Low-Energy Basis Preconditioning for Elliptic Substructured Solvers Based on Unstructured Spectral/hp Element Discretization

A Multigrid Method for Nonlinear Unstructured Finite Element Elliptic Equations

This paper presents an application of the element agglomeration-based coarsening procedure (agglomeration AMGe) proposed in [10], to build the components of a multigrid method for solving nonlinear finite element elliptic equations on general unstructured meshes. The agglomeration-based AMGe offers the ability to define coarse elements and element matrices, provided access to elements and eleme...

Finite Element Preconditioning on Spectral Element Discretizations for Coupled Elliptic Equations

Experiments on Instance Preconditioning for Combinatorial Solvers

Preconditioning of matrices, with the objective to solve large systems of linear equations more efficiently, is an active area of research. In contrast, there is no comparable systematic effort to precondition graph-based instances before solving them with a combinatorial solver. This paper asks the question: Does an existing preconditioning technique with known merits in solving systems of lin...

Study of B-Splines finite element discretization of Physics-based Preconditioning for fluid mechanics models

The numerical simulation of large-scale MHD instabilities in confined magnetic fusion devices (called a tokamak geometry), relies on solving a Fluid model coupled with Maxwell equations. Solving these equations in the complicated geometry of the tokamak is a highly demanding task due to the strong temporal and spatial multi-scale nature of the problem and the anisotropies induced by the magneti...

Discretization Methods and Iterative Solvers Based on Domain Decomposition

In what case do you like reading so much? What about the type of the discretization methods and iterative solvers based on domain decomposition book? The needs to read? Well, everybody has their own reason why should read some books. Mostly, it will relate to their necessity to get knowledge from the book and want to read just to get entertainment. Novels, story book, and other entertaining boo...