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In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for…
Climate change has resulted in a year over year increase in adverse weather and weather conditions which contribute to increasingly severe fire seasons. Without effective mitigation, these fires pose a threat to life, property, ecology,…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
Rapid detection and well-timed intervention are essential to mitigate the impacts of wildfires. Leveraging remote sensed data from satellite networks and advanced AI models to automatically detect hotspots (i.e., thermal anomalies caused by…
Integrate-and-fire is a resource efficient time-encoding mechanism that summarizes into a signed spike train those time intervals where a signal's charge exceeds a certain threshold. We analyze the IF encoder in terms of a very general…
We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…
Time-implicit schemes are attractive since they allow numerical time steps that are much larger than those permitted by the Courant-Friedrich-Lewy criterion characterizing time-explicit methods. This advantage comes, however, with a cost:…
The aim of this paper is to develop stable and accurate numerical schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting boundary…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
This simulation study compares statistical approaches for estimating extreme quantile regression, with a specific application to fire risk forecasting. A simulation-based framework is designed to evaluate the effectiveness of different…
This research paper addresses the challenge of detecting obscured wildfires (when the fire flames are covered by trees, smoke, clouds, and other natural barriers) in real-time using drones equipped only with RGB cameras. We propose a novel…
The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…
This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…
Implicit schemes require important sub-iterations when dealing with highly nonlinear problems such as the combined heat and moisture transfer through porous building elements. The computational cost rises significantly when the…
In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behaviour of wildland fires across the landscape. This series of review papers…
An extended immersed boundary method utilizing a semi-implicit direct forcing approach for the simulation of confined incompressible viscous thermal flow problems is presented. The method utilizes a Schur complement approach to enforce the…
Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…
In this article we present a parallel algorithm for simulation of the heat conduction process inside the so-called pulse cryogenic cell. This simulation is important for designing the device for portion injection of working gases into…
The shift in chemical equilibria due to isotope substitution is often exploited to gain insight into a wide variety of chemical and physical processes. It is a purely quantum mechanical effect, which can be computed exactly using…
In this paper, we propose a novel computational implicit method, which we call Isogeometric Residual Minimization (iGRM) with direction splitting. The method mixes the benefits resulting from isogeometric analysis, implicit dynamics,…