Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials

Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms....

Comparison of the deflated preconditioned conjugate gradient method and parallel direct solver for composite materials

The demand for large FE meshes increases as parallel computing becomes the standard in FE simulations. Direct and iterative solution methods are used to solve the resulting linear systems. Many applications concern composite materials, which are characterized by large discontinuities in the material properties. An example of such a material is...

A Comparison of Two-Level Preconditioners Based on Multigrid and Deflation

It is well known that two-level and multilevel preconditioned conjugate gradient (PCG) methods provide efficient techniques for solving large and sparse linear systems whose coefficient matrices are symmetric and positive definite. A two-level PCG method combines a traditional (one-level) preconditioner, such as incomplete Cholesky, with a...

Fast and robust solvers for pressure correction in bubbly flow problems

Theoretical comparison of two-level preconditioners based on multigrid and deflation