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 Two-Level Preconditioners Derived from Deflation, Domain Decomposition and Multigrid Methods

For various applications, it is well-known that a multi-level, in particular two-level, preconditioned CG (PCG) method is an efficient method for solving large and sparse linear systems with a coefficient matrix that is symmetric positive definite. The corresponding two-level preconditioner combines traditional and projection-type...