Multilevel preconditioners for Lagrange multipliers in domain imbedding.
Multilevel preconditioning.
Multilevel Schwarz methods.
Multiparameter extrapolation and deflation methods for solving equation systems.
Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems
In this paper we introduce and analyze some non-overlapping multiplicative Schwarz methods for discontinuous Galerkin (DG) approximations of elliptic problems. The construction of the Schwarz preconditioners is presented in a unified framework for a wide class of DG methods. For symmetric DG approximations we provide optimal convergence bounds for the corresponding error propagation operator, and we show that the resulting methods can be accelerated by using suitable Krylov space solvers. A discussion...
Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing
We analyze a general multigrid method with aggressive coarsening and polynomial smoothing. We use a special polynomial smoother that originates in the context of the smoothed aggregation method. Assuming the degree of the smoothing polynomial is, on each level , at least , we prove a convergence result independent of . The suggested smoother is cheaper than the overlapping Schwarz method that allows to prove the same result. Moreover, unlike in the case of the overlapping Schwarz method, analysis...
Neumann-Neumann algorithms for spectral elements in three dimensions
Neumann-Neumann methods for vector field problems.
New iterative codes for𝓗-tensors and an application
New iterative codes for identifying 𝓗 -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given. Advantages of results obtained are illustrated by numerical examples.
New mixed finite volume methods for second order eliptic problems
In this paper we introduce and analyze new mixed finite volume methods for second order elliptic problems which are based on H(div)-conforming approximations for the vector variable and discontinuous approximations for the scalar variable. The discretization is fulfilled by combining the ideas of the traditional finite volume box method and the local discontinuous Galerkin method. We propose two different types of methods, called Methods I and II, and show that they have distinct advantages over...
New SOR-like methods for solving the Sylvester equation
We present new iterative methods for solving the Sylvester equation belonging to the class of SOR-like methods, based on the SOR (Successive Over-Relaxation) method for solving linear systems. We discuss convergence characteristics of the methods. Numerical experimentation results are included, illustrating the theoretical results and some other noteworthy properties of the Methods.
Newton iteration for the closest normal matrix of order two.
Noise propagation in regularizing iterations for image deblurring.
Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements will be considered in two and three dimensions. The simplicial elements will be based on P1, as for conforming elements; however, it is necessary to introduce new elements in the rectangular case. Optimal order error estimates are demonstrated in all cases with respect to a broken norm in H1(Ω)...
Nonexpansive matrices with applications to solutions of linear systems by fixed point iterations.
Non-stationary parallel multisplitting AOR methods.
Normes et algorithmes associés à une découpe de matrice. (Itération du principe de Gauss-Seidel).
Note about the parallel projection method for solution of system of linear algebraic equations
Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM
This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in (n ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ωc:= . The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping (NtD)...