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We apply a recently proposed [5] robust overlapping Schwarz method with a certain spectral construction of the coarse space in the setting of element agglomeration algebraic multigrid methods (or agglomeration AMGe) for elliptic problems with high-contrast coefficients. Our goal is to design multilevel iterative methods that converge independent of the contrast in the coefficients. We present simplified bounds for the condition number of the preconditioned operators. These bounds imply convergence that is independent of the contrast. In the presented preliminary numerical tests, we use geometric agglomerates; however, the algorithm is general and offers some simplifications over the previously proposed spectral agglomerate AMGe methods (cf., [3, 2]). [ABSTRACT FROM AUTHOR]

The search for efficient preconditioners for H(curl) problems on unstructured meshes has intensified in the last few years. The attempts to directly construct AMG (algebraic multigrid) methods had some success, see [10, 1, 6]. Exploiting available multilevel methods on auxiliary mesh for the same bilinear form led to efficient auxiliary mesh preconditioners to unstructured problems as shown in [7, 4]. A computationally more attractive approach was recently announced in [5]. Their method borrows the main tool from the above mentioned auxiliary mesh preconditioners, namely, the interpolation operator Πh that maps functions from H(curl) into the lowest order Nédélec finite element space Vh. The method of [5] and its motivation are outlined in Section 2. In particular, we describe briefly their Nédélec space decomposition, which is the basis of the auxiliary space AMG preconditioners. [ABSTRACT FROM AUTHOR]

In recent years, several extensions of the classical AMG method (see [2] and [10]) to handle more general finite element matrices have been proposed (see, e.g., [3], [9], and [7]). Other extensions are related to the so-called smoothed aggregation method; see e.g., [11] and the papers cited therein. For the most recent versions of both the AMG and smoothed aggregation approaches, we refer to [5] and [4]. [ABSTRACT FROM AUTHOR]

The main theme of the minisymposium was centered around the construction of advanced multigrid techniques for the solution of large scale linear systems that typically arise from the discretization of systems of PDEs. Examples of such PDEs are found in numerical models used in electromagnetics, flow simulation, and elasticity. In the present proceedings two papers are included; one deals with a multilevel hierarchical basis preconditioner for 3D elliptic problems discretized by the DG (discontinuous Galerkin) method, whereas the second one deals with a new auxiliary space preconditioning method for (semi—)definite time domain Maxwell (H(curl)) problems. [ABSTRACT FROM AUTHOR]