A class of domain decomposition preconditioners for hp-discontinuous Galerkin finite element methods

In this article we address the question of efficiently solving the algebraic linear system of equations arising from the discretization of a symmetric, elliptic boundary value problem using hp-version discontinuous Galerkin finite element methods. In particular, we introduce a class of domain decomposition preconditioners based on the Schwarz framework, and prove bounds on the condition number of the resulting iteration operators. Numerical results confirming the theoretical estimates are also presented.

Document analysis of PDF files: methods, results and implications

A strategy for document analysis is presented which uses Portable Document Format (PDF the underlying file structure for Adobe Acrobat software) as its starting point. This strategy examines the appearance and geometric position of text and image blocks distributed over an entire document. A blackboard system is used to tag the blocks as a first stage in deducing the fundamental relationships existing between them. PDF is shown to be a useful intermediate stage in the bottom-up analysis of document structure. Its information on line spacing and font usage gives important clues in bridging the semantic gap between the scanned bitmap page and its fully analysed, block-structured form. Analysis of PDF can yield not only accurate page decomposition but also sufficient document information for the later stages of structural analysis and document understanding.