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An algebraic multilevel iteration method for solving system of linear algebraic equations arising in $H(mathrm{curl})$ and $H(mathrm{div})$ spaces are presented. The algorithm is developed for the discrete problem obtained by using the space of lowest order Nedelec and Raviart-Thomas-Nedelec elements. The theoretical analysis of the method is based only on some algebraic sequences and generalized eigenvalues of local (element-wise) problems. In the hierarchical basis framework, explicit recursion formulae are derived to compute the element matrices and the constant $gamma$ (which measures the quality of the space splitting) at any given level. It is proved that the proposed method is robust with respect to the problem parameters, and is of optimal order complexity. Supporting numerical results, including the case when the parameters have jumps, are also presented.
This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for
We present algebraic multilevel iteration (AMLI) methods for isogeometric discretization of scalar second order elliptic problems. The construction of coarse grid operators and hierarchical complementary operators are given. Moreover, for a uniform m
Edge (or Nedelec) finite elements are theoretically sound and widely used by the computational electromagnetics community. However, its implementation, specially for high order methods, is not trivial, since it involves many technicalities that are n
We present a class of discretisation spaces and H(div)-conformal elements that can be built on any polytope. Bridging the flexibility of the Virtual Element spaces towards the elements shape with the divergence properties of the Raviart-Thomas elemen
For irrotational dust the shear tensor is consistently diagonalizable with its covariant time derivative: $sigma_{ab}=0=dot{sigma}_{ab},; a eq b$, if and only if the divergence of the magnetic part of the Weyl tensor vanishes: $div~H = 0$. We show he