Fourier-Gegenbauer integral-Galerkin method for solving the advection-diffusion equation with periodic boundary conditions
KT Elgindy - arxiv preprint arxiv:2501.02307, 2025 - arxiv.org
This study presents the Fourier-Gegenbauer Integral-Galerkin (FGIG) method, a novel and
efficient numerical framework for solving the one-dimensional advection-diffusion equation …
efficient numerical framework for solving the one-dimensional advection-diffusion equation …
Efficient parallelization for volume-coupled multiphysics simulations on hierarchical Cartesian grids
One of the main challenges for multiphysics simulations of volume-coupled problems is data
exchange, which becomes a serious bottleneck for large-scale applications executed on …
exchange, which becomes a serious bottleneck for large-scale applications executed on …
The inverse distance weighted interpolation applied to a particular form of the path tubes Method: Theory and computation for advection in incompressible flow
N Henderson, L Pena - Applied Mathematics and Computation, 2017 - Elsevier
A simplified version of the inverse distance weighted interpolation formula was
mathematically analyzed and employed in the context of a semi-Lagrangian scheme for the …
mathematically analyzed and employed in the context of a semi-Lagrangian scheme for the …
[HTML][HTML] Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contexts
When the flow is sufficiently rarefied, a temperature gradient, for example, between two walls
separated by a few mean free paths, induces a gas flow—an observation attributed to the …
separated by a few mean free paths, induces a gas flow—an observation attributed to the …
Evaluation of a minimally synchronous algorithm for 2: 1 octree balance
The p4est library implements octree-based adaptive mesh refinement (AMR) and has
demonstrated parallel scalability beyond 100,000 MPI processes in previous weak scaling …
demonstrated parallel scalability beyond 100,000 MPI processes in previous weak scaling …
High Accuracy Methods for Boltzmann Equation And Related Kinetic Models
S Jaiswal - 2021 - search.proquest.com
The Boltzmann equation, an integro-differential equation for the molecular distribution
function in the physical and velocity phase space, governs the fluid flow behavior at a wide …
function in the physical and velocity phase space, governs the fluid flow behavior at a wide …
DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions
For many problems in computational science and engineering, the so-called forward
problem—solution of the underlying mathematical model to yield output quantities of …
problem—solution of the underlying mathematical model to yield output quantities of …
Fast integral equation solver for variable coefficient elliptic PDEs in complex geometries
D Malhotra - 2017 - repositories.lib.utexas.edu
This dissertation presents new numerical algorithms and related software for the numerical
solution of elliptic boundary value problems with variable coefficients on certain classes of …
solution of elliptic boundary value problems with variable coefficients on certain classes of …