Fast solvers for simulation, inversion, and control of wave propagation problems

Abstract

From 26 to 28 of September 2011, a European Science Foundation (ESF) workshop 'Fast solvers for simulation, inversion, and control of wave propagation problems', OPTPDE 2011, was organized, in Würzburg, Germany, with approximately 50 participants from many different countries.The workshop aimed at fostering development and application of fast computational techniques to direct and inverse wave problems, which are of primal importance in strategic engineering areas. Regarding applications, there were several researchers dealing with propagating and standing wave phenomena, and also inverse problems concerning design, control, and parameter estimation were often discussed. Within this general framework, the following topics were addressed: modeling, data assimilation, fast computational strategies for direct and inverse wave problems, Helmholtz problems, model order reduction, uncertainty quantification, and related applications.This special issue in Numerical Linear Algebra with Applications gives an overview of some of the highly interesting achievements that were presented during the workshop in Würzburg.In the contribution [1], 'Convergence Analysis for Hyperbolic Evolution Problems in Mixed Norm', D. Boffi, A. Buffa, and L. Gastaldi present a convergence analysis for the space discretization of hyperbolic evolution problems in mixed form. In particular, this paper discusses the relation between the approximation of an underlying eigenvalue problem and the space discretization of the evolution problem.In the paper [2], 'A Block Krylov Subspace Time-Exact Solution Method for Linear ODE Systems' by M.A. Botchev, a residual-based block Krylov subspace method that solves certain classes of linear systems of ordinary differential equations is discussed. This method consists of two steps that involve an accurate piecewise polynomial approximation of the source term, constructed with