All-at-once preconditioning in PDE-constrained optimization

The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound constraints for the control are introduced. Numerical results will illustrate the competitiveness of our techniques

A strongly conservative finite element method for the coupling of Stokes and Darcy flow

https://scholars.carroll.edu/romansarcophagus_file5/1145/thumbnail.jp

The deal.II Library, Version 8.3

deal.II version 8.3 was released August 1, 2015. This paper provides an overview of the new features of this release and serves as a citable reference for the deal.II software library version 8.3. deal.II is an object-oriented finite element library used around the world in the development of finite element solvers. It is available for free under the GNU Lesser General Public License (LGPL) from the deal.II homepage at http://www.dealii.org/

Numerical Computations with H(div)-Finite Elements for the Brinkman Problem

The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant permeability. A hybridization technique for the problem is presented, complete with a convergence analysis and numerical verification. Finally, the numerical convergence studies are complemented with numerical examples of applications to domain decomposition and adaptive mesh refinement.Comment: Minor clarifications, added references. Reordering of some figures. To appear in Computational Geosciences, final article available at http://www.springerlink.co

ESR observations of paramagnetic centers in intrinsic hydrogenated microcrystalline silicon

Paramagnetic centers in hydrogenated microcrystalline silicon, µc-Si:H have been studied using dark and light-induced electron-spin resonance (ESR). In dark ESR measurements only one center is observed. The g values obtained empirically from powder-pattern line-shape simulations are g=2.0096 and g'=2.0031. We suggest that this center may be due to defects in the crystalline phase. During illumination at low temperatures, an additional ESR signal appears. This signal is best described by two powder patterns indicating the presence of two centers. One center is asymmetric (gi=1.999, g'=1.996), while the other is characterized by large, unresolved broadening such that unique g values cannot be obtained. The average g value for this center is 1.998. The light-induced signal, which we interpret as coming from carriers trapped in the band tails at the crystalline grain boundaries, remains for at least several minutes after the light is turned off. Although the time scales of the decay curves are very different for two samples prepared by different techniques, both decays can be fitted using the assumption of recombination due to distant pairs of electrons and holes trapped in localized band-tail states