Showing papers by "Sebastian Schöps published in 2013"

Winding functions in transient magnetoquasistatic field-circuit coupled simulations

Abstract: Purpose – The purpose of this paper is to review the mutual coupling of electromagnetic fields in the magnetic vector potential formulation with electric circuits in terms of (modified) nodal and loop analyses. It aims for an unified and generic notation. Design/methodology/approach – The coupled formulation is derived rigorously using the concept of winding functions. Strong and weak coupling approaches are proposed and examples are given. Discretization methods of the partial differential equations and in particular the winding functions are discussed. Reasons for instabilities in the numerical time domain simulation of the coupled formulation are presented using results from differential-algebraic-index analysis. Findings – This paper establishes a unified notation for different conductor models, e.g. solid, stranded and foil conductors and shows their structural equivalence. The structural information explains numerical instabilities in the case of current excitation. Originality/value – The presentat...

Dynamic Iteration for Coupled Problems of Electric Circuits and Distributed Devices

Abstract: Coupled systems of differential-algebraic equations (DAEs) may suffer from instabilities during a dynamic iteration We extend the existing analysis on recursion estimates, error propagation, and stability to (semiexplicit) index-1 DAEs In this context, we discuss the influence of certain coupling structures and the computational sequence of the subsystems on the rate of convergence Furthermore, we investigate in detail convergence and divergence for two coupled problems stemming from refined electric circuit simulation These are the semiconductor-circuit and field-circuit couplings We quantify the convergence rate and behavior also using Lipschitz constants and suggest an enhanced modeling of the coupling interface in order to improve convergence

Reduction of Linear Subdomains for Non-Linear Electro-Quasistatic Field Simulations

Abstract: A method is presented that reduces the degrees of freedom (DoFs) in linear subdomains in transient non-linear electro-quasistatic (EQS) field finite-element method (FEM) simulations. The electro-quasistatic field model yields a suitable approximation to simulate high-voltage devices such as insulators or surge arresters featuring non-linear resistive field grading materials. These materials are usually applied as thin layers, i.e., they represent only a very small volume part in the overall model. Despite the application of unstructured FEM meshes, commonly most of the DoFs are located in the domain with constant material parameters. The non-linear subdomain is much smaller with respect to the number of DoFs than the part with constant materials. The application of model order reduction techniques, in particular proper orthogonal decomposition (POD), is proposed to minimize the DoFs in the linear subdomain of the simulation model. POD captures the dynamic in the linear subdomain. Large reduction factors can be achieved for low dynamic exterior domains, thus considerably reducing the computational costs. Numerical results are presented for an IEC norm surge arrester and a typical 11 kV insulator design with a field grading inlay.

Quantification of Uncertainty in the Field Quality of Magnets Originating from Material Measurements

Abstract: A challenge in accelerator magnet design is the strong nonlinear behavior due to magnetic saturation In practice, the underlying nonlinear saturation curve is modeled according to measurement data that typically contain uncertainties The electromagnetic fields and in particular the multipole coefficients that heavily affect the particle beam dynamics inherit this uncertainty In this paper, we propose a stochastic model to describe the uncertainties and we demonstrate the use of generalized polynomial chaos for the uncertainty quantification of the multipole coefficients In contrast to previous works we propose to start the stochastic analysis from uncertain measurement data instead of uncertain material properties and we propose to determine the sensitivities by a Sobol decomposition

GPU Acceleration of Finite Difference Schemes Used in Coupled Electromagnetic/Thermal Field Simulations

Abstract: The solution procedure of coupled electromagnetic-/thermal-simulations with high resolution requires efficient solvers. High performance computing libraries and languages like Nvidia's CUDA help in unlocking the massively parallel capabilities of GPUs to accelerate calculations. They reduce the time needed to solve real world problems. In this paper, the speed-up is discussed, which is obtained by using GPUs for coupled time domain simulations with finite difference schemes. A tailor-made implementation of the time consuming sparse matrix vector multiplication is shown to have advantages over standard CUDA-libraries like cuSparse.

