Applications of Alternating Direction Solver for simulations of time-dependent problems

This paper deals with application of Alternating Direction solver (ADS) to nonstationarylinear elasticity problem solved with isogeometric FEM. Employingtensor product B-spline basis in isogeometric analysis under some restrictionsleads to system of linear equations with matrix possessing tensor product structure.Alternating Direction Implicit algorithm is a direct method that exploitsthis structure to solve the system in O (N ), where N is a number of degreesof freedom (basis functions). This is asymptotically faster than state-of-theartgeneral purpose multi-frontal direct solvers. In this paper we also presentthe complexity analysis of ADS incorporating dependence on order of B-splinebasis

Solver algorithm for stabilized space-time formulation of advection-dominated diffusion problem

This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using higher-order continuous B-spline basis functions in its spatial and temporal dimensions. This problem is very difficult to solve numerically using the standard Galerkin finite element method due to artificial oscillations present when the advection term dominates the diffusion term. However, a first-order constraint least-square formulation allows us to obtain numerical solutions avoiding oscillations. The advantages of space-time formulations are the use of high-order methods and the feasibility of developing space-time mesh adaptive techniques on well-defined discrete problems. We develop a solver for a least-square formulation to obtain a stabilized and symmetric problem on finite element meshes. The computational cost of our solver is bounded by the cost of the inversion of the space-time mass and stiffness (with one value fixed at a point) matrices and the cost of the GMRES solver applied for the symmetric and positive definite problem. We illustrate our findings on an advection-dominated diffusion space-time model problem and present two numerical examples: one with isogeometric analysis discretizations and the second one with an adaptive space-time finite element method.Comment: 24 pages, 7 figures, 2 table

First insight into microbial community composition in a phosphogypsum waste heap soil

The aim of this study was to investigate the soil microbial communities of a phosphogypsum waste heap. The soil microbial community structures can differ over time, as they are affected by the changing environmental conditions caused by a long-term exposure to different kinds of pollutions, like is the case of soil in the post-production waste area in Wiślinka (in the northern part of Poland) currently undergoing restoration. Our analyses indicated that the most abundant phyla were Proteobacteria, Acidobacteria, and Actinobacteria, and generally such an abundance is common for most of the studied soils. The most dominant class were Alphaproteobacteria, with their participation in 33.46% of the total reads. Among this class, the most numbered order was Sphingomonadales, whereas among this order the Sphingomonadaceae family was the most abundant one. The Sphingomonadaceae family is currently in the center of interest of many researchers, due to the ability of some of its members to utilize a wide range of naturally occurring organic compounds and many types of environmental contaminants. This kind of knowledge about microbial populations can support efforts in bioremediation and can improve monitoring changes in the contaminated environments

Misfit landforms imposed by ill-conditioned inverse parametric problems

In the paper, we put forward a new topological taxonomy which allows to distinguish and separate multiple solutions to the ill-conditioned parametric inverse problems appearing in engineering, geophysics, medicine, etc. This taxonomy distinguishes the areas of insensitivity to parameters, called landforms of the misfit landscape, be it around minima (lowlands), maxima (uplands), or stationary points (shelves). We proved their important separability and completeness conditions. In particular, lowlands, uplands and shelves are pairwise disjoint and there are no other subsets of the positive measure in the admissible domain on which misfit function takes a constant value. The topological taxonomy is related to the second, 'local' one, which characterizes the types of ill-conditioning of the particular solutions. We hope that the proposed results will be helpful for a better and more precise formulation of the ill-conditioned inverse problems and for selecting and profiling complex optimization strategies used to solve these problems

ADI-based, conditionally stable schemes for seismic P-wave and elastic wave propagation problems

The modeling of P-waves has essential applications in seismology. This is because the detection of the P-waves is the first warning sign of the incoming earthquake. Thus, P-wave detection is an important part of an earthquake monitoring system. In this paper, we introduce a linear computational cost simulator for three-dimensional simulations of P-waves. We also generalize our formulations and derivation for elastic wave propagation problems. We use the alternating direction method with isogeometric finite elements to simulate seismic P-wave and elastic propagation problems. We introduce intermediate time steps and separate our differential operator into a summation of the blocks, acting along the particular coordinate axis in the sub-steps. We show that the resulting problem matrix can be represented as a multiplication of three multi-diagonal matrices, each one with B-spline basis functions along the particular axis of the spatial system of coordinates. The resulting system of linear equations can be factorized in linear $\mathcal{O}$ (N) computational cost in every time step of the semi-implicit method. We use our method to simulate P-wave and elastic wave propagation problems. We derive the condition for the stability for seismic waves; namely, we show that the method is stable when τ < C min{ h$_{x}$,h$_{y}$,h$_{z}$}, where C is a constant that depends on the PDE problem and also on the degree of splines used for the spatial approximation. We conclude our presentation with numerical results for seismic P-wave and elastic wave propagation problems

Effective inhibition of lytic development of bacteriophages λ, P1 and T4 by starvation of their host, Escherichia coli

BACKGROUND: Bacteriophage infections of bacterial cultures cause serious problems in genetic engineering and biotechnology. They are dangerous not only because of direct effects on the currently infected cultures, i.e. their devastation, but also due to a high probability of spreading the phage progeny throughout a whole laboratory or plant, which causes a real danger for further cultivations. Therefore, a simple method for quick inhibition of phage development after detection of bacterial culture infection should be very useful. RESULTS: Here, we demonstrate that depletion of a carbon source from the culture medium, which provokes starvation of bacterial cells, results in rapid inhibition of lytic development of three Escherichia coli phages, λ, P1 and T4. Since the effect was similar for three different phages, it seems that it may be a general phenomenon. Moreover, similar effects were observed in flask cultures and in chemostats. CONCLUSION: Bacteriophage lytic development can be inhibited efficiently by carbon source limitation in bacterial cultures. Thus, if bacteriophage contamination is detected, starvation procedures may be recommended to alleviate deleterious effects of phage infection on the culture. We believe that this strategy, in combination with the use of automated and sensitive bacteriophage biosensors, may be employed in the fermentation laboratory practice to control phage outbreaks in bioprocesses more effectively

Parallel Fast Isogeometric Solvers for Explicit Dynamics

This paper presents a parallel implementation of the fast isogeometric solvers for explicit dynamics for solving non-stationary time-dependent problems. The algorithm is described in pseudo-code. We present theoretical estimates of the computational and communication complexities for a single time step of the parallel algorithm. The computational complexity is O(p^6 N/c t_comp) and communication complexity is O(N/(c^(2/3)t_comm) where p denotes the polynomial order of B-spline basis with Cp-1 global continuity, N denotes the number of elements and c is number of processors forming a cube, t_comp refers to the execution time of a single operation, and t_comm refers to the time of sending a single datum. We compare theoretical estimates with numerical experiments performed on the LONESTAR Linux cluster from Texas Advanced Computing Center, using 1 000 processors. We apply the method to solve nonlinear flows in highly heterogeneous porous media