Multigrid in a nutshell

Multigrid is an iterative method that is particularly suited for solving large, sparse linear systems, in the form of . When we have a sparse matrix at hand, direct methods, such as LU decomposition, for solving the equation becomes undesirable, because we might lose the sparsity and end up with a dense matrix. The best … More Multigrid in a nutshell

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Multigrid applied to Incompressible Navier-Stokes Equation

Equations for fluid dynamics In one of my research projects, I study numerical methods for fluid-structure interaction (FSI) problems. Examples of this type of problems are ubiquitous in nature, industries, and laboratories. For instance, as organisms swim in a liquid, the parts that generate propulsion, such as flagella and fins, are the solid structures that … More Multigrid applied to Incompressible Navier-Stokes Equation

Hybrid parallelized multigrid with OpenMP, GPU acceleration, and MPI

Many problems in computational sciences require solving linear systems, in the form of . Examples includes integrating an system of ordinary differential equations (ODEs) or solving partial differential equations (PDEs), image processing and analysis, etc. When the problems become large, direct methods, such as LU decomposition, become inefficient. This makes using an iterative method, such … More Hybrid parallelized multigrid with OpenMP, GPU acceleration, and MPI