We present a discontinuous finite element method to resolve the skin effect in conductors on coarse meshes. The idea is to take into account the exponential decay in the finite element trial space, which enables to resolve the skin layer independent of the size of the mesh cells. The spatial discretization of the magnetic vector potential formulation of magnetoquasistatic field problems results in an infinitely stiff differential-algebraic equation system. It is transformed into a finitely stiff ordinary differential equation system by applying a generalized Schur complement.

Applying the explicit Euler time integration scheme to this system results in a small maximum stable time step size. Fast computations are required in every time step to yield an acceptable overall simulation time. Several acceleration methods are presented.

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We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and a maximum angle condition holds. Therefore, optimal order of convergence can be shown. Moreover, it can be shown that an appropriate choice of the basis functions yields an optimal condition number of the stiffness matrix.

## Computer Science and Applied Mathematics

The method is applied to an optimal design problem for an electric motor where the interface between different materials evolves in the course of the optimization procedure. Within analysis of dynamical systems embracing uncertain impacts the output can be generally viewed as a function defined in a random domain with dependence on time or frequency.

Without loss of generality, a function defined on the normalized random domain, i. Variance-based global sensitivity indices provide adequate estimates for the influence of random variables and become one of the most powerful instruments in sensitivity analysis. Alternatively, if the function is differentiable, the derivative-based sensitivity measures have received much attention due to lower computational costs.

We introduce numerical strategies for computing derivative-based sensitivity indices in the case of high-dimensional hypercubes and present numerical simulations of a test example which models the linear electric circuit of a band-stop filter.

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The design process of integrated circuits IC aims at a high yield as well as a good IC-performance. The distribution of measured output variables will not be standard Gaussian anymore. In fact, the corresponding probability density function has a more flat shape than in case of standard Gaussian. In order to optimize the yield one needs a statistical model for the observed distribution.

One of the promising approaches is to use the so-called Generalized Gaussian distribution function and to estimate its defining parameters. We propose a numerical fast and reliable method for computing these parameters. Modern electronics systems involved in communication and identification impose demanding constraints on both reliability and robustness of components.

On the one hand, it results from the influence of manufacturing tolerances within the continuous down-scaling process into the output characteristics of electronic devices. On the other hand, the increasing integration process of various systems on a single die force a circuit designer to make some trade-offs in preventing interference issues and in compensating coupling effects.

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Thus, constraints in terms of statistical moments have come in a natural way into optimization formulations of electronics products under uncertainties. Therefore, in this paper, for the careful assessment of the propagation of uncertainties through a model of a device a type of Stochastic Collocation Method SCM with Polynomial Chaos PC was used.

In this way a response surface model can be included in a stochastic, constrained optimization problem.

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Achieved results for the optimization confirmed efficiency and robustness of the proposed methodology. Jan W. Recently, the block-diagonal structured model order reduction method for electro-thermal coupled problems with many inputs BDSM-ET was proposed in Banagaaya et al. Model order reduction for nanoelectronics coupled problems with many inputs. However, the reduced electrical subsystem has dense matrices and the nonlinear part of the reduced-order thermal subsystem is computationally expensive.

Simulation of a very large-scale model with up to one million state variables shows that the proposed method achieves significant speed-up as compared with the BDSM-ET method. We consider linear dynamical systems including random variables to model uncertainties of physical parameters. The output of the system is expanded into a series with orthogonal basis functions.

Our aim is to identify a sparse approximation, where just a low number of basis functions is required for a sufficiently accurate representation. The coefficient functions of the expansion are approximated by a quadrature method or a sampling technique. The performance of a quadrature scheme can be described by a larger linear dynamical system, which is weakly coupled. We apply methods of model order reduction to the coupled system, which results in a sparse approximation of the original expansion.

The approximation error is estimated by Hardy norms of transfer functions. Furthermore, we present numerical results for a test example modelling the electric circuit of a band pass filter. The accurate and efficient treatment of eddy-current problems with movement is still a challenge. Extra Content.

## Scientific Computing in Electrical Engineering | seaegacelceeco.cf

Janssen, J. Niehof and W. Ionescu, Jacquelien M. Pulch, E. Vollebregt, T. Bechtold, A. Verhoeven, E. Ilievski, H. Xu, A.

Schilders, R. Gramsch, A. Blaszczyk, H. Lbl, S.

## Computers & Electrical Engineering

Verhoeven, B. Event website:. This series of conferences has played a key role in promoting parallel scientific computing, algorithms for parallel systems, and parallel numerical algorithms. The conference is unique in its emphasis on the intersection between high performance scientific computing and scalable algorithms, architectures, and software.

The conference provides a forum for communication among the applied mathematics, computer science, and computational science and engineering communities. Event listing ID:. The IMECS conferences serve as good platforms for our members and the entire engineering community to meet with each other and to exchange ideas.