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Surface acoustic wave filters are widely used for frequency filtering in telecommunications. These devices mainly consist of a piezoelectric substrate with periodically arranged electrodes on the surface. The periodic structure of the electrodes subdivides the frequency domain into stop-bands and pass-bands. This means only piezoelectric waves excited at frequencies belonging to the pass-band-region can pass the devices undamped.

We present geometric (GMG) and algebraic multigrid (AMG) preconditioners for data-sparse boundary element matrices. Data-sparse approximation schemes such as adaptive cross approximation (ACA) yield an almost linear behavior in Nh, where Nh is the number of (boundary) unknowns. The treated system matrix represents the discretized single layer potential operator (SLP) resulting from the interior Dirichlet boundary value problem for the Laplace equation. It is well known, that the SLP has converse spectral properties compared to usual finite element matrices. Therefore, multigrid components have to be adapted properly. In the case of GMG we present convergence rate estimates for the data-sparse ACA version. Again, uniform convergence can be shown for the V-cycle. Iterative solvers dramatically suffer from the ill-conditioness of the underlying system matrix for growing Nh. Our multigrid-preconditioners avoid the increase of the iteration numbers and result in almost optimal solvers with respect to the total complexity. The corresponding numerical 3D experiments are confirming the superior preconditioning properties for the GMG as well as for the AMG approach.

Domain decomposition methods nowadays provide powerful tools for constructing efficient parallel solvers for large-scale systems of algebraic equations arising from the discretization of partial differential equations. The classical alternating Schwarz method and the classical substructuring technique have led to advanced overlapping and nonoverlapping domain decomposition solvers (preconditioners), that can be analyzed from a unified point of view now called Schwarz theory. This survey article starts with a brief historical overview, provides the basic results of the Schwarz theory, looks at some overlapping domain decomposition methods (preconditioners) in brief, and discusses more extensively various nonoverlapping domain decomposition techniques. Keywords: domain decomposition; Schwarz theory; preconditioning; overlapping domain decomposition; nonoverlapping domain decomposition; iterative substructuring techniques; Neumann–Neumann; FETI, mortar

To date, sparse information is available on the mechanical properties of municipal solid waste and the results of published work are often hard to compare due to differences in waste composition and therefore properties. To allow comparison, a unified classification system for waste is deemed crucial. Existing classification systems are presented and discussed. For a geotechnical classification, mechanical properties, size, shape and degradability potential of waste components have to be taken into account. A new and improved classification system for waste components is proposed, which complies with the requirements of a geotechnical classification system. It classifies waste components based on: (1) their material engineering properties (e.g., shear, compressive and tensile strength), (2) a size distribution of the components, (3) the component shape (reinforcing, compressible and incompressible), and (4) the degree of degradability. The proposed classification system is applied to data from the literature and methods for presenting classification information are demonstrated. Further work required to develop a full classification system for waste bodies is highlighted.

This paper presents the multiharmonic analysis of a distributed parabolic optimal control problem in a time-periodic setting. We first provide the existence and uniqueness of the solution of some weak space-time variational formulation for the timeperiodic parabolic boundary value problem appearing in the constraints for the optimal control problem. The existence of a solution operator immediately leads to the existence of a unique solution of the original parabolic optimal control problem. In order to solve this optimal control problem, we state its optimality system and discretize it by the multiharmonic finite element method. More precisely, we expand the desired state as well as the unknown functions into Fourier series and truncate them. The Fourier coefficients are approximated by the finite element method. Due to the linearity and the orthogonality of the cosine and sine functions, the whole system of linear algebraic equations decouples into smaller systems depending only on the Fourier coefficients with respect to a single mode. Following [1], we construct preconditioners for these systems which yield robust convergence rates and (almost) optimal complexity for the preconditioned minimal residual method. All systems can be solved totally in parallel. Furthermore, we present a complete analysis for the error introduced by the multiharmonic finite element discretization. Finally, we draw some conclusions.

In this note, we present some of our recent work on domain decomposition solvers for the fluid-structure interaction problems with nearly incompressible and anisotropic elasticity models. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The method of element preconditioning requires the construction of an M-matrix which is as close as possible to a given symmetric positive definite matrix in the spectral sense. In this paper we give a symbolic solution of the arising optimization problem for various subclasses. This improves the performance of the resulting algorithm considerably.

