FE/BE coupling for an acoustic fluid-structure interaction problem. Residual a posteriori error estimates

This is the author's accepted manuscript. The final published article is available from the link below. Copyright © 2011 John Wiley & Sons, Ltd.In this paper, we developed an a posteriori error analysis of a coupling of finite elements and boundary elements for a fluid–structure interaction problem in two and three dimensions. This problem is governed by the acoustic and the elastodynamic equations in time-harmonic vibration. Our methods combined integral equations for the exterior fluid and FEMs for the elastic structure. It is well-known that because of the reduction of the boundary value problem to boundary integral equations, the solution is not unique in general. However, because of superposition of various potentials, we consider a boundary integral equation that is uniquely solvable and avoids the irregular frequencies of the negative Laplacian operator of the interior domain. In this paper, two stable procedures were considered; one is based on the nonsymmetric formulation and the other is based on a symmetric formulation. For both formulations, we derived reliable residual a posteriori error estimates. From the estimators we computed local error indicators that allowed us to develop an adaptive mesh refinement strategy. For the two-dimensional case we performed an adaptive algorithm on triangles, and for the three-dimensional case we used hanging nodes on hexahedrons. Numerical experiments underline our theoretical results.DFG German Research Foundatio

Adaptive FE-BE Coupling for Strongly Nonlinear Transmission Problems with Coulomb Friction

We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation on the exterior domain. The problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which is then solved using the Uzawa algorithm and adaptive mesh refinements based on a gradient recovery scheme. The Galerkin approximations are shown to converge to the unique solution of the variational problem in a suitable product of L^p- and L^2-Sobolev spaces.Comment: 27 pages, 3 figure

Adaptive time domain boundary element methods and engineering applications

Time domain Galerkin boundary elements provide an efficient tool for the numerical solution of boundary value problems for the homogeneous wave equation. We review recent advances in their a posteriori error analysis and the resulting adaptive mesh refinement procedures, as well as basic algorithmic aspects of these methods. Numerical results for adaptive mesh refinements are discussed in 2 and 3 dimensions, as are benchmark problems in a half space related to the transient emission of traffic noise.Parts of this work were funded by BMWi under the project SPERoN 2020, part II, Leiser StraB enverkehr, grant number 19 U 10016 F. H. G. acknowledges support by ERC Advanced Grant HARG 268105

Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM

© EDP Sciences, SMAI 2011This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in Rn (n ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ωc := Rn\￣Ω. The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping (NtD) given in terms of boundary integral operators. The resulting variational formulation becomes a variational inequality with a linear operator. Then we treat the corresponding numerical scheme and discuss an approximation of the NtD mapping with an appropriate discretization of the inverse Poincar´e-Steklov operator. In particular, assuming some abstract approximation properties and a discrete inf-sup condition, we show unique solvability of the discrete scheme and obtain the corresponding a-priori error estimate. Next, we prove that these assumptions are satisfied with Raviart- Thomas elements and piecewise constants in Ω, and continuous piecewise linear functions on Γ. We suggest a solver based on a modified Uzawa algorithm and show convergence. Finally we present some numerical results illustrating our theory

Lane Localization for Autonomous Model Cars

Mobile robotics is a rapidly growing field and has countless applications including exploration, logistics, rescue operations, as well as domestic and military use. One particularly interesting example of ist use is the construction of autonomous, "self-driving" cars. Imagine that car accidents caused by human error are a thing of the past, or that your car can find ist own parking spot after you have left the vehicle. In many cases, mobile robots need to plan and make decisions autonomously while interacting with their environment. A necessary prerequisite for them to execute most non-trivial tasks is to have a concept of their environment and their location in it. Determining this location is a fundamental problem in mobile robotics known as localization. Autonomous cars need to know where they are on the road, both on a small scale to stay in lane and on a large scale to navigate

Charakterisierung Ionenkanal-bildender Substanzen aus dem Regurgitat von Lepidoptera-Larven

Die vorliegende Arbeit befasst sich mit den sehr frühen Ereignissen während des Befalls von Pflanzen durch Raupen. Als erste Reaktion der Pflanze wird eine Depolarisation der Plasmamembran gemessen. Als Auslöser hierfür gelten beispielsweise Fettsäure- Aminosäurekonjugate oder Wasserstoffperoxid im Regurgitat von Raupen. In dieser Arbeit wurde eine weitere mögliche Ursache für die Depolarisation beschrieben und untersucht. Im Regurgitat von Raupen finden sich Ionenkanal-bildende Substanzen. Diese wurden durch die BLM-Technik nachgewiesen. Mit Hilfe dieser Technik wurde gezeigt, dass die genannten Ionenkanal-bildenden Substanzen spontan in künstliche, planare Lipiddoppelschichten aus pflanzlichen Lipiden ohne Membranproteine inserieren und dadurch die Leitfähigkeit der Membran erheblich erhöhen. Derartige Ionenkanal-bildenden Verbindungen ließen sich im Regurgitat der Larven von acht verschiedenen Arten aus vier Familien nachweisen. Die phylogenetisch weite Verbreitung dieser Ionenkanal-bildenden Substanzen weist auf generelle Bedeutung für die Larven von Lepidopteren hin. Die Ionenkanäle, die durch das Regurgitat von S. exigua in planaren Lipiddoppelschichten erzeugt wurden, besitzen eine Kationenselektivität bei Kaliumchlorid von etwa 5:1. Es ist gelungen, die Ionenkanal-bildenden Substanzen aus dem Regurgitat von S. littoralis weitgehend aufzureinigen. Die Modellsubstanz Alamethicin war in der Lage, das Membranpotenzial in Blättern von Phaseolus lunatus lokal und von Hordeum vulgare auch systemisch zu depolarisieren. Durch diesen Nachweis wurde die experimentelle Lücke geschlossen und gezeigt, dass Ionenkanal-bildende Substanzen auch bei Pflanzen zur Depolarisation der Plasmamembran führen können. Diese Depolarisation wiederum, wie sie auch bei dem Fressen von Raupen an Pflanzen gemessen wird, kann sowohl Signalcharakter für die Pflanze besitzen als auch ein Versuch des Insekts sein, die Reaktionsfähigkeit der pflanzlichen Zelle zu beeinflussen