Cache optimization for structured and unstructured grid multigrid.
Characterization of Linear Stationary Iterative Processes for Solving a Singular System of Linear Equations.
Chebyshev approximation via polynomial mappings and the convergence behaviour of Krylov subspace methods.
Chebyshev semi-iteration in preconditioning for problems including the mass matrix.
Circulant preconditioners for convolution-like integral equations with higher-order quadrature rules.
Coarsening invariance and bucket-sorted independent sets for algebraic multigrid.
Combining the preconditioned conjugate gradient method and a matrix iterative method
The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated. The initial approximation for conjugate gradient is constructed as a result of a matrix iteration method after steps. The behaviour of the error vector for such a combined method is studied and special numerical tests and conclusions are made.
Comparing multilevel coarsening strategies.
Comparison between different numerical discretizations for a Darcy-Forchheimer model.
Comparison of Linear System Solvers Applied to Diffusion-Type Finite Element Equations.
Comparison of preconditioning and deflation techniques of FETI methods for problem of 2D linear elasticity
This paper deals with the basic preconditioning and deflation variants of the FETI-1 and TFETI-1 methods, with (T)FETI-1 with deflation being called (T)FETI-2. It also presents the results of numerical experiments performed on a simple benchmark 2D problem of linear elasticity to compare the computational efficiency of FETI-1 and TFETI-1 and each variant of their preconditioning or deflation in terms of number of executed CG iterations.
Comparison of Splittings Used with the Conjugate Gradient Algorithm.
Comparison theorems for weak nonnegative splittings of -monotone matrices.
Comparison theorems for weak splittings of bounded operators.
Comparisons of Regular Splittings of Matrices.
Comparisons of Weak Regular Splittings and Multisplitting Methods.
Complexity of an algorithm for solving saddle-point systems with singular blocks arising in wavelet-Galerkin discretizations
The paper deals with fast solving of large saddle-point systems arising in wavelet-Galerkin discretizations of separable elliptic PDEs. The periodized orthonormal compactly supported wavelets of the tensor product type together with the fictitious domain method are used. A special structure of matrices makes it possible to utilize the fast Fourier transform that determines the complexity of the algorithm. Numerical experiments confirm theoretical results.
Composite grid finite element method: Implementation and iterative solution with inexact subproblems
This paper concerns the composite grid finite element (FE) method for solving boundary value problems in the cases which require local grid refinement for enhancing the approximating properties of the corresponding FE space. A special interest is given to iterative methods based on natural decomposition of the space of unknowns and to the implementation of both the composite grid FEM and the iterative procedures for its solution. The implementation is important for gaining all benefits of the described...
Computing exponential for iterative splitting methods: algorithms and applications.
Concerning decomposition of a system of linear algebraic equations