Quasi-optimal mesh sequence construction through smoothed adaptive finite element methods

We propose a new algorithm for adaptive finite element methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PDEs). The algorithm is inspired by the ascending phase of the V-cycle multigrid method: we replace accurate algebraic solutions in intermediate cycles of the classical AFEM with the application of a prolongation step, followed by the application of a smoother. Even though these intermediate solutions are far from the exact algebraic solutions, their a posteriori error estimation produces a refinement pattern that is substantially equivalent to the one that would be generated by classical AFEM, at a considerable fraction of the computational cost. We provide a qualitative analysis of how the error propagates throughout the algorithm, and we present a series of numerical experiments that highlight the efficiency and the computational speedup of S-AFEM

A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library

We present the implementation of a solution scheme for fluid-structure interaction problems via the finite element software library deal.II. The solution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method

Space use of wild boar (Sus Scrofa) in Budapest: are they resident or transient city dwellers?

In our study, we examined the movement of two wild boars marked with GPS/GSM transmitters in city of Budapest. We hypothesised that: the wild boars do not leave the urban area (H1); the wild boars prefer places that are less disturbed by people, and which are rich in potential hiding places (H2); and their home ranges would be smaller than that of wild boars living in non-urban environment (H3). Based on our results, we accepted our first hypothesis, as the wild boars had not left the area of Budapest. However, we partly rejected our second hypothesis: the wild boars preferred urban areas that were forested and richly covered with vegetation; however, human presence therefore disturbance was also high in those areas. The home range sizes of both marked wild boar sows were remarkably smaller than those of the wild boars living in natural environment (H3). City habitat modification, e.g. clearing undergrowth vegetation, could result that wild boars cannot find any hiding places. The significant part of food sources will disappear with the elimination of these places. By eliminating the two main factors together could prevent wild boars finding their living conditions within the city

Quantitative cytometry of MHC class I digestion from living cells

Digestion of crude membrane preparations with papain releases the extracellular portion of major histocompatibility complex (MHC) class I molecules. MHC class I molecules are integral membrane glycoprotein complexes formed by the noncovalent association of 2 invariant molecules, the heavy chain and the beta2-microglobulin (beta2-m), to a wide array of peptides. The cleaved soluble moiety retains the antigenic properties of the intact membrane-bound complex. Here we show that MHC class I digestion may be carried out on living cells, and we quantitate the surface expression of MHC complexes by a combined cytometric/high performance liquid chromatographic (HPLC) approach. Papain digestion results in time- and dose-dependent disappearance of membrane MHC-associated-fluorescence as detected by FACS analysis with MHC-specific monoclonal antibodies (mAbs). beta2-m and peptides became detectable by HPLC analysis and western blotting in the digestion buffer and were quantitated by comparison with purified standards. The cytometric assessment of the digestion allows one to simultaneously monitor efficacy and toxicity of the treatment. The procedure we describe allows to selectively retrieve by affinity chromatography MHC from the cell membrane, avoiding any contamination due to intracellular, "immature" MHC molecules

Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems

We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigenvalue problem posed in a polygonal domain. The algorithm is motivated by the analysis of inexact (perturbed) inverse iteration algorithms in numerical linear algebra. We couple the perturbed inverse iteration approach with mesh refinement strategy based on residual estimators. We demonstrate our approach on model problems in two and three dimensions

An Immersed Finite Element Method Approach for Brain Biomechanics

Mechanics of Biological Systems and Materials, Volume 5: Proceedings of the 2012 Annual Conference on Experimental and Applied Mechanics, the fifth volume of seven from the Conference, brings together 31 contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Experimental and Applied Mechanics, including papers on: Biological Materials & Mechanics Cell Mechanics Mechanics of Biomimetic Materials Mechanics of Brain Tissues and Structures Mechanics of Bone and Related Materials Multi-Scale Mechanics of Natural Fibers Indentation Methods in Soft Materials Imaging Methods in Biological Systems and Materials Mechanics of Tissue Damage Mechanics of Soft Materials and Tissue

On the hyper-elastic formulation of the immersed boundary method

The immersed boundary (IB) method is both a mathematical formulation and a numerical method for fluid-structure interaction problems, in which immersed incompressible visco-elastic bodies or boundaries interact with an incompressible fluid. Previous formulations of the IB method were not able to treat appropriately immersed materials of finite, nonzero thickness modeled by general hyper-elastic constitutive laws because of the lack of appropriate transmission conditions between the immersed body and the surrounding fluid in the case of a nonzero jump in normal stress at the solid-fluid interface. (Such a jump does not arise when the solid is comprised of fibers that run parallel to the interface, but typically does arise in other cases, e.g., when the solid contains elastic fibers that terminate at the solid-fluid interface.) We present a derivation of the IB method that takes into account in an appropriate way the missing term. The derivation presented in this paper starts from a separation of the stress that appears in the principle of virtual work. The stress is divided into its fluid-like and solid-like components, and each of these two terms is treated in its natural framework, i.e., the Eulerian framework for the fluid-like stress and the Lagrangian framework for the solid-like stress. We describe how the IB method can be used in conjunction with standard formulations of continuum mechanics models for immersed incompressible elastic materials and present some illustrative numerical experiments

Data-driven solutions of ill-posed inverse problems arising from doping reconstruction in semiconductors

ABSTRACTThe non-destructive estimation of doping concentrations in semiconductor devices is of paramount importance for many applications ranging from crystal growth to defect and inhomogeneity detection. A number of technologies (such as LBIC, EBIC and LPS) have been developed which allow the detection of doping variations via photovoltaic effects. The idea is to illuminate the sample at several positions and detect the resulting voltage drop or current at the contacts. We model a general class of such photovoltaic technologies by ill-posed global and local inverse problems based on a drift-diffusion system which describes charge transport in a self-consistent electrical field. The doping profile is included as a parametric field. To numerically solve a physically relevant local inverse problem, we present three approaches, based on least squares, multilayer perceptrons, and residual neural networks. Our data-driven methods reconstruct the doping profile for a given spatially varying voltage signal induced by a laser scan along the sample's surface. The methods are trained on synthetic data sets which are generated by finite volume solutions of the forward problem. While the linear least square method yields an average absolute error around 10%, the nonlinear networks roughly halve this error to 5%