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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...
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.
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...
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.
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)...
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)...
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...
This paper discusses finite element discretization and preconditioning strategies for the iterative solution of nonsymmetric indefinite linear algebraic systems of equations arising in modelling of glacial rebound processes. Some numerical experiments for the purely elastic model setting are provided. Comparisons of the performance of the iterative solution method with a direct solution method are included as well.
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