A domain decomposition method based on the finite-element tearing and interconnecting (FETI) algorithm is presented for the solution of the large sparse matrices associated with the finite-element method (FEM) solution of the vector wave equation. The FETI algorithm is based on the method of Lagrange multipliers and leads to a reduced-order system, which is solved using the biconjugate gradient method (BiCGM). It is shown that this method is highly scalable and is more efficient on parallel platforms when solving large matrices than traditional iterative methods such as a preconditioned conjugate gradient algorithm. This is especially true when a perfectly matched layer (PML) absorbing medium is used to terminate the problem domain.

ArgumentOur aim in this paper is to show the importance of the notion oféconomie animale in Montpellier vitalism as a hybrid concept which brings together the structural and functional dimensions of the living body -dimensions which hitherto had primarily been studied according to a mechanistic model, or were discussed within the framework of Stahlian animism. The celebrated image of the bee-swarm expresses this structural-functional understanding of living bodies quite well: "One sees them press against each other, mutually supporting each other, forming a kind of whole, in which each living part, in its own way, by means of the correspondence and directions of its motions, enables this kind of life to be sustained in the body" (Ménuret 1765c, Enc. XI, 319a). What is important here is that every component part is always a living part, i.e., every structural unit is always functional. Interestingly, while the twin notions of "animal economy" and organisation are presented as improvements over a mechanistic perspective, they are nonetheless compatible with an expanded sense of mechanism, and by extension, with materialism as reflected notably in the writings of Ménuret and Bordeu. We thus propose both a revision and reconstruction of the historical status of the "animal economy," and a reflection on its conceptual status.

The organism is neither a discovery like the circulation of the blood or the glycogenic function of the liver, nor a particular biological theory like epigenesis or preformationism. It is rather a concept which plays a series of roles -sometimes overt, sometimes masked -throughout the history of biology, and frequently in very normative ways, also shifting between the biological and the social. Indeed, it has often been presented as a key-concept in life science and the 'theorization' of Life, but conversely has also been the target of influential rejections: as just an instrument of transmission for the selfish gene, but also, historiographically, as part of an outdated 'vitalism'. Indeed, the organism, perhaps because it is experientially closer to the 'body' than to the 'molecule', is often the object of quasi-affective theoretical investments presenting it as essential, sometimes even as the pivot of a science or a particular approach to nature, while other approaches reject or attack it with equal force, assimilating it to a mysterious 'vitalist' ontology of extra-causal forces, or other pseudo-scientific doctrines. This paper does not seek to adjudicate between these debates, either in terms of scientific validity or historical coherence; nor does it return to the well-studied issue of the organism-mechanism tension in biology. Recent scholarship has begun to focus on the emergence and transformation of the concept of organism, but has not emphasized so much the way in which organism is a shifting, 'go-between' concept -invoked as 'natural' by some thinkers to justify their metaphysics, but then presented as value-laden by others, over and against the natural world. The organism as go-between concept is also a hybrid, a boundary concept or an epistemic limit case, all of which partly overlap with the idea of 'nomadic concepts'. Thereby the concept of organism continues to function in different contexts -as a heuristic, an explanatory challenge, 2 a model of order, of regulation, etc. -despite having frequently been pronounced irrelevant and reduced to molecules or genes. Yet this perpetuation is far removed from any 'metaphysics of organism', or organismic biology.

Wolfe Charles, « La catégorie d' « organisme » dans la philosophie de la biologie. » Retour sur les dangers du réductionnisme,

Georges Canguilhem is known to have regretted, with some pathos, that Life no longer serves as an orienting question in our scientific activity. He also frequently insisted on a kind of uniqueness of organisms and/or living bodiestheir inherent normativity, their value-production and overall their inherent difference from mere machines. In addition, Canguilhem acknowledged a major debt to the German neurologist-theoretician Kurt Goldstein, author most famously of The Structure of the Organism in 1934; along with Merleau-Ponty, Canguilhem was the main figure who introduced the work of Goldstein and his 'phenomenology of embodiment' into France. In this paper I inquire if we should view Canguilhem and Goldstein as 'biochauvinists', that is, as thinkers who consider that there is something inherently unique about biological entities as such, and if so, of what sort.

The species of vitalism discussed here is a malleable construct, often with a poisonous reputation (but which I want to rehabilitate), hovering in the realms of the philosophy of biology, the history of medicine, and the scientific background of the Radical Enlightenment (case in point, the influence of vitalist medicine on Diderot). This is a more vital vitalism, or at least a more 'biologistic', 'embodied', medicalized vitalism. I distinguish between what I would call 'substantival' and 'functional' forms of vitalism, as applied to the eighteenth century. Substantival vitalism presupposes the existence of something like a (substantive) vital force which either plays a causal role in the natural world as studied by scientific means, or remains a kind of hovering, extra-causal entity. Functional vitalism tends to operate 'post facto', from the existence of living bodies to the desire to find explanatory models that will do justice to their uniquely 'vital' properties in a way that fully mechanistic models (one thinks e.g. of Cartesian mechanism) cannot. I discuss some representative figures of the Montpellier school as being functional rather than substantival vitalists, particularly as regards the models of organic organization which they develop, and make some suggestions as to how these relate to the then-nascent science of biology.

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Despite the renewed attention paid in recent years to the doctrine or doctrines associated with the Faculty of Medicine of the Université de Montpellier in the second half of the eighteenth century, and known as “vitalism” – chiefly Roselyne Rey's 1987 thèse d'État, which only appeared in print in 2000, and works by François Duchesneau, Elizabeth Williams, Timo Kaitaro, and Dominique Boury, some of whom have contributed to this volume – the existence of a specifically medical vitalism in the eighteenth century still continues to pose a problem. Commentators speaking in rather monolithic terms continue to describe vitalism in terms entirely derived from late nineteenth- or early twentieth-century “neo-vitalism,” that is, in the language of vital force, of supplemental, extra-causal agents powering the living body. Philosophers of biology and, more surprisingly, historians of ideas tend to sound like the very confident Francis Crick, speaking like a prophet from a mountaintop to the entire scientific community: “To those of you who may be vitalists, I would make this prophecy: what everyone believed yesterday, and you believe today, only cranks will believe tomorrow” (Crick 1966, 99). In less prophetic, but still very polarizing tones, a recent review discussion on biological development promotes “organicism” as a scientifically viable view – one which the authors of the review quickly distinguish from the more metaphysically laden “vitalism,” according to which (they write), “living matter is ontologically greater than the sum of its parts because of some life force (‘entelechy,’ ‘élan vital,’ ‘vis essentialis,’ etc.)” (Gilbert and Sarkar 2000, 1).