Low-rank approximate inverse for preconditioning tensor-structured linear systems

In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable distance to the inverse operator. It provides a sequence of approximations that are defined as the projections of the inverse operator in an increasing sequence of linear subspaces of operators. These subspaces are obtained by the tensorization of bases of operators that are constructed from successive rank-one corrections. In order to handle high-order tensors, approximate projections are computed in low-rank Hierarchical Tucker subsets of the successive subspaces of operators. Some desired properties such as symmetry or sparsity can be imposed on the approximate inverse operator during the correction step, where an optimal rank-one correction is searched as the tensor product of operators with the desired properties. Numerical examples illustrate the ability of this algorithm to provide efficient preconditioners for linear systems in tensor format that improve the convergence of iterative solvers and also the quality of the resulting low-rank approximations of the solution

Stability of incompressible formulations enriched with X-FEM

The treatment of (near-)incompressibility is a major concern for applications involving rubber-like materials, or when important plastic ows occurs as in forming processes. The use of mixed nite element methods is known to prevent the locking of the nite element approximation in the incompressible limit. However, it also introduces a critical condition for the stability of the formulation, called the infsup or LBB condition. Recently, the nite element method has evolved with the introduction of the partition of unity. The eXtended Finite Element Method (XFEM) uses the partition of unity to remove the need to mesh physical surfaces or to remesh them as they evolve. The enrichment of the displacement eld makes it possible to treat surfaces of discontinuity inside nite elements. In this paper, some strategies are proposed for the enrichment of mixed nite element approximations in the incompressible setting. The case of holes, material interfaces and cracks are considered. Numerical examples show that for well chosen enrichment strategies, the nite element convergence rate is preserved and the inf-sup condition is passed

Estimation of crack opening from a two-dimensional continuum-based finite element computation

Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one dimensional approach for estimating a crack opening from a continuum based fi nite element calculation to two dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post treatment procedure. The orig inal one dimensional problem devised in Dufour et al . [4] is recovered as pro fi les of deformation orthog onal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing fi nite element deformation pro fi les and theoretical pro fi les corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the pro fi les are assumed to be equal; in the weak approach, the integrals of each pro fi le are set equal. Two dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, de fi ned as the distance between the numerical and theoretical pro fi les, are less than a few percentages. In the case of a three point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack ( > 40 m m

Étude de la stabilité d'une formulation incompressible traitée par X-FEM

The treatment of (near-)incompressibility is a major concern for the simulation of rubber-like parts, or forming processes. The use of mixed finite element methods is known to prevent the locking of the F.E. approximation in the incompressible limit. However, the stability of these formulations is conditionned by the fullfilment of the inf-sup condition. Recently, finite elements method has evolved with the introduction of the partition of unity. The X-FEM uses it to remove the need to mesh (and remesh) physical surfaces. In this paper, a strategy is proposed for the treatment of holes within X-FEM in the incompressible setting. Numerical examples show that F.E. convergence rate is preserved and that the inf-sup condition is passed

Embodied pain—negotiating the boundaries of possible action

Pain is a protective strategy, which emerges from on-going interaction between body and world. However, pain is often thought of as a unitary output—an end product experienced as an intrusion upon an often unsuspecting perceiver.55 We know a lot about how nociception relates to pain, informed by both biological and psychological influences,30,68,96 how pain intrudes into awareness,5,26,29,34 and how it relates to clinical variables, such as suffering and disability.35 However, despite significant advances, the mechanisms of pain intrusion remain elusive.62 In this article, we stress a functional view of pain as more than experience, as defensive action operating in the context of uncertain threat.Although traditional characterisations of perception as a product of sensory information have been critiqued,19,41,52 including in pain,87,94 there is now a well-advanced contemporary view that all perception is embodied and embedded.41,46,65,77,84,86 Here, embodied is defined by action, the premise that cognition extends beyond the brain so that an ever-changing body is at the core of how our experiences are shaped; this may be the unconscious workings of our immune system or the collaborative efforts made to avoid movement. Embedded refers to the situated interaction between the embodied being and the external environment, in both place (current context) and time (evolutionary context).From this view, all experience is inferential,78 dynamic,22,54 and related to action in the world.2,21,24 Thus, to describe the experience of pain, we must understand it within its evolved, learned, and ultimately threat-defined context.33,99 Theories of embodied experience are well advanced elsewhere, most notably in cybernetics,4,23,79 evolutionary biology,39,73,80 and consciousness.81,82 Its provenance can be traced to structural psychology,91 phenomenology,47,52,61 and perception.41,75 However, embodied domains have avoided pain, considering it either too simple32 or paradoxically too difficult.6Our embodied view, in many ways, complements the existing literature,18,27,36,42,93,95 supporting the growing understanding of pain as an experience inferred from uncertain information.3,17,83,98 However, it critically looks to extend this work beyond a passive information processing model that has come to dominate.48 Here, we emphasise the body, not separate from the brain nor the world, but part of the facility that actively shapes our experience of pain. This perspective defines pain in terms of action: an experience that, as part of a protective strategy, attempts to defend one's self in the presence of inferred threat