Nowadays the multigrid technique is one of the most efficient methods for solving a large class of problems including elliptic boundary value problems for partial differential equations (PDEs) or systems of PDEs. Our lecture notes start with a motivation for the multigrid idea and a brief review of the multigrid history, its situation and the perspectives. The next part of our paper is devoted to the algorithmical aspects of the construction of multigrid methods including also algebraic approaches and parallelization techniques. Algebraic multigrid methods are now quite popular in practical applications because they can be included in conventional finite element packages without changing the data structure of the package. In the theoretical part of our lecture, we present some general approaches to the convergence and efficiency analysis of multigrid methods. Finally, we discuss implementation issues and present some numerical results obtained from the application of our algebraic multigrid package PEBBLES to large-scale problems in medicine and engineering.

This paper deals with minimizing the mass of the frame of an injection moulding machine as an example for a typical optimal sizing problem. Due to lack of space we omit the shape optimization part (see [5]). Since we want to use standard optimization procedures (such as SQP) we focus our interest on the efficient and flexible calculation of the gradients. Since implementing analytic derivatives is an improper approach, we present a very flexible approach using automatic differentiation. In order to get also an efficient and fast method, automatic differentiation has to be coupled with a well-known approach from shape optimization — the so-called adjoint method. Numerical results show the strength of this approach.

We consider minimizing the mass of the frame of an injection moulding machine as an example of optimal sizing. The deformation of the frame is described by a generalized plane stress state with an elasticity modulus scaled by the thickness. The resulting constrained nonlinear optimization problem is solved by sequential quadratic programming (SQP), which requires gradients of the objective and the constraints with respect to the design parameters. As long as the number of design parameters is small, finite differences may be. For several hundreds of varying thickness parameters, we use the reverse mode of automatic differentiation (AD). AD works fine but requires huge memory and disk capabilities and limits the use of iterative solvers for the governing state equations. Therefore, we combine AD with the adjoint method to get a fast and flexible hybrid gradient evaluation procedure. Numerical results show the potential of this approach and imply that this method can also be used for finding an initial guess for a shape optimization.

The practical applicability of microreaction technology is an unsolved problem. A program has been developed for potential users of microreaction technology to predict the feasibility of applying this technology for a specific synthesis in a microreactor. The program consists of two parts. In the first part basic process equations and parameters and a simplified model of the microreactor are used to obtain preliminary information on the applicability of the microreactor. The second part provides a more detailed consideration of the potential of applying a microreactor, using a detailed microreactor model (CPU intensive). This study presents the program structure and features, and also test cases on technically relevant reactions.

Anfangswertaufgaben (AWA) fur Systeme gewohnlicher Differentialgleichungen sind uns bereits im Kapitel 7 nach der Ortsdiskretisierung eines instationaren Warmeleitproblems (Prototyp einer parabolischen ARWA) und einer Schwingungsgleichung (Prototyp einer hyperbolischen ARWA) begegnet. Im parabolischen Fall haben wir das System (7.8) gewohnlicher Differentialgleichungen erster Ordnung und im hyperbolischen Fall das System (7.20) gewohnlicher Differentialgleichungen zweiter Ordnung erhalten. In diesem Kapitel geben wir einen systematischen Uberblick uber die wichtigsten Verfahren zur numerischen Losung von AWA fur Systeme gewohnlicher Differentialgleichungen erster Ordnung. Wie wir im ersten Abschnitt dieses Kapitels sehen werden, ist dies keine Einschrankung der Allgemeinheit, da wir durch eine geschickte Substitution Systeme zweiter Ordnung immer auf Systeme gewohnlicher Differentialgleichungen erster Ordnung zuruckfuhren konnen. Im Abschnitt 8.1 werden wir daruber hinaus die wichtigsten Fakten zu AWA fur Systeme gewohnlicher Differentialgleichungen erster Ordnung kurz zusammenstellen. Der Abschnitt 8.2 beschaftigt sich mit den Einschrittverfahren.

The numerical simulation of technical 3D magnetic field problems requires fast solvers for the resulting systems of equations. Geometric or algebraic multigrid methods can be used depending on whether a mesh hierarchy is available or not. The paper presents the main ideas of the sequential methods and describes the necessary adaptations for the parallelization. Performance results for both, sequential and parallel solvers underline the high efficiency of the methods.

