Alternate strip-based substructuring algorithms for elliptic PDEs in two dimensions

The alternate strip-based substructuring algorithms are efficient preconditioning techniques for the discrete systems which arise from the finite-element approximation of symmetric elliptic boundary-value problems in 2D Euclidean spaces. The new approach is based on alternate decomposition of the given domain into a finite number of strips. Each strip is a union of non-overlapping subdomains and the global interface between subdomains is partitioned as a union of edges between strips and edges between subdomains that belong to the same strip. Both scalability and efficiency are achieved by alternating the direction of the strips. This approach generates algorithms in two stages and allows the use of a two-grid V cycle. Numerical estimates illustrate the behaviour of the new domain decomposition techniques