Fast iterative solvers for Cahn-Hilliard problems

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Dissertation, 2016

Fast iterative solvers for time-dependent PDE-constrained optimization problems

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Kumulative Habilitation, 2016

An Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity.

Parallel direct Poisson and biharmonic solvers /

"NSF - OCA - GJ-36936 - 000006."

Fast Transforms for Acoustic Imaging-Part I: Theory

The classical approach for acoustic imaging consists of beamforming, and produces the source distribution of interest convolved with the array point spread function. This convolution smears the image of interest, significantly reducing its effective resolution. Deconvolution methods have been proposed to enhance acoustic images and have produced significant improvements. Other proposals involve covariance fitting techniques, which avoid deconvolution altogether. However, in their traditional presentation, these enhanced reconstruction methods have very high computational costs, mostly because they have no means of efficiently transforming back and forth between a hypothetical image and the measured data. In this paper, we propose the Kronecker Array Transform ( KAT), a fast separable transform for array imaging applications. Under the assumption of a separable array, it enables the acceleration of imaging techniques by several orders of magnitude with respect to the fastest previously available methods, and enables the use of state-of-the-art regularized least-squares solvers. Using the KAT, one can reconstruct images with higher resolutions than was previously possible and use more accurate reconstruction techniques, opening new and exciting possibilities for acoustic imaging.

Fast Transforms for Acoustic Imaging-Part II: Applications

In Part I [""Fast Transforms for Acoustic Imaging-Part I: Theory,"" IEEE TRANSACTIONS ON IMAGE PROCESSING], we introduced the Kronecker array transform (KAT), a fast transform for imaging with separable arrays. Given a source distribution, the KAT produces the spectral matrix which would be measured by a separable sensor array. In Part II, we establish connections between the KAT, beamforming and 2-D convolutions, and show how these results can be used to accelerate classical and state of the art array imaging algorithms. We also propose using the KAT to accelerate general purpose regularized least-squares solvers. Using this approach, we avoid ill-conditioned deconvolution steps and obtain more accurate reconstructions than previously possible, while maintaining low computational costs. We also show how the KAT performs when imaging near-field source distributions, and illustrate the trade-off between accuracy and computational complexity. Finally, we show that separable designs can deliver accuracy competitive with multi-arm logarithmic spiral geometries, while having the computational advantages of the KAT.

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

Mixing Snapshots and Fast Time Integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin sys- tem (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC inter- vals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computa- tional e®ort is associated with the snapshots calculation in the ¯rst INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be con- structed adapting the snapshots calculated in other runs to drastically reduce the size of the ¯rst INC interval and thus the involved computational cost. The strategy is success- fully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

Multiscale Schemes for the BGK--Vlasov--Poisson System in the Quasi-Neutral and Fluid Limits. Stability Analysis and First Order Schemes

This paper deals with the development and the analysis of asymptotically stable and consistent schemes in the joint quasi-neutral and fluid limits for the collisional Vlasov-Poisson system. In these limits, the classical explicit schemes suffer from time step restrictions due to the small plasma period and Knudsen number. To solve this problem, we propose a new scheme stable for choices of time steps independent from the small scales dynamics and with comparable computational cost with respect to standard explicit schemes. In addition, this scheme reduces automatically to consistent discretizations of the underlying asymptotic systems. In this first work on this subject, we propose a first order in time scheme and we perform a relative linear stability analysis to deal with such problems. The framework we propose permits to extend this approach to high order schemes in the next future. We finally show the capability of the method in dealing with small scales through numerical experiments.

High-throughput Analysis By Sp-ldi-ms For Fast Identification Of Adulterations In Commercial Balsamic Vinegars.

Balsamic vinegar (BV) is a typical and valuable Italian product, worldwide appreciated thanks to its characteristic flavors and potential health benefits. Several studies have been conducted to assess physicochemical and microbial compositions of BV, as well as its beneficial properties. Due to highly-disseminated claims of antioxidant, antihypertensive and antiglycemic properties, BV is a known target for frauds and adulterations. For that matter, product authentication, certifying its origin (region or country) and thus the processing conditions, is becoming a growing concern. Striving for fraud reduction as well as quality and safety assurance, reliable analytical strategies to rapidly evaluate BV quality are very interesting, also from an economical point of view. This work employs silica plate laser desorption/ionization mass spectrometry (SP-LDI-MS) for fast chemical profiling of commercial BV samples with protected geographical indication (PGI) and identification of its adulterated samples with low-priced vinegars, namely apple, alcohol and red/white wines.

Fast And Direct Na And K Determination In Table, Marine, And Low-sodium Salts By X-ray Fluorescence And Chemometrics.

X-ray fluorescence (XRF) is a fast, low-cost, nondestructive, and truly multielement analytical technique. The objectives of this study are to quantify the amount of Na(+) and K(+) in samples of table salt (refined, marine, and light) and to compare three different methodologies of quantification using XRF. A fundamental parameter method revealed difficulties in quantifying accurately lighter elements (Z < 22). A univariate methodology based on peak area calibration is an attractive alternative, even though additional steps of data manipulation might consume some time. Quantifications were performed with good correlations for both Na (r = 0.974) and K (r = 0.992). A partial least-squares (PLS) regression method with five latent variables was very fast. Na(+) quantifications provided calibration errors lower than 16% and a correlation of 0.995. Of great concern was the observation of high Na(+) levels in low-sodium salts. The presented application may be performed in a fast and multielement fashion, in accordance with Green Chemistry specifications.