Anfangsrandwertaufgaben (ARWA) sind uns bereits im Kapitel 2 in Form des instationaren Warmeleitproblems begegnet (siehe ARWA (2.12), S. 50, und (2.13), S. 51). Das instationare Warmeleitproblem ist der Prototyp einer parabolischen ARWA. Wir werden im Abschnitt 7.2 auch hyperbolische ARWA betrachten. Die Wellengleichung und die Schwingungsgleichung sind Prototypen hyperbolischer partieller Differentialgleichungen. Durch die Wellengleichung kann zum Beispiel das Ausbreiten von Druckwellen in der Akustik modelliert werden. Die Schwingungsgleichung spielt in der Mechanik zur Beschreibung der Dynamik schwingender Systeme eine wichtige Rolle (siehe Abschnitt 2.2.2, Gleichung (2.22), S. 57). Mit der Linienmethode ersetzen wir die ARWA durch eine semidiskrete Ersatzaufgabe. Im Fall einer parabolischen ARWA ist das eine Anfangswertaufgabe (AWA) fur ein grosdimensioniertes System gewohnlicher Differentialgleichungen 1. Ordnung zur Bestimmung der zeitabhangigen Koeffizienten im Galerkin-Ansatz (siehe Abschnitt 7.1). Entsprechend ergeben hyperbolische ARWA ein grosdimensioniertes System gewohnlicher Differentialgleichungen 2. Ordnung (siehe Abschnitt 7.2).

This paper is devoted to optimal sizing. As a model example we consider the minimization of the mass of the frame of an injection moulding machine. The deformation of the frame is described by a generalized plane stress state with an elasticity modulus scaled by the thickness. This constrained nonlinear optimization problem is solved by sequential quadratic programming (SQP) which requires gradients of the objective and the constraints with respect to the design parameters.

The use of the FEM and BEM in different subdomains of a non-overlapping Domain Decomposition (DD) and their coupling over the coupling boundaries (interfaces) brings about several advantages in many practical applications. The paper presents parallel solvers for large-scaled coupled FE-BE-DD equations approximating linear and nonlinear plane magnetic field problems as well as plane linear elasticity problems. The parallel algorithms presented are of asymptotically optimal, or, at least, almost optimal complexity and of high parallel efficiency.

Future passenger safety systems must ensure that there is an unequivocal classification of each passenger occupying a passenger seat. Corresponding legislative regulations mandate that, for babies in reboard seats and for infants with a weight of up to 33 kg, the airbags either do not deploy at all or deploy only incrementally. A classification to meet these requirements can be achieved by accurately determining the weight of each seated passenger. At Robert Bosch GmbH, a variety of load measurement bolts have been developed. After simulations of various types of bolts as well as the design of functional models and laboratory tests, a load measurement bolt with a Hall-IC was found to be the best solution. In a cooperation with the FH Cologne, this bolt was optimized for the application in vehicles.

This paper presents new algebraic multigrid preconditioners for sparse representations of boundary element matrices which arise from the so-called adaptive-cross-approximation to dense boundary element matrices resulting from the standard collocation, or Galerkin boundary element discretization of the single layer potential operator.

Gebietszerlegungstechniken eroffnen eine Vielzahl von Moglichkeiten zur Entwicklung paralleler Losungsstrategien fur Finite-Elemente (F.E.) Gleichungen groser Dimension. Die auf der nichtuberlappenden Gebietszerlegung beruhende F.E. Substrukturtechnik und die damit verbundene Datenverteilung fuhrt zu einer Parallelisierung des CG-Verfahrens, die sich besonders fur Mehrprozessorrechner mit lokalem Speicher und Botschaftenaustausch uber Links eignet. Fur diese parallelisierte Version des CG-Verfahrens werden im vorliegenden Beitrag vier verschiedene Vorkonditionierungen vorgeschlagen, mit denen die Konvergenz des CG-Verfahrens erheblich beschleunigt werden kann, ohne das im Vergleich zur nichtvorkonditionierten Variante zusatzliche Kommunikation entsteht. Die auf einem Transputerhypercube durchgefuhrten numerischen Experimente zeigen die Effektivitat der vorgeschlagenen Vorkonditionierungen.