How the pain of others enhances our pain: Searching the cerebral correlates of ‘compassional hyperalgesia’

International audienceObserving other people's pain increases our own reports to painful stimuli, a phenomenon that can be defined as 'compassional hyperalgesia' (CH). This functional magnetic resonance imaging study examined the neural correlates of CH, and whether CH could emerge when exposure to the driving stimulus was subliminal. Subjects received electric somatosensory stimuli while observing images of people undergoing painful or enjoyable somatic sensations, presented during a period allowing or not allowing conscious perception. The intensity attributed to painful stimuli increased significantly when these were delivered close to images showing human pain, but only when such images were consciously perceived. The basic core of the Pain Matrix (SI, SII, insula, mid-anterior cingulate) was activated by painful stimuli, but its activation magnitude did not increase during CH. Compassional hyperalgesia was associated with increased activity in polymodal areas involved in emotional tuning (anterior prefrontal, pregenual cingulated) and areas involved in multisensory integration and short-term memory (dorsolateral prefrontal, temporo-parieto-occipital junction). CH appears as a high-order phenomenon needing conscious appraisal of the eliciting visual stimulus, and supported by polymodal areas distinct from the basic Pain Matrix. This suggests that compassion to pain does not result from a mere 'sensory resonance' in pain networks, but rather from an interaction between the output of a first-line processing in the Pain Matrix, and the activity of a high-order network involving multisensory integration (temporo-parietal), encoding of internal states (mid-prefrontal) and short-time memory encoding (dorsolateral prefrontal). The Pain Matrix cannot be considered as an 'objective' correlate of the pain experience in all situations

The effect of dehydroepiandrosterone on regional blood flow in prepubertal anaesthetized pigs

Dehydroepiandrosterone has been implicated in vascular disease and its associated insulin resistance and hypertension, though little is known about its vascular effects. We have recently shown in prepubertal anaesthetized pigs that intravenous infusion of dehydroepiandrosterone caused coronary vasoconstriction through the inhibition of a vasodilatory β-adrenergic receptor-mediated effect related to the release of nitric oxide. The present study was designed to investigate the effect of dehydroepiandrosterone on mesenteric, renal and iliac vascular beds. In prepubertal pigs of both sexes anaesthetized with sodium pentobarbitone, changes in superior mesenteric, left renal and left external iliac blood flow caused by intravenous infusion of dehydroepiandrosterone were assessed using electromagnetic flowmeters. Changes in heart rate and arterial blood pressure were prevented by atrial pacing and by connecting the arterial system to a pressurized reservoir containing Ringer solution. In 22 pigs, infusion of 1 mg h(−1) of dehydroepiandrosterone decreased mesenteric, renal and iliac blood flow. In a further 10 pigs, dose–response curves were obtained by graded increases in the infused dose of hormone between 0.03 and 4 mg h(−1). The mechanisms of the above response were studied in the 22 pigs by repeating the experiment after haemodynamic variables had returned to the control values observed before infusion. Blockade of α-adrenoceptors with intravenous phentolamine (five pigs) did not affect the dehydroepiandrosterone-induced mesenteric, renal and iliac vasoconstriction. This response was abolished by blockade of β(2)-adrenoceptors with intravenous butoxamine (five pigs) and by blockade of mesenteric, renal and iliac nitric oxide synthase with intra-arterial administration of N(ω)-nitro-l-arginine methyl ester (seven pigs), even after reversing the increase in local vascular resistance caused by the two blocking agents with intravenous infusion of papaverine. In five pigs, the increase in measured blood flow caused by intravenous infusion of isoproterenol (isoprenaline) was significantly reduced by infusion of dehydroepiandrosterone. The present study showed that intravenous infusion of dehydroepiandrosterone primarily caused mesenteric, renal and iliac vasoconstriction. The mechanisms of this response were shown to be due to the inhibition of a vasodilatory β(2)-adrenergic receptor-mediated effect, which possibly involved the release of nitric oxide