A Capped Optimal Stopping Problem for the Maximum Process

This paper concerns an optimal stopping problem driven by the running maximum of a spectrally negative Lévy process X. More precisely, we are interested in capped versions of the American lookback optimal stopping problem (Gapeev in J. Appl. Probab. 44:713–731, 2007; Guo and Shepp in J. Appl. Probab. 38:647–658, 2001; Pedersen in J. Appl. Probab. 37:972–983, 2000), which has its origins in mathematical finance, and provide semi-explicit solutions in terms of scale functions. The optimal stopping boundary is characterised by an ordinary first-order differential equation involving scale functions and, in particular, changes according to the path variation of X. Furthermore, we will link these capped problems to Peskir’s maximality principle (Peskir in Ann. Probab. 26:1614–1640, 1998).     

A deflated conjugate gradient method for multiple right hand sides and multiple shifts

We consider the task of computing solutions of linear systems that only differ by a shift with the identity matrix as well as linear systems with several different right-hand sides. In the past, Krylov subspace methods have been developed which exploit either the need for solutions to multiple right-hand sides (e.g. deflation type methods and block methods) or multiple shifts (e.g. shifted CG) with some success. In this paper we present a block Krylov subspace method which, based on a block Lanczos process, exploits both features—shifts and multiple right-hand sides—at once. Such situations arise, for example, in lattice quantum chromodynamics (QCD) simulations within the Rational Hybrid Monte Carlo (RHMC) algorithm. We present numerical evidence that our method is superior compared to applying other iterative methods to each of the systems individually as well as, in typical situations, to shifted or block Krylov subspace methods.     

Toward a formalism of modeling and simulation using model theory

This article proposes a Modeling and Simulation (M&S) formalism using Model Theory. The article departs from the premise that M&S is the science that studies the nature of truth using models and simulations. Truth in models and simulations is relative as they seek to answer specific modeling questions. Consequently, truth in M&S is relative because every model is a purposeful abstraction of reality. We use Model Theory to express the proposed formalism because it is built from the premise that truth is relative. The proposed formalism allows us to: (1) deduce formal definitions and explanations of areas of study in M&S, including conceptual modeling, validity, and interoperability, and (2) gain insight into which tools can be used to semi‐automate validation and interoperation processes. © 2013 Wiley Periodicals, Inc. Complexity 19: 56–63, 2014     

A thermodynamically consistent constitutive model for fluid mud

In this contribution, an approach towards a thermodynamically consistent constitutive model for fluid mud is presented. Fluid mud exhibits highly non-Newtonian, thixotropic behaviour. It can be classified as a structured fluid. Typically, its viscosity is modeled using Bingham-type rheological models of different complexity [1, 2]. Here, the three-dimensional non-Newtonian constitutive behaviour will be modeled based on a visco-elasto-plastic model. At the current stage, a Drucker-Prager-like yield function has been formulated. Viscosity is assumed to be a function of shear viscosity. First results show the general ability to represent experimental data. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A gradient-enhanced continuum damage model for fibre-reinforced materials at finite strains

The assumption of purely local continuum damage formulations may imply a loss of well-posedness of the underlying boundary value problem. With regard to numerical methods such as the finite element method, this may lead to mesh-dependent solutions, a vanishing localised damage zone upon mesh refinement, and hence physically questionable results. In order to circumvent these deficiencies, i.e. to regularise the problem, we, in this contribution, apply a non-local gradient-based damage formulation within a geometrically non-linear setting allowing for large deformations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uncertainty and Sensitivity Analysis of Different Models of Brake Squeal

In this contribution, the brake-squeal phenomenon is investigated using the pin-on-disc setup. The setup is analyzed numerically using the finite element method. The finite element model is evaluated in the time domain, and the vibration mechanism leading to squeal as well as the limit cycles of the vibration are analyzed. Against the background of the high computational costs, it is evaluated to what extent the Hoffmann-Gaul minimal model can reproduce the results of the finite element model. Moreover, as brake squeal is very sensitive with respect to parametric uncertainties, the influence of several parametric uncertainties on the limit cycles is analyzed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal Control of Large Deformation Elasticity by Fiber Tension

Object of our interest is an elastic body Ω ⊂ ℝ³ which we can deform by applying a tension along certain given short fibers inside the body. The deformation of the body is desribed by a hyperelastic model with polyconvex energy density and a special energy functional for the tension along the fibers. We seek to apply (possibly large) deformations to the body so that a desired shape is obtained. To this end, we formulate an optimal control problem for the fiber tension field. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of numerical homogenization techniques in BT-CFO multiferroic particle composites

This work is restricted to linear material behavior, i.e. the structure is considered to be in a perfectly poled state. Different numerical homogenization methods are investigated and used to calculate effective properties of a 0-2 composite modelled in reprensentative volume elements. Bariumtitanate (BT) and cobaltferrite (CFO) are employed in the Finite Element model, where the roles of matrix and inclusion are mutable in principle. Mixed magnetoelectromechanical boundary conditions based on different homogenization theories are applied to the model. The calculated macroscopic behaviors described by the different approaches are compared and presented in the paper. The special focus is on the prediction of coefficients of magnetoelectric coupling with respect to an optimization of the structural arrangement of the composite. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of Surfactant Concentration in a Coupled Bulk Surface Problem

Surface active agents (surfactants) are on high interest for physical and chemical industries. Their presence lowers the surface tension of fluids. This is used to achieve special flow properties. These mechanisms are not only influenced by the overall amount of surfactant. They highly depend on the local surfactant distribution. The surfactant concentration is modeled by two convection diffusion equations, one in the bulk and the other on its surface. Adsorption- and desorption processes are included and lead to a (non linear) coupling of both equations. We present a numerical scheme for solving the coupled problem. Additionally, first analytical results will be given. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A class of distributed optimization methods with event-triggered communication

We present a class of methods for distributed optimization with event-triggered communication. To this end, we extend Nesterov’s first order scheme to use event-triggered communication in a networked environment. We then apply this approach to generalize the proximal center algorithm (PCA) for separable convex programs by Necoara and Suykens. Our method uses dual decomposition and applies the developed event-triggered version of Nesterov’s scheme to update the dual multipliers. The approach is shown to be well suited for solving the active optimal power flow (DC-OPF) problem in parallel with event-triggered and local communication. Numerical results for the IEEE 57 bus and IEEE 118 bus test cases confirm that approximate solutions can be obtained with significantly less communication while satisfying the same accuracy estimates as solutions computed without event-triggered communication.