Engineering topics

Barnard, Richard C.

Publications and source records attributed to Barnard, Richard C..

7 records

DOE OSTI2024

Modeling information flow in a computer processor with a multi-stage queuing model

In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another. The model is formulated as a spatially-extended, continuous-time Markov chain where space represents different stages. This model is equivalent to a spatially-extended version of the M/M/s queue. The main modeling feature is the throttling function which describes the processor slowdown when the amount of information falls below a certain threshold. We derive the stationary distribution for this stochastic model and develop a closure for a deterministic ODE system that approximates the evolution of the mean and variance of the stochastic model. In conclusion, we demonstrate the validity of the closure with numerical simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A mathematical model of asynchronous data flow in parallel computers *

Abstract We present a simplified model of data flow on processors in a high-performance computing framework involving computations necessitating inter-processor communications. From this ordinary differential model, we take its asymptotic limit, resulting in a model which treats the computer as a continuum of processors and data flow as an Eulerian fluid governed by a conservation law. We derive a Hamilton–Jacobi equation associated with this conservation law for which the existence and uniqueness of solutions can be proven. We then present the results of numerical experiments for both discrete and continuum models; these show a qualitative agreement between the two and the effect of variations in the computing environment’s processing capabilities on the progress of the modelled computation.

Barnard, Richard C.↗

DOE OSTI2018

Total variation-based neutron computed tomography

We perform the neutron computed tomography reconstruction problem via an inverse problem formulation with a total variation penalty. In the case of highly under-resolved angular measurements, the total variation penalty suppresses high-frequency artifacts which appear in filtered back projections. Here, in order to efficiently compute solutions for this problem, we implement a variation of the split Bregman algorithm; due to the error-forgetting nature of the algorithm, the computational cost of updating can be significantly reduced via very inexact approximate linear solvers. We present the effectiveness of the algorithm in the significantly low-angular sampling case using synthetic test problems as well as data obtained from a high flux neutron source. Finally, the algorithm removes artifacts and can even roughly capture small features when an extremely low number of angles are used.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Scientific data interpolation with low dimensional manifold model

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

$L^1$ penalization of volumetric dose objectives in optimal control of PDEs

This work is concerned with a class of PDE-constrained optimization problems that are motivated by an application in radiotherapy treatment planning. Here the primary design objective is to minimize the volume where a functional of the state violates a prescribed level, but prescribing these levels in the form of pointwise state constraints leads to infeasible problems. We therefore propose an alternative approach based on L 1 penalization of the violation that is also applicable when state constraints are infeasible. We establish well-posedness of the corresponding optimal control problem, derive first-order optimality conditions, discuss convergence of minimizers as the penalty parameter tends to infinity, and present a semismooth Newton method for their efficient numerical solution. Finally, the performance of this method for a model problem is illustrated and contrasted with an alternative approach based on (regularized) state constraints.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model

In this paper, we study the sensitivities of electron dose calculations with respect to stopping power and transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker–Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker–Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion (P N ) and an Harten-Lax-van Leer finite volume method. Our method is verified by comparison to finite difference approximations of the sensitivities. Finally, we present numerical results of the sensitivities for the normalized average dose deposition depth with respect to the stopping power and the transport coefficients, demonstrating the increase in relative sensitivities as beam energy decreases. In conclusion, this in turn gives estimates on the uncertainty in the normalized average deposition depth, which we present.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2016

A convex penalty for switching control of partial differential equations

A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.

97 MATHEMATICS AND COMPUTING↗