Enhanced multigrid solver for anisotropic equations with non-standard components: 3-Color Jacobi, mesh-tripling, and Fourier Analysis
Faculty / School
School of Mathematics and Computer Science (SMCS)
Department
Department of Mathematical Sciences
Was this content written or created while at IBA?
Yes
Document Type
Article
Source Publication
Partial Differential Equations in Applied Mathematics
Keywords
Multigrid methods, Local Fourier Analysis, Relaxation, Singularly perturbed convection–diffusion equations
Disciplines
Mathematics
Abstract
In this paper, the authors introduce an enhanced multigrid solver that offers an efficient solution method which is quite robust across a variety of boundary value problems. The solver’s theoretical foundation includes a framework for deriving optimal relaxation parameters, and features an auto-tuned, customizable meshing approach. It employs a hierarchical structure capable of handling various grid configurations, optimized through Local Fourier Analysis (LFA). Although primarily developed for the anisotropic diffusion equation, we extend the investigation to include the singularly perturbed convection diffusion equation; where we fine-tune meshing parameters, refine discretization techniques, and implement customized multigrid operators to address its unique challenges. Numerical experiments are included that demonstrate the solver’s robustness and efficiency, thereby making a strong case for its use across a wide range of second order elliptic problems.
Citation/Publisher Attribution
Shahid, M., & bin Zubair Syed, H. (2025). Enhanced multigrid solver for anisotropic equations with non-standard components: 3-Color Jacobi, mesh-tripling, and Fourier Analysis. Partial Differential Equations in Applied Mathematics, 101133.
Recommended Citation
Ashraf, M., & Syed, H. (2025). Enhanced multigrid solver for anisotropic equations with non-standard components: 3-Color Jacobi, mesh-tripling, and Fourier Analysis. Partial Differential Equations in Applied Mathematics, 13, 1-14. Retrieved from https://ir.iba.edu.pk/faculty-research-articles/249
Publication Status
Published
Rights Information
Note: This article is available under the Creative Commons CC-BY-NC-ND license and permits non-commercial use of the work as published, without adaptation or alteration provided the work is fully attributed.