arXiv subjects

Barry D. Ganapol

Publications and source records attributed to Barry D. Ganapol.

7 recordsLinked to original sources

arXiv2026

Neural Operator Surrogates for Two-Dimensional Neutron Flux Estimation

This work extends our one-dimensional single-sweep neural-operator studies to two dimensions. We consider one-group transport with isotropic scattering. As in the one-dimensional work, we use Fourier neural operators (FNOs) to approximate the high-fidelity scalar flux. Additionally, we also investigate U-shaped neural operators (UNOs) in this study. We consider three surrogates. The first two map the material and source fields directly to the flux, one using an FNO and one using a UNO. The third is an FNO that additionally takes the scalar flux after one source iteration, the single-sweep approximation, as an input. Each case is solved to high fidelity with a verified discrete-ordinates solver, and an average relative L_2 error norm is used to characterize the quality of the inferred maps. We train every surrogate over three random seeds so that differences between them can be assessed against run-to-run variability. Two questions guide the study: whether the single-sweep input improves accuracy over the direct maps, and whether training on the logarithm of the flux improves accuracy in the strongly attenuated regions relevant to shielding.

cs.LG↗

arXiv2025

Evolutionary Discovery of Sequence Acceleration Methods for Slab Geometry Neutron Transport

We present a genetic programming approach to automatically discover convergence acceleration methods for discrete ordinates solutions of neutron transport problems in slab geometry. Classical acceleration methods such as Aitken's delta-squared and Wynn epsilon assume specific convergence patterns and do not generalize well to the broad set of transport problems encountered in practice. We evolved mathematical formulas specifically tailored to SN convergence characteristics in this work. The discovered accelerator, featuring second differences and cross-product terms, achieved over 75 percent success rate in improving convergence compared to raw sequences - almost double that observed for classical techniques for the problem set considered. This work demonstrates the potential for discovering novel numerical methods in computational physics via genetic programming and attempts to honor Prof. Ganapol's legacy of advancing experimental mathematics applied to neutron transport.

cs.NE↗

arXiv2023

Assessing Nonlinear Diffusion Acceleration for Boltzmann Fokker Planck Equation in Slab Geometry

The convergence of Boltzmann Fokker Planck solution can become arbitrarily slow with iterative procedures like source iteration. This paper derives and investigates a nonlinear diffusion acceleration scheme for the solution of the Boltzmann Fokker Planck equation in slab geometry. This method is a conventional high order low order scheme with a traditional diffusion-plus-drift low-order system. The method, however, differs from the earlier variants as the definition of the low order equation, which is adjusted according to the zeroth and first moments of the Boltzmann Fokker Planck equation. For the problems considered, we observe that the NDA-accelerated solution follows the unaccelerated well and provides roughly an order of magnitude savings in iteration count and runtime compared to source iteration.

math.NA↗

arXiv2020

Matrix riccati equation solution of the 1d radiative transfer equation

In recent years, the first author has developed three successful numerical methods to solve the 1D radiative transport equation yielding highly precise benchmarks. The second author has shown a keen interest in novel solution methodologies and an ability for their implementation. Here, we combine talents to generate yet another high precision solution, the Matrix Riccati Equation Method (MREM). MREM features the solution to two of the four matrix Riccati ODEs that arise from the interaction principle of particle transport. Through interaction coefficients, the interaction principle describes how particles reflect from- and transmit through- a single slab. On combination with Taylor series and doubling, a high quality numerical benchmark, to nearly seven places, is established.

physics.comp-ph↗

arXiv2019

Towards a Multiphysics Model for Tumor Response to Combined-Hyperthermia-Radiotherapy Treatment

We develop a multiphysics-based model to predict the response of localized tumors to combined-hyperthermia-radiotherapy (CHR) treatment. This procedure combines hyperthermia (tumor heating) with standard radiotherapy to improve efficacy of the overall treatment. In addition to directly killing tumor cells, tumor heating amends several parameters within the tumor microenvironment. This leads to radiosensitization, which improves the performance of radiotherapy while reducing the side-effects of excess radiation in the surrounding normal tissue. Existing tools to model this kind of treatment consider each of the physics separately. The model presented in this paper accounts for the synergy between hyperthermia and radiotherapy providing a more realistic and holistic approach to simulate CHR treatment. Our model couples radiation transport and heat-transfer with cell population dynamics.

q-bio.TO↗

arXiv2016

Particle Transport in a 3D duct by adding and doubling

Particle transport through a duct by Lambertian reflection from duct walls is again considered. This popular transport example has been solved by most numerical transport methods except notably one- the method of doubling. We shall show that the method of doubling provides every bit as, or more, accurate reflectances and transmittances as the numerical discrete ordinates (NDO) and analytical discrete ordinates (ADO) methods with less mathematical and numerical effort.

physics.comp-ph↗

arXiv2010

An Accurate Numerical Solution to the Kinetics of Breakable Filament Assembly

Proteinaceous aggregation occurs through self-assembly-- a process not entirely understood. In a recent article [1], an analytical theory for amyloid fibril growth via secondary rather than primary nucleation was presented. Remarkably, with only a single kinetic parameter, the authors were able to unify growth characteristics for a variety of experimental data. In essence, they seem to have uncovered the underlying allometric laws governing the evolution of filament elongation simply from two coupled non-linear ordinary differential equations (ODEs) stemming from a master equation. While this work adds significantly to our understanding of filament self-assembly, it required an approximate analytical solution representation. Here, we show that the same results are found by purely numerical means once a straightforward and reliable numerical solution to the set of ODEs has been established.

physics.bio-ph↗