degrades image quality.In this work, we investigate the sensitivity of registration quality on imageresolution: potentially, by employing spatial undersampling, the acquisition timeof MR images for the purpose of deformable image registration can be reducedsignificantly.On a volunteer, 3D-MR imaging data was sampled in a navigator-gated manner, acquiring one axial volume (360×260×100mm{sup 3}) per 3s during exhale phase. A T1-weighted FFE sequence was used with an acquired voxel size of (2.5mm{sup 3}) for a duration of 17min. Deformation vector fields were evaluated for 100 imaging cycles with respect to the initial anatomy using deformable image registration based on optical flow. Subsequently, the imaging data was downsampled by a factor of 2, simulating a fourfold acquisition speed. Displacements of the downsampled volumes were then calculated by the same process.In kidneyliver boundaries and the region around stomach/duodenum, prominent organ drifts could be observed in both the original and the downsampled imaging data. An increasing displacement of approximately 2mm was observed for the kidney, while an area around the stomach showed sudden displacements of 4mm. Comparison of the motile points over time showed high reproducibility between the displacements of high-resolution and downsampled volumes: over a 17min acquisition, the componentwise RMS error was not more than 0.38mm.Based on the synthetic experiments, 3D nonrigid image registration shows little sensitivity to image resolution and the displacement information is preserved even when halving the resolution. This can be employed to greatly reduce image acquisition times for interventional applications in real-time. This work was funded by the SoRTS consortium, which includes the industry partners Elekta, Philips and Technolution.

60 APPLIED LIFE SCIENCES↗