Related papers: Exponential methods for anisotropic diffusion
Cosmic ray transport on galactic scales depends on the detailed properties of the magnetized, multiphase interstellar medium (ISM). In this work, we post-process a high-resolution TIGRESS magnetohydrodynamic simulation modeling a local…
An efficient route to the displacement field around a rigid spherical inclusion in an infinitely extended homogeneous elastic medium is presented in a slightly alternative way when compared to some common textbook methods. Moreover, two…
Time fractional PDEs have been used in many applications for modeling and simulations. Many of these applications are multiscale and contain high contrast variations in the media properties. It requires very small time step size to perform…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
Anisotropic light transport is extremely common among scattering materials, yet a comprehensive picture of how macroscopic diffusion is determined by microscopic tensor scattering coefficients is not fully established yet. In this work, we…
In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…
In this article, we consider elliptic diffusion problems with an anisotropic random diffusion coefficient. We model the notable direction in terms of a random vector field and derive regularity results for the solution's dependence on the…
We present a new computation method for simulating reflection high-energy electron diffraction and the total-reflection high-energy positron diffraction experiments. The two experiments are used commonly for the structural analysis of…
In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying…
In the last decade, a number of experiments dealt with the problem of measuring the arrival direction distribution of cosmic rays, looking for information on the propagation mechanisms and the identification of their sources. Any deviation…
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in [Chac\'on et al., JCP, 272, 719-746, 2014] to use a fully implicit time…
Cosmic ray (CR) transport and acceleration is essential for many astrophysical problems, e.g., CMB foreground, ionization of molecular clouds and all high energy phenomena. Recent advances in MHD turbulence call for revisions in the…
The Cellular Potts Model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or…
We present results of explicit asymptotic approximations applied to neutrino--electron scattering in a representative model of neutrino population evolution under conditions characteristic of core-collapse supernova explosions or binary…
For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions,…
By implementing the exact density matrix for the rotating anisotropic harmonic trap, we derive a class of very fast and accurate fourth order algorithms for evolving the Gross-Pitaevskii equation in imaginary time. Such fourth order…
This work demonstrates algorithms to accurately compute solutions to thermal radiation transport problems using a reduced floating-point precision implementation of the Implicit Monte Carlo method. Several techniques falling into the…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…