Structural aspects of regularized full Maxwell electrodynamic potential formulations using FIT

Abstract: In this paper regularized electrodynamic potential formulations for full Maxwell are presented within the framework of the Finite Integration Technique. The reformulation of the semi-discrete Maxwell Equations into two second order wave equations for the magnetic vector potential and a scalar electric potential is feasible with a Lorenz-type gauge condition. On the other hand, a Coulomb-type condition yields a numerically ill-posed formulation. This is shown using the differential-algebraic equation index concept.

Space-time discretization of Maxwell's equations in the setting of Geometric Algebra

Abstract: The Geometric Algebra (GA) for Minkowski space-time and Maxwell's equations in the setting of GA are briefly outlined. The constitutive equations are discussed in more detail. A discrete version of GA for a Cartesian grid is investigated and is shown to be equivalent to Tonti's approach. Furthermore, under quite natural assumptions both schemes coincide with the Finite Integration Technique (in 3D space) and Leap-Frog time integration.

A Parallel FEM Matrix Assembly for Electro-Quasistatic Problems on GPGPU Systems

Abstract: This paper introduces a new matrix assembly algorithm for nonlinear problems that decomposes the problem into parts that are well suited for parallel computation on GPGPUs. It has the strength that recomputations in nonlinear entries of the stiffness matrices are embarrassingly parallel. The algorithm is used to solve electro-quasistatic problems. The proposed discretization includes the handling of Dirichlet and homogeneous Neumann boundary conditions.

Discretization of Maxwell's equations in the setting of geometric algebra

Abstract: In this paper geometric algebra of space-time is used to state Maxwell's equations in an ellegant differential and integral form The proposed integral form involves no derivative with respect to time and is coordinate-free in contrast to what is usually refered as the integral form The Maxwell's equations are discretized in a very natural manner using their integral form The discretization of the material equations is discussed in detail It is directly related to the efficiency of the resulting scheme Finally, the relation to traditional approaches is shown

An Optimal p‐Refinement Strategy for Dynamic Iteration of Ordinary and Differential Algebraic Equations

Abstract: Multiphysical simulation tasks are often numerically solved by dynamic iteration schemes. Usually, this demands the efficient and stable coupling of existing simulation software for the contributing physical subdomains or subsystem. Since the coupling is weakened by such a simulation strategy, iteration is needed to enhance the quality of the numerical approximation. By the means of error recursions, one obtains estimates for the approximation order and the reduction of error per iteration (convergence rate). It is know that the first iterations can be coarsely sampled (in time), but the last iterations need to be refined (h-refinement) to obtain the accuracy gain of latter iterations (‘sweeps’). In this work we discuss an optimal choice of the approximation order p used in the time integration with respect to the iteration ‘sweep’ count. It is deduced from the analytical error recursion and yields a p-refinement strategy. Numerical experiments show that our estimates are sharp and give a precise prediction of the correct convergence. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Linear Subspace Reduction for Quasistatic Field Simulations

Abstract: Simulating eddy-current problems in time domain using the magnetic vector potential formulation leads to a nonlinear system of differential-algebraic equations. Typically a large number of degrees of freedom (DoF) are in domains with constant material, for example air or vacuum in exterior domains. In this work a new method is presented that reduces only the DoFs in these exterior domains by using the proper orthogonal decomposition (POD) method. The POD method involves a singular value decomposition (SVD) to capture the system dynamics and extract the essential dynamical behavior with a low number of DoFs. A simple transformer example is given to proof the concept.

Second Moment Analysis of the Nonlinear Eddy Current Model with Material Uncertainties

Abstract: In this paper we study the eddy current problem with uncertainties in the nonlinear material characteristic originating, e.g., from measurements. In the case of small input uncertainties adjoint techniques can be used to efficiently approximate the solutions statistics (first order second moment method) at very low computational cost. We will carry out the corresponding sensitivity analysis and investigate the methods approximation properties. The main contribution of the present work is the extension to nonlinear problems. Numerical results for an electrical transformer and a comparison with the standard Monte Carlo method are given.