Algebraic Multigrid Methods and Their Application to Generalized Finite Element Methods

Project: Research project

Project Details

Description

The research in this proposal is on the study and applications of efficient algebraic multigrid methods for the solution of linear algebraic systems arising from the discretization of second order partial differential equations by the generalized finite element method. The proposed research will focus on the development and analysis of adaptive techniques in the construction of hierarchy of nested spaces and the choice of approximate subspace solvers that lead to the efficient and robust multigrid methods applicable to wide range of generalized finite element discretizations. The rapid increase in the power of today's supercomputers has made it feasible for the scientific community to use numerical simulations to model physical phenomena to produce meaningful results. One of the modern techniques that can deliver quantitative results via such simulations is the generalized finite element method. This method has proved to be a very robust discretization tool, applicable in various branches of engineering and sciences, for example, in simulating and determining the elastic, electromagnetic and other important physical properties of heterogeneous materials. Like most other discretization techniques, most often the majority of computation in such simulations is devoted to the solution of the resulting linear systems of equations. Hence, it is very important to develop efficient solvers for these systems. The results from the proposed research are thus expected to have a broad and noticeable impact by providing the much needed iterative multilevel solution techniques for the discrete linear systems arising from numerical models in many applications. The proposed research is also expected to have an educational impact as it will provide a solid base for training of graduate students in the modern theoretical and practical aspects of numerical methods for problems in science and engineering.

StatusFinished
Effective start/end date9/15/058/31/09

Funding

  • National Science Foundation: $120,000.00
  • National Science Foundation: $120,000.00

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