Applied and Numerical Partial Differential Equations: by William E. Fitzgibbon, Jacques F. Périaux (auth.), W.

By William E. Fitzgibbon, Jacques F. Périaux (auth.), W. Fitzgibbon, Y.A. Kuznetsov, Pekka Neittaanmäki, Jacques Périaux, Olivier Pironneau (eds.)

The current quantity is made from contributions solicited from invitees to meetings held on the college of Houston, Jyväskylä collage, and Xi’an Jiaotong collage honoring the seventieth birthday of Professor Roland Glowinski. even if scientists convened on 3 assorted continents, the Editors wish to view the conferences as unmarried occasion. the 3 locales represent the very fact Roland has acquaintances, collaborators and admirers around the globe.

The contents span quite a lot of issues in modern utilized arithmetic starting from inhabitants dynamics, to electromagnetics, to fluid mechanics, to the maths of finance. besides the fact that, they don't absolutely replicate the breath and variety of Roland’s medical curiosity. His paintings has regularly been on the intersection arithmetic and clinical computing and their program to mechanics, physics, engineering sciences and extra lately biology. He has made seminal contributions within the parts of equipment for technological know-how computation, fluid mechanics, numerical controls for disbursed parameter structures, and reliable and structural mechanics in addition to form optimization, stellar movement, electron delivery, and semiconductor modeling. primary topics come up from the corpus of Roland’s paintings. the 1st is that numerical equipment may still reap the benefits of the mathematical homes of the version. they need to be moveable and computable with computing assets of the foreseeable destiny in addition to with modern assets. the second one topic is that each time attainable one should still validate numerical with experimental data.

The quantity is written at a complicated medical point and no attempt has been made to make it self contained. it truly is meant to be of to either the researcher and the practitioner besides complex scholars in computational and utilized arithmetic, computational technological know-how and engineers and engineering.

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V ˜ 1nC ,nL , w ˜ 1nC ,nL ) : (˜ ˜ ki,j ) ∈ Vi,j VF = (˜ v01,1 , w vki,j , w & (11), (12) hold , k k where Vi,j are the function spaces (9) corresponding to the struts Ri,j . 48 J. Tambaˇca et al. Now the weak formulation for the stent frame structure consisting of curved rods is given by the following: ˜ 01,1 , . . , u ˜ 1nC ,nL , ω ˜ 1nC ,nL ) ∈ VF is a weak soluDefinition 2. Function (˜ u01,1 , ω tion to the stent frame problem if nC nL i=1 j=1 k=0,1 ls ls ˜ ki,j ) · (w ˜ ki,j ) ds = Qki,j H(Qki,j )T (ω 0 k ˜f k · v i,j ˜ i,j ds (15) 0 ˜ 01,1 , .

Springer, New York, 1984. 14. J. -P. Zol´esio. Introduction to shape optimization. Shape sensitivity analysis. Springer, Berlin, 1992. O. net Summary. We present a novel mathematical model to study the mechanical properties of endovascular stents in their expanded state. The model is based on the theory of slender curved rods. Stent struts are modeled as linearly elastic curved rods that satisfy the kinematic and dynamic contact conditions at the vertices where the struts meet. A weak formulation for the stent problem is defined and a Finite Element Method for a numerical computation of its solution is used to study mechanical properties of two commonly used coronary stents (Palmaz-like and Xience-like stent) in their expanded, fractured state.

Le Tallec. Numerical methods in sensitivity analysis and shape optimization. Birkh¨ auser, 2003. 12. B. Mohammadi and O. Pironneau. Applied shape optimization for fluids. Oxford University Press, 2001. 13. O. Pironneau. Optimal shape design for elliptic systems. Springer Series in Computational Physics. Springer, New York, 1984. 14. J. -P. Zol´esio. Introduction to shape optimization. Shape sensitivity analysis. Springer, Berlin, 1992. O. net Summary. We present a novel mathematical model to study the mechanical properties of endovascular stents in their expanded state.

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