A new coarse space for domain decomposition methods is presented for nodal ellipticproblems in two dimensions. The coarse space is derived from the novel virtual elementmethods and therefore can accommodate quite irregular ...

A bound is obtained for the condition number of a BDDC algorithm for problems posed in H(curl) in two dimensions, where the subdomains are only assumed to be uniform in the sense of Peter Jones. For the primal variable ...

On the other hand, Virtual Element Methods (VEM) [1, 12, 13] allow to handle general polygonal elements. In the case of triangular elements, VEM reduces to the usual FEM. Thus, VEM is a natural choice for constructing space ...

Consider the discrete quadratic phase Hilbert Transform acting on $\ell^{2}(\mathbb{Z})$ finitely supported functions $$ H^{\alpha} f(n) : = \sum_{m \neq 0} \frac{e^{i\alpha m^2} f(n - m)}{m}. $$ We prove that, ...

There has recently been a considerable activity in developing adaptive methods for the selection of primal constraints for BDDC algorithms and, in particular, for BDDC deluxe variants. The primal constraints of a BDDC or ...

A new extension operator for a virtual coarse space is presented which can be used in domain decomposition methods for nodal elliptic problems in two dimensions. In particular, a two-level overlapping Schwarz algorithm is ...