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 parallelization for volume-coupled multiphysics simulations on hierarchical Cartesian grids

M Schlottke-Lakemper, A Niemoeller, M Meinke… - Computer Methods in …, 2019 - Elsevier
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 …

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 …

[HTML][HTML] Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contexts

S Jaiswal, A Pikus, A Strongrich, IB Sebastiao, J Hu… - Physics of …, 2019 - pubs.aip.org
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 …

Evaluation of a minimally synchronous algorithm for 2: 1 octree balance

H Suh, T Isaac - SC20: International Conference for High …, 2020 - ieeexplore.ieee.org
The p4est library implements octree-based adaptive mesh refinement (AMR) and has
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 …

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

K Willcox, R Juanes, Y Marzouk - 2019 - osti.gov
For many problems in computational science and engineering, the so-called forward
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 …