433 research outputs found
Modeling of Spatial Uncertainties in the Magnetic Reluctivity
In this paper a computationally efficient approach is suggested for the
stochastic modeling of an inhomogeneous reluctivity of magnetic materials.
These materials can be part of electrical machines, such as a single phase
transformer (a benchmark example that is considered in this paper). The
approach is based on the Karhunen-Lo\`{e}ve expansion. The stochastic model is
further used to study the statistics of the self inductance of the primary coil
as a quantity of interest.Comment: submitted to COMPE
Multigrid-reduction-in-time for Eddy Current problems
Parallel-in-time methods have shown success for reducing the simulation time
of many time-dependent problems. Here, we consider applying the
multigrid-reduction-in-time (MGRIT) algorithm to a voltage-driven eddy current
model problem.Comment: Contribution from GAMM 2019 conferenc
ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations
Recently, ParaExp was proposed for the time integration of linear hyperbolic
problems. It splits the time interval of interest into sub-intervals and
computes the solution on each sub-interval in parallel. The overall solution is
decomposed into a particular solution defined on each sub-interval with zero
initial conditions and a homogeneous solution propagated by the matrix
exponential applied to the initial conditions. The efficiency of the method
depends on fast approximations of this matrix exponential based on recent
results from numerical linear algebra. This paper deals with the application of
ParaExp in combination with Leapfrog to electromagnetic wave problems in
time-domain. Numerical tests are carried out for a simple toy problem and a
realistic spiral inductor model discretized by the Finite Integration
Technique.Comment: Corrected typos. arXiv admin note: text overlap with arXiv:1607.0036
GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields
Electro-quasistatic field problems involving nonlinear materials are commonly
discretized in space using finite elements. In this paper, it is proposed to
solve the resulting system of ordinary differential equations by an explicit
Runge-Kutta-Chebyshev time-integration scheme. This mitigates the need for
Newton-Raphson iterations, as they are necessary within fully implicit time
integration schemes. However, the electro-quasistatic system of ordinary
differential equations has a Laplace-type mass matrix such that parts of the
explicit time-integration scheme remain implicit. An iterative solver with
constant preconditioner is shown to efficiently solve the resulting multiple
right-hand side problem. This approach allows an efficient parallel
implementation on a system featuring multiple graphic processing units.Comment: 4 pages, 5 figure
Multiple Right-Hand Side Techniques in Semi-Explicit Time Integration Methods for Transient Eddy Current Problems
The spatially discretized magnetic vector potential formulation of
magnetoquasistatic field problems is transformed from an infinitely stiff
differential algebraic equation system into a finitely stiff ordinary
differential equation (ODE) system by application of a generalized Schur
complement for nonconducting parts. The ODE can be integrated in time using
explicit time integration schemes, e.g. the explicit Euler method. This
requires the repeated evaluation of a pseudo-inverse of the discrete curl-curl
matrix in nonconducting material by the preconditioned conjugate gradient (PCG)
method which forms a multiple right-hand side problem. The subspace projection
extrapolation method and proper orthogonal decomposition are compared for the
computation of suitable start vectors in each time step for the PCG method
which reduce the number of iterations and the overall computational costs.Comment: 4 pages, 5 figure
Parallel-In-Time Simulation of Eddy Current Problems Using Parareal
In this contribution the usage of the Parareal method is proposed for the
time-parallel solution of the eddy current problem. The method is adapted to
the particular challenges of the problem that are related to the differential
algebraic character due to non-conducting regions. It is shown how the
necessary modification can be automatically incorporated by using a suitable
time stepping method. The paper closes with a first demonstration of a
simulation of a realistic four-pole induction machine model using Parareal
Determination of Bond Wire Failure Probabilities in Microelectronic Packages
This work deals with the computation of industry-relevant bond wire failure
probabilities in microelectronic packages. Under operating conditions, a
package is subject to Joule heating that can lead to electrothermally induced
failures. Manufacturing tolerances result, e.g., in uncertain bond wire
geometries that often induce very small failure probabilities requiring a high
number of Monte Carlo (MC) samples to be computed. Therefore, a hybrid MC
sampling scheme that combines the use of an expensive computer model with a
cheap surrogate is used. The fraction of surrogate evaluations is maximized
using an iterative procedure, yielding accurate results at reduced cost.
Moreover, the scheme is non-intrusive, i.e., existing code can be reused. The
algorithm is used to compute the failure probability for an example package and
the computational savings are assessed by performing a surrogate efficiency
study.Comment: submitted to Therminic 2016, available at
http://ieeexplore.ieee.org/document/7748645
Waveform Relaxation for the Computational Homogenization of Multiscale Magnetoquasistatic Problems
This paper proposes the application of the waveform relaxation method to the
homogenization of multiscale magnetoquasistatic problems. In the monolithic
heterogeneous multiscale method, the nonlinear macroscale problem is solved
using the Newton--Raphson scheme. The resolution of many mesoscale problems per
Gauss point allows to compute the homogenized constitutive law and its
derivative by finite differences. In the proposed approach, the macroscale
problem and the mesoscale problems are weakly coupled and solved separately
using the finite element method on time intervals for several waveform
relaxation iterations. The exchange of information between both problems is
still carried out using the heterogeneous multiscale method. However, the
partial derivatives can now be evaluated exactly by solving only one mesoscale
problem per Gauss point.Comment: submitted to JC
A Structural Analysis of Field/Circuit Coupled Problems Based on a Generalised Circuit Element
In some applications there arises the need of a spatially distributed
description of a physical quantity inside a device coupled to a circuit. Then,
the in-space discretised system of partial differential equations is coupled to
the system of equations describing the circuit (Modified Nodal Analysis) which
yields a system of Differential Algebraic Equations (DAEs). This paper deals
with the differential index analysis of such coupled systems. For that, a new
generalised inductance-like element is defined. The index of the DAEs obtained
from a circuit containing such an element is then related to the topological
characteristics of the circuit's underlying graph. Field/circuit coupling is
performed when circuits are simulated containing elements described by
Maxwell's equations. The index of such systems with two different types of
magnetoquasistatic formulations (A* and T-) is then deduced by showing
that the spatial discretisations in both cases lead to an inductance-like
element
Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples
We present a new approach to three-dimensional electromagnetic scattering
problems via fast isogeometric boundary element methods. Starting with an
investigation of the theoretical setting around the electric field integral
equation within the isogeometric framework, we show existence, uniqueness, and
quasi-optimality of the isogeometric approach. For a fast and efficient
computation, we then introduce and analyze an interpolation-based fast
multipole method tailored to the isogeometric setting, which admits competitive
algorithmic and complexity properties. This is followed by a series of
numerical examples of industrial scope, together with a detailed presentation
and interpretation of the results
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