[comparative Study Between Fast And Slow Induction Of Propofol Given By Target-controlled Infusion: Expected Propofol Concentration At The Effect Site. Randomized Controlled Trial].

studies have shown that rate of propofol infusion may influence the predicted propofol concentration at the effect site (Es). The aim of this study was to evaluate the Es predicted by the Marsh pharmacokinetic model (ke0 0.26min(-1)) in loss of consciousness during fast or slow induction. the study included 28 patients randomly divided into two equal groups. In slow induction group (S), target-controlled infusion (TCI) of propofol with plasma, Marsh pharmacokinetic model (ke0 0.26min(-1)) with target concentration (Tc) at 2.0-μg.mL(-1) were administered. When the predicted propofol concentration at the effect site (Es) reached half of Es value, Es was increased to previous Es + 1μg.mL(-1), successively, until loss of consciousness. In rapid induction group (R), patients were induced with TCI of propofol with plasma (6.0μg.ml(-1)) at Es, and waited until loss of consciousness. in rapid induction group, Tc for loss of consciousness was significantly lower compared to slow induction group (1.67±0.76 and 2.50±0.56μg.mL(-1), respectively, p=0.004). the predicted propofol concentration at the effect site for loss of consciousness is different for rapid induction and slow induction, even with the same pharmacokinetic model of propofol and the same balance constant between plasma and effect site.

A Simple and Fast Method for the Production and Characterization of Methylic and Ethylic Biodiesels from Tucum Oil via an Alkaline Route

A simple, fast, and complete route for the production of methylic and ethylic biodiesel from tucum oil is described. Aliquots of the oil obtained directly from pressed tucum (pulp and almonds) were treated with potassium methoxide or ethoxide at 40 degrees C for 40 min. The biodiesel form was removed from the reactor and washed with 0.1 M HCl aqueous solution. A simple distillation at 100 degrees C was carried out in order to remove water and alcohol species from the biodiesel. The oxidative stability index was obtained for the tucum oil as well as the methylic and ethylic biodiesel at 6.13, 2.90, and 2.80 h, for storage times higher than 8 days. Quality control of the original oil and of the methylic and ethylic biodiesels, such as the amount of glycerin produced during the transesterification process, was accomplished by the TLC, GC-MS, and FT-IR techniques. The results obtained in this study indicate a potential biofuel production by simple treatment of tucum, an important Amazonian fruit.

Fast ray-tracing algorithm for circumstellar structures (FRACS) II. Disc parameters of the B[e] supergiant CPD-57 degrees 2874 from VLTI/MIDI data

Context. B[e] supergiants are luminous, massive post-main sequence stars exhibiting non-spherical winds, forbidden lines, and hot dust in a disc-like structure. The physical properties of their rich and complex circumstellar environment (CSE) are not well understood, partly because these CSE cannot be easily resolved at the large distances found for B[e] supergiants (typically greater than or similar to 1 kpc). Aims. From mid-IR spectro-interferometric observations obtained with VLTI/MIDI we seek to resolve and study the CSE of the Galactic B[e] supergiant CPD-57 degrees 2874. Methods. For a physical interpretation of the observables (visibilities and spectrum) we use our ray-tracing radiative transfer code (FRACS), which is optimised for thermal spectro-interferometric observations. Results. Thanks to the short computing time required by FRACS (<10 s per monochromatic model), best-fit parameters and uncertainties for several physical quantities of CPD-57 degrees 2874 were obtained, such as inner dust radius, relative flux contribution of the central source and of the dusty CSE, dust temperature profile, and disc inclination. Conclusions. The analysis of VLTI/MIDI data with FRACS allowed one of the first direct determinations of physical parameters of the dusty CSE of a B[e] supergiant based on interferometric data and using a full model-fitting approach. In a larger context, the study of B[e] supergiants is important for a deeper understanding of the complex structure and evolution of hot, massive stars.

BONA FIDE, STRONG-VARIABLE GALACTIC LUMINOUS BLUE VARIABLE STARS ARE FAST ROTATORS: DETECTION OF A HIGH ROTATIONAL VELOCITY IN HR CARINAE

We report optical observations of the luminous blue variable (LBV) HR Carinae which show that the star has reached a visual minimum phase in 2009. More importantly, we detected absorptions due to Si lambda lambda 4088-4116. To match their observed line profiles from 2009 May, a high rotational velocity of nu(rot) similar or equal to 150 +/- 20 km s(-1) is needed (assuming an inclination angle of 30 degrees), implying that HR Car rotates at similar or equal to 0.88 +/- 0.2 of its critical velocity for breakup (nu(crit)). Our results suggest that fast rotation is typical in all strong-variable, bona fide galactic LBVs, which present S-Dor-type variability. Strong-variable LBVs are located in a well-defined region of the HR diagram during visual minimum (the ""LBV minimum instability strip""). We suggest this region corresponds to where nu(crit) is reached. To the left of this strip, a forbidden zone with nu(rot)/nu(crit) > 1 is present, explaining why no LBVs are detected in this zone. Since dormant/ex LBVs like P Cygni and HD 168625 have low nu(rot), we propose that LBVs can be separated into two groups: fast-rotating, strong-variable stars showing S-Dor cycles (such as AG Car and HR Car) and slow-rotating stars with much less variability (such as P Cygni and HD 168625). We speculate that supernova (SN) progenitors which had S-Dor cycles before exploding (such as in SN 2001ig, SN 2003bg, and SN 2005gj) could have been fast rotators. We suggest that the potential difficulty of fast-rotating Galactic LBVs to lose angular momentum is additional evidence that such stars could explode during the LBV phase.