A BDDC algorithm with deluxe scaling for three-dimensional \(H(\mathbf{curl})\) problems (Q2802897)

The authors are concerned with an application of the finite elements method to approximately solving the boundary value problem for a class of partial differential equation of elliptic type NEWLINE\[NEWLINE \Delta u = f, \text{ on }\Omega \subset \mathbb R^{3},\quad u = g, \quad x\in \partial \Omega. NEWLINE\]NEWLINE A discretized problem is obtained using the lowest-order Nédeléc elements method with the unknowns given on the edge of tetrahedral elements of the partitioned domain \( \Omega \). Each subdomain face satisfies supplementary conditions. This method is named BDDC, i.e. balancing domain decomposition by constraints method. In the reviewer's opinion, the exposition of the main subject is unsuccessful.