A recently developed multigrid simulation scheme for coupled magneto-mechanical systems is presented. This scheme allows the efficient calculation of 3D dynamic motions of elastic ferromagnetic materials in a magnetic field. The 3D mechanical problem is discretized with nodal elements and the 3D magnetic problem with edge elements. Both meshes may be chosen independently and therefore, they can be adapted to the physical requirements of the mechanical and magnetic field. By applying fast multigrid solution techniques, very short solution times can be achieved even for large scale 3D problems. Using the developed scheme the transient behavior of a solenoid valve is calculated.

This study presents the molecular conductance measurement of a labyrinth seal introduced for the Contamination Control Cover which is protecting the cryogenic optical surfaces of the mid-infrared instrument of the James Webb Space Telescope against molecular contaminants from the environment. The conductance has been measured in the molecular pressure regime between 10−7 and 10−3 mbar within a temperature range of 300 K and 10 K for several typical components of the expected residual gas such as H2O, NH3, CO2, H2, NO, alcohols and hydrocarbons as well as standard gases such as N2 and He. The measurements have been repeated with a thin orifice to verify the systematics. The results are well consistent with numerically derived values and demonstrate a robust understanding of the design and performance of the labyrinth seal.

In this paper we study and compare some preconditioned conjugate gradient methods for solving large-scale higher-order finite element schemes approximating two- and three-dimensional linear elasticity boundary value problems. The preconditioners discussed in this paper are derived from hierarchical splitting of the finite element space first proposed by O. Axelsson and I. Gustafsson. We especially focus our attention to the implicit construction of preconditioning operators by means of some fixpoint iteration process including multigrid techniques. Many numerical experiments confirm the efficiency of these preconditioners in comparison with classical direct methods most frequently used in practice up to now.

Alternative zu einer publizierten Vorschrift kann die Titelverbindung 4 – die als formales 1,3-Photoaddukt von Kohlendioxid an Benzol und als Prostaglandin-Baustein von allgemeinem Interesse ist – bequem durch Dehydrobromierung des tricyclischen Bromlactons 12 dargestellt werden. Sie ist ebenfalls durch sensibilisierte Photooxidation von Bicyclo[3.1.0]hex-2-en-endo-6-carbonsaure (5a) zuganglich. Methods of Formation and Characterization of 4-Oxatricyclo[3.3.0.02,8]oct-6-en-3-one Alternatively to a published procedure, the title compound 4 – being of general interest both as formal 1,3-photo-adduct of carbon dioxide to benzene and as building block in prostaglandin synthesis – is prepared conveniently by dehydrobromination of the tricyclic bromolactone 12. It is also accessible by sensitized photooxidation of bicyclo[3.1.0]hex-2-ene-endo-6-carboxylic acid (5a).

In this paper we study convergence properties of Uzawa-type algorithms for the iterative solution of mixed finite element approximations to two-dimensional boundary value problems with equality constraints, such as the plane Stokes problem or the plane incompressible elasticity problem. We present estimates of the convergence factors which are optimal with respect to the discretization parameter h. It is shown, in particular, that for the problems mentioned the convergence factor of the classical Uzawa-algorithm is independent of h.

Though loss parameters in SAW propagation are used as input for fast analysis models for the simulation of SAW devices, the quantitatively correct description of loss mechanisms is still a challenging task. Therefore, it is important to develop exact measurement and simulation methods which are able to determine these loss parameters accurately. By the use of special boundary conditions, the finite element method (FEM) is able to fulfill these requirements. Regarding the periodic substructure of common SAW devices, we have incorporated periodic boundary conditions (PBCs) in our simulation code. The piezoelectric substrate of SAW devices operating at high frequencies can be modeled as a semi-infinite half space. Therefore, we introduce newly evolved absorbing boundary conditions. They allow us to examine effects emerging from bulk acoustic wave (BAW) radiation (e.g. bulk wave onset frequencies) and assess propagation loss due to leakage and bulk wave conversion accurately.

This article is about the cogging torque sensitivity of brushless permanent magnet machines. Thereby, the sensitivity calculation of the On-/Off-method is used for determining the change of the cogging torque due to varying material behavior of the ferromagnetic parts of the motor. The results are obtained by using finite element calculations and the sensitivity is separately derived for each finite element. A practical example is examined, where two different machine designs are compared with respect to their nominal cogging torque values and their cogging torque changes for varying material characteristics. From the insights gained by this analysis it can be followed that sensitivity analyses will get more and more important for future machine design optimization.