Condition number analysis and preconditioning of the finite cell method

The (Isogeometric) Finite Cell Method - in which a domain is immersed in a structured background mesh - suffers from conditioning problems when cells with small volume fractions occur. In this contribution, we establish a rigorous scaling relation between the condition number of (I)FCM system matrices and the smallest cell volume fraction. Ill-conditioning stems either from basis functions being small on cells with small volume fractions, or from basis functions being nearly linearly dependent on such cells. Based on these two sources of ill-conditioning, an algebraic preconditioning technique is developed, which is referred to as Symmetric Incomplete Permuted Inverse Cholesky (SIPIC). A detailed numerical investigation of the effectivity of the SIPIC preconditioner in improving (I)FCM condition numbers and in improving the convergence speed and accuracy of iterative solvers is presented for the Poisson problem and for two- and three-dimensional problems in linear elasticity, in which Nitche's method is applied in either the normal or tangential direction. The accuracy of the preconditioned iterative solver enables mesh convergence studies of the finite cell method

Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics

In this article, we study the effect of small-cut elements on the critical time-step size in an immersogeometric context. We analyze different formulations for second-order (membrane) and fourth-order (shell-type) equations, and derive scaling relations between the critical time-step size and the cut-element size for various types of cuts. In particular, we focus on different approaches for the weak imposition of Dirichlet conditions: by penalty enforcement and with Nitsche's method. The stability requirement for Nitsche's method necessitates either a cut-size dependent penalty parameter, or an additional ghost-penalty stabilization term is necessary. Our findings show that both techniques suffer from cut-size dependent critical time-step sizes, but the addition of a ghost-penalty term to the mass matrix serves to mitigate this issue. We confirm that this form of `mass-scaling' does not adversely affect error and convergence characteristics for a transient membrane example, and has the potential to increase the critical time-step size by orders of magnitude. Finally, for a prototypical simulation of a Kirchhoff-Love shell, our stabilized Nitsche formulation reduces the solution error by well over an order of magnitude compared to a penalty formulation at equal time-step size

Sexual Cannibalism: High Incidence in a Natural Population with Benefits to Females

10 pages, 3 figures.[Background] Sexual cannibalism may be a form of extreme sexual conflict in which females benefit more from feeding on males than mating with them, and males avoid aggressive, cannibalistic females in order to increase net fitness. A thorough understanding of the adaptive significance of sexual cannibalism is hindered by our ignorance of its prevalence in nature. Furthermore, there are serious doubts about the food value of males, probably because most studies that attempt to document benefits of sexual cannibalism to the female have been conducted in the laboratory with non-natural alternative prey. Thus, to understand more fully the ecology and evolution of sexual cannibalism, field experiments are needed to document the prevalence of sexual cannibalism and its benefits to females.[Methodology/Principal Findings] We conducted field experiments with the Mediterranean tarantula (Lycosa tarantula), a burrowing wolf spider, to address these issues. At natural rates of encounter with males, approximately a third of L. tarantula females cannibalized the male. The rate of sexual cannibalism increased with male availability, and females were more likely to kill and consume an approaching male if they had previously mated with another male. We show that females benefit from feeding on a male by breeding earlier, producing 30% more offspring per egg sac, and producing progeny of higher body condition. Offspring of sexually cannibalistic females dispersed earlier and were larger later in the season than spiderlings of non-cannibalistic females.[Conclusions/Significance] In nature a substantial fraction of female L. tarantula kill and consume approaching males instead of mating with them. This behaviour is more likely to occur if the female has mated previously. Cannibalistic females have higher rates of reproduction, and produce higher-quality offspring, than non-cannibalistic females. Our findings further suggest that female L. tarantula are nutrient-limited in nature and that males are high-quality prey. The results of these field experiments support the hypothesis that sexual cannibalism is adaptive to females.This paper has been written under a Ramón y Cajal research contract from the Spanish Ministry of Science and Technology (MCYT) to JML and an I3P-BPD2004-CSIC scholarship to RRB. This work has been funded by MEC grants CGL2004-03153 and CGL2007-60520 to JML, MARG, RRB, CFM and DHW.Peer reviewe

