Related papers: An efficient asymptotic preserving Monte Carlo met…

We develop a novel Monte Carlo strategy for the simulation of the Boltzmann-BGK model with both low-collisional and high-collisional regimes present. The presented solution to maintain accuracy in low-collisional regimes and remove…

Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…

We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo (FPKMC) algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions. The…

During the past years several variance reduction techniques for Monte Carlo electron transport have been developed in order to reduce the electron computation time transport for absorbed dose distribution. We have implemented the Macro…

Radiative transfer (RT) simulations are a powerful tool that enables the calculation of synthetic images of a wide range of astrophysical objects. These simulations are often based on the Monte Carlo (MC) method, as it provides the needed…

We propose and analyze a new asymptotic preserving (AP) finite volume scheme for the multidimensional compressible barotropic Euler equations to simulate low Mach number flows. The proposed scheme uses a stabilized upwind numerical flux,…

Kinetic descriptions of runaway electrons (RE) are usually based on Fokker-Planck models that determine the probability distribution function (PDF) of RE in 2-dimensional momentum space. Despite of the simplification involved, the…

In this paper we study asymptotic properties of different data-augmentation-type Markov chain Monte Carlo algorithms sampling from mixture models comprising discrete as well as continuous random variables. Of particular interest to us is…

We propose Continual Repeated Annealed Flow Transport Monte Carlo (CRAFT), a method that combines a sequential Monte Carlo (SMC) sampler (itself a generalization of Annealed Importance Sampling) with variational inference using normalizing…

We present Diffusion Restore, a real-time framework for diffusion-based MCMC light transport. MCMC methods are highly suitable for sampling from complex high-dimensional distributions and for approximating integrals over them. In practice,…

Auxiliary Field Quantum Monte Carlo (AFQMC) has emerged as a powerful framework for treating strongly correlated electronic systems, offering a favorable balance between computational cost and accuracy. In this paper, we present a novel…

We consider a linear kinetic transport equation under a diffusive scaling, that converges to a diffusion equation as the Knudsen number $\varepsilon\rightarrow0$. In [3, 21], to achieve the asymptotic preserving (AP) property and…

The Active Flux (AF) method is a compact, high-order finite volume scheme that enhances flexibility by introducing point values at cell interfaces as additional degrees of freedom alongside cell averages. The method of lines is employed…

The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic…

Monte Carlo statistical ray-tracing methods are commonly employed to simulate carrier transport in nanostructured materials. In the case of a large degree of nanostructuring and under linear response (small driving fields), these…

We present a conservative numerical method for radiation magnetohydrodynamics with frequency-dependent full transport in stationary spacetimes. This method is stable and accurate for both large and small optical depths and radiation…

For linear transport and radiative heat transfer equations with random inputs, we develop new generalized polynomial chaos based Asymptotic-Preserving stochastic Galerkin schemes that allow efficient computation for the problems that…

We consider the simulation of isentropic flow in pipelines and pipe networks. Standard operating conditions in pipe networks suggest an emphasis to simulate low Mach and high friction regimes -- however, the system is stiff in these regimes…

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…

We analyze the line radiative transfer in protoplanetary disks using several approximate methods and a well-tested Accelerated Monte Carlo code. A low-mass flaring disk model with uniform as well as stratified molecular abundances is…