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We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…
In this work, we prove rigorous error estimates for a hybrid method introduced in [15] for solving the time-dependent radiation transport equation (RTE). The method relies on a splitting of the kinetic distribution function for the…
We investigate the behavior of microscopic heavy particles settling in homogeneous air turbulence. The regimes are relevant to the airborne transport of dust and droplets: the Taylor-microscale Reynolds number is Re = 289 - 462, the…
This paper presents approximation methods for time-dependent thermal radiative transfer problems in high energy density physics. It is based on the multilevel quasidiffusion method defined by the high-order radiative transfer equation (RTE)…
We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…
Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…
This paper develops a computational framework for Multi-Period Martingale Optimal Transport (MMOT), addressing convergence rates, algorithmic efficiency, and financial calibration. Our contributions include: (1) Theoretical analysis: We…
A fully implicit finite difference scheme has been developed to solve the hydrodynamic equations coupled with radiation transport. Solution of the time dependent radiation transport equation is obtained using the discrete ordinates method…
Deterministic models for radiation transport describe the density of radiation particles moving through a background material. In radiation therapy applications, the phase space of this density is composed of energy, spatial position and…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…
We propose Hierarchical Optimization Time Integration (HOT) for efficient implicit time-stepping of the Material Point Method (MPM) irrespective of simulated materials and conditions. HOT is an MPM-specialized hierarchical optimization…
Coherent oceanic mesoscale structures, especially the non-filamenting cores of oceanic eddies, have gained a lot of attention in recent years. These Lagrangian structures are considered to play a significant role in oceanic transport…
Efficient variance reduction of Monte Carlo simulations is desirable to avoid wasting computational resources. This paper presents an automated weight window algorithm for solving time-dependent particle transport problems. The weight…
Optimal transport methods have recently established state of the art accuracy and efficiency for holographic laser beam shaping. However, use of such methods is hindered by severe $\mathcal{O}(N^2)$ memory and $\mathcal{O}(N^2)$ time…
We develop a time-dependent multi-group multidimensional relativistic radiative transfer code, which is required to numerically investigate radiation from relativistic fluids involved in, e.g., gamma-ray bursts and active galactic nuclei.…
This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images $\rho_0$ and…
The manipulation of a collection of fluid particles in a low Reynolds number environment has several important applications. As we demonstrate in this paper, this manipulation problem is related to the scientific question of how fluid flow…
This paper presents a new Monte Carlo (MC) algorithm for time-dependent particle transport problems with global variance reduction based on automatic weight windows (WWs). The centers of WWs at a time step are defined by the solution of an…
We present a numerical implementation for the solution of the relativistic radiation hydrodynamics and magnetohydrodynamics equations, designed as an independent module within the freely available code PLUTO. The radiation transfer…