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Implicit-Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity of interest for…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
The cavity method is a well established technique for solving classical spin models on sparse random graphs (mean-field models with finite connectivity). Laumann et al. [arXiv:0706.4391] proposed recently an extension of this method to…
In this paper, we propose a variable time-step linear relaxation scheme for time-fractional phase-field equations with a free energy density in general polynomial form. The $L1^{+}$-CN formula is used to discretize the fractional…
Wildfires, as an integral component of the Earth system, are governed by a complex interplay of atmospheric, oceanic, and terrestrial processes spanning a vast range of spatiotemporal scales. Modeling their global activity on large…
The Visible Infrared Imaging Radiometer Suite (VIIRS) active fire product is widely used for global fire monitoring, yet its confidence classification scheme exhibits an undocumented systematic pattern. Through analysis of 21,540,921 fire…
In this paper, we develop a class of high-order conservative methods for simulating non-equilibrium radiation diffusion problems. Numerically, this system poses significant challenges due to strong nonlinearity within the stiff source terms…
We propose a novel family of asymptotically stable, implicit-explicit, adaptive, time integration method (denoted with the $\theta$-method) for the solution of the fractional advection-diffusion-reaction (FADR) equations. This family of…
In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…
We consider the Dirichlet-Neumann iteration for partitioned simulation of thermal fluid-structure interaction, also called conjugate heat transfer. We analyze its convergence rate for two coupled fully discretized 1D linear heat equations…
Intense wildfire seasons require critical prioritization decisions to allocate scarce suppression resources over a dispersed geographical area. This paper develops a predictive and prescriptive approach to jointly optimize crew assignments…
We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body…
We present implicit-explicit (IMEX) kinetic simulations of weakly collisional parallel plasma transport in magnetic mirror configurations using the continuum code \textsc{COGENT}. The numerical scheme employs a Jacobian-free Newton--Krylov…
This work proposes an extension of phase change and latent heat models for the simulation of metal powder bed fusion additive manufacturing processes on the macroscale and compares different models with respect to accuracy and numerical…
In recent years, increased wildfires have caused irreversible damage to forest resources worldwide, threatening wildlives and human living conditions. The lack of accurate frontline information in real-time can pose great risks to…
We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems effectively acting as their own environment. Combining a variety of concepts of quantum many-body theory, notably the…
In weakly collisional, strongly magnetised plasmas such as the intracluster medium (ICM), hot accretion flows and the solar corona, the transport of heat and momentum occurs primarily along magnetic field lines. In this paper we present a…
We address the possibility of performing numerical Monte Carlo simulations for the thermodynamics of quantum dissipative systems. Dissipation is considered within the Caldeira-Leggett formulation, which describes the system in the…
Wildland-Urban Interface (WUI) fires represent a compound disaster resulting from the interactions between natural ecosystems and human settlements, characterized by significantly dynamic evolving risks. However, most current risk…
Despite the growing interest in parallel-in-time methods as an approach to accelerate numerical simulations in atmospheric modelling, improving their stability and convergence remains a substantial challenge for their application to…