Multi-Level quasi-Newton methods for the partitioned simulation of fluid-structure interaction

In previous work of the authors, Fourier stability analyses have been performed of Gauss-Seidel iterations between the flow solver and the structural solver in a partitioned fluid-structure interaction simulation. These analyses of the flow in an elastic tube demonstrated that only a number of Fourier modes in the error on the interface displacement are unstable. Moreover, the modes with a low wave number are most unstable and these modes can be resolved on a coarser grid. Therefore, a new class of quasi-Newton methods with more than one grid level is introduced. Numerical experiments show a significant reduction in run time

MgB2 superconducting thin films with a transition temperature of 39 Kelvin

We report the growth of high-quality c-axis-oriented epitaxial MgB2 thin films by using a pulsed laser deposition technique. The thin films grown on (1`1 0 2) Al2O3 substrates show a Tc of 39 K. The critical current density in zero field is ~ 6 x 10^6 A/cm2 at 5 K and ~ 3 x 10^5 A/cm^2 at 35 K, suggesting that this compound has great potential for electronic device applications, such as microwave devices and superconducting quantum interference devices. For the films deposited on Al2O3, X-ray diffraction patterns indicate a highly c-axis-oriented crystal structure perpendicular to the substrate surface.Comment: 3 pages and 3 figure

Stability analysis of second-order time accurate schemes for ALE-FEM

In this work we will introduce and analyze the Arbitrary Lagrangian Eulerian formulation for a model problem of a scalar advection-diffusion equation defined on a moving domain. Moving from the results illustrated in our previous work [J. Num. Math. 7 (1999) 105], we will consider first and second-order time advancing schemes and analyze how the movement of the domain might affect accuracy and stability properties of the numerical schemes with respect to their counterpart on fixed domains. Theoretical and numerical results will be presented, showing that stability properties are not, in general, preserved, while accuracy is maintained. (C) 2004 Elsevier B.V. All rights reserved

New Challenges in Grid Generation and Adaptivity for Scientific Computing

This volume collects selected contributions from the “Fourth Tetrahedron Workshop on Grid Generation for Numerical Computations”, which was held in Verbania, Italy in July 2013. The previous editions of this Workshop were hosted by the Weierstrass Institute in Berlin (2005), by INRIA Rocquencourt in Paris (2007), and by Swansea University (2010). This book covers different, though related, aspects of the field: the generation of quality grids for complex three-dimensional geometries; parallel mesh generation algorithms; mesh adaptation, including both theoretical and implementation aspects; grid generation and adaptation on surfaces – all with an interesting mix of numerical analysis, computer science and strongly application-oriented problems

An unfitted formulation for the interaction of an incompressible fluid with a thick structure via an XFEM/DG approach

A numerical procedure that combines an extended finite element formulation and a discontinuous Galerkin technique is presented, with the final aim of providing an effective tool for the simulation of three-dimensional (3D) fluid-structure interaction problems. In this work we consider a thick structure immersed in a fluid. We describe the numerical models and discuss the specific implementation issues arising in three dimensions. Finally, 3D numerical results are provided to show the effectiveness of the approach

reduced models for blood flow in curved vessels

Flow in curved pipes has been intensively investigated and applications to arterial o w are relevant both in physiological and pathological conditions. A comprehensive survey of the work devel- oped over almost one century from experimental and modelling point of view is carried out. Despite its complex nature, the 3D curved o w can be modeled, under reasonable assumptions, accounting only for 2, or even 1, geometrical dimensions. A couple of dieren t reduced models are presented and discussed here. Results of numerical simulations demonstrate the role of curvature in the formation of the secondary o w patterns and in the asymmetry of wall shear stresses. Both the above features can have important haemodynamical eects and clinical diagnostic velocimeters should be equipped with correction algorithms for the measurement bias induced by vessel curvature

Mesh update techniques for free-surface flow solvers using spectral element method

This paper presents a novel mesh-update technique for unsteady free-surface Newtonian flows using spectral element method and relying on the arbitrary Lagrangian--Eulerian kinematic description for moving the grid. Selected results showing compatibility of this mesh-update technique with spectral element method are given

Optimally Adapted Meshes for Finite Elements of Arbitrary Order and W1p Norms

Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its interpolation on the associated finite element space, over all triangulations of at most N elements. The error is studied in the W1p norm and we consider Lagrange finite elements of arbitrary polynomial order m-1. We establish sharp asymptotic error estimates as N tends to infinity when the optimal anisotropic triangulation is used. A similar problem has been studied earlier, but with the error measured in the Lp norm. The extension of this analysis to the W1p norm is crucial in order to match more closely the needs of numerical PDE analysis, and it is not straightforward. In particular, the meshes which satisfy the optimal error estimate are characterized by a metric describing the local aspect ratio of each triangle and by a geometric constraint on their maximal angle, a second feature that does not appear for the Lp error norm. Our analysis also provides with practical strategies for designing meshes such that the interpolation error satisfies the optimal estimate up to a fixed multiplicative constant. We discuss the extension of our results to finite elements on simplicial partitions of a domain of arbitrary dimension, and we provide with some numerical illustration in two dimensions.Comment: 37 pages, 6 figure