Domain-DecompositionMethods for Parabolic Problems in Multi- dimensions with error-estimates

In this paper we consider parabolic equations with multi-physical processes for applications in porous media. For the solver method we apply an overlapping Schwarz wave form relaxation method, see [1]. We describe the theory for a multidimensional convection-diffusion-reaction equations and present an error-estimate for the domain-decomposition-method. The exactness and the efficiency of the methods are investigated through solutions of model problems of convection-diffusion-reaction equation. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Wipe sampling procedure coupled to LC–MS/MS analysis for the simultaneous determination of 10 cytotoxic drugs on different surfaces

A simple wipe sampling procedure was developed for the surface contamination determination of ten cytotoxic drugs: cytarabine, gemcitabine, methotrexate, etoposide phosphate, cyclophosphamide, ifosfamide, irinotecan, doxorubicin, epirubicin and vincristine. Wiping was performed using Whatman filter paper on different surfaces such as stainless steel, polypropylene, polystyrol, glass, latex gloves, computer mouse and coated paperboard. Wiping and desorption procedures were investigated: The same solution containing 20% acetonitrile and 0.1% formic acid in water gave the best results. After ultrasonic desorption and then centrifugation, samples were analysed by a validated liquid chromatography coupled to tandem mass spectrometry (LC–MS/MS) in selected reaction monitoring mode. The whole analytical strategy from wipe sampling to LC–MS/MS analysis was evaluated to determine quantitative performance. The lowest limit of quantification of 10 ng per wiping sample (i.e. 0.1 ng cm⁻²) was determined for the ten investigated cytotoxic drugs. Relative standard deviation for intermediate precision was always inferior to 20%. As recovery was dependent on the tested surface for each drug, a correction factor was determined and applied for real samples. The method was then successfully applied at the cytotoxic production unit of the Geneva University Hospitals pharmacy.     

Mobile and immobile gaseous transport: Embedded analytical solutions to finite volume methods

The motivation is driven by deposition processes based on chemical vapor problems. The underlying model problem is based on coupled transport–reaction equations with mobile and immobile areas. We deal with systems of ordinary and partial differential equations. Such equation systems are delicate to solve and we introduce a novel solver method, that takes into account ways to solve analytically parts of the transport and reaction equations. The main idea is to embed the analytical and semianalytical solutions, which can then be explicitly given to standard numerical schemes of higher order. The numerical scheme is based on flux‐based characteristic methods, which is a finite volume method. Such a method is an attractive alternative to the standard numerical schemes, which fully discretize the full equations. We instead reduce the computational time while embedding fast computable analytical parts. Here, we can accelerate the solver process, with a priori explicitly given solutions. We will focus on the derivation of the analytical solutions for general and special solutions of the characteristic methods that are embedded into a finite volume method. In the numerical examples, we illustrate the higher‐order method for different benchmark problems. Finally, the method is verified with realistic results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012     

Iterative splitting methods for solving time-dependent problems

There is increasing motivation for solving time-dependent differential equations with iterative splitting schemes. While Magnus expansion has been intensively studied and widely applied for solving explicitly time-dependent problems, the combination with iterative splitting schemes can open up new areas. The main problems with the Magnus expansion are the exponential character and the difficulty of deriving practical higher order algorithms. An alternative method is based on iterative splitting methods that take into account a temporally inhomogeneous equation. In this work, we show that the ideas derived from the iterative splitting methods can be used to solve time-dependent problems. Examples are discussed.     

Spatially-dependent and nonlinear fluid transport: coupling framework

We introduce a solver method for spatially dependent and nonlinear fluid transport. The motivation is from transport processes in porous media (e.g., waste disposal and chemical deposition processes). We analyze the coupled transport-reaction equation with mobile and immobile areas.     

Notiz über die algebraischen Minimumsflächen

Ohne Zusammenfassung     

Fourth-Order Splitting Methods for Time-Dependant Differential Equations

This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.