Diversity, Loss, and Gain of Malaria Parasites in a Globally Invasive Bird

Invasive species can displace natives, and thus identifying the traits that make aliens successful is crucial for predicting and preventing biodiversity loss. Pathogens may play an important role in the invasive process, facilitating colonization of their hosts in new continents and islands. According to the Novel Weapon Hypothesis, colonizers may out-compete local native species by bringing with them novel pathogens to which native species are not adapted. In contrast, the Enemy Release Hypothesis suggests that flourishing colonizers are successful because they have left their pathogens behind. To assess the role of avian malaria and related haemosporidian parasites in the global spread of a common invasive bird, we examined the prevalence and genetic diversity of haemosporidian parasites (order Haemosporida, genera Plasmodium and Haemoproteus) infecting house sparrows (Passer domesticus). We sampled house sparrows (N = 1820) from 58 locations on 6 continents. All the samples were tested using PCR-based methods; blood films from the PCR-positive birds were examined microscopically to identify parasite species. The results show that haemosporidian parasites in the house sparrows' native range are replaced by species from local host-generalist parasite fauna in the alien environments of North and South America. Furthermore, sparrows in colonized regions displayed a lower diversity and prevalence of parasite infections. Because the house sparrow lost its native parasites when colonizing the American continents, the release from these natural enemies may have facilitated its invasion in the last two centuries. Our findings therefore reject the Novel Weapon Hypothesis and are concordant with the Enemy Release Hypothesis

Different Host Exploitation Strategies in Two Zebra Mussel-Trematode Systems: Adjustments of Host Life History Traits

The zebra mussel is the intermediate host for two digenean trematodes, Phyllodistomum folium and Bucephalus polymorphus, infecting gills and the gonad respectively. Many gray areas exist relating to the host physiological disturbances associated with these infections, and the strategies used by these parasites to exploit their host without killing it. The aim of this study was to examine the host exploitation strategies of these trematodes and the associated host physiological disturbances. We hypothesized that these two parasite species, by infecting two different organs (gills or gonads), do not induce the same physiological changes. Four cellular responses (lysosomal and peroxisomal defence systems, lipidic peroxidation and lipidic reserves) in the host digestive gland were studied by histochemistry and stereology, as well as the energetic reserves available in gonads. Moreover, two indices were calculated related to the reproductive status and the physiological condition of the organisms. Both parasites induced adjustments of zebra mussel life history traits. The host-exploitation strategy adopted by P. folium would occur during a short-term period due to gill deformation, and could be defined as “virulent.” Moreover, this parasite had significant host gender-dependent effects: infected males displayed a slowed-down metabolism and energetic reserves more allocated to growth, whereas females displayed better defences and would allocate more energy to reproduction and maintenance. In contrast, B. polymorphus would be a more “prudent” parasite, exploiting its host during a long-term period through the consumption of reserves allocated to reproduction

Preconditioned iterative solution techniques for immersed finite element methods:with applications in immersed isogeometric analysis for solid and fluid mechanics

Efficient solution methods for numerical simulations of complex geometrie

A note on the stability parameter in Nitsche's method for unfitted boundary value problems

Nitsche's method is a popular approach to implement Dirichlet-type boundary conditions in situations where a strong imposition is either inconvenient or simply not feasible. The method is widely applied in the context of unfitted finite element methods. Of the classical (symmetric) Nitsche's method it is well-known that the stabilization parameter in the method has to be chosen sufficiently large to obtain unique solvability of discrete systems. In this short note we discuss an often used strategy to set the stabilization parameter and describe a possible problem that can arise from this. We show that in specific situations error bounds can deteriorate and give examples of computations where Nitsche's method yields large and even diverging discretization errors. \u3cbr/\u3

Preconditioning immersed isogeometric finite element methods with application to flow problems

Immersed finite element methods generally suffer from conditioning problems when cut elements intersect the physical domain only on a small fraction of their volume. We present a dedicated Additive-Schwarz preconditioner that targets the underlying mechanism causing the ill-conditioning of these methods. This preconditioner is applicable to problems that are not symmetric positive definite and to mixed problems. We provide a motivation for the construction of the Additive-Schwarz preconditioner, and present a detailed numerical investigation into the effectiveness of the preconditioner for a range of mesh sizes, isogeometric discretization orders, and partial differential equations, among which the Navier–Stokes equations