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In this paper, 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. This paper closes with the first demonstration of a simulation of a realistic four-pole induction machine model using Parareal. [ABSTRACT FROM AUTHOR]

In this paper, the concept of multirate partial differential equations (MPDEs) is applied to obtain an efficient solution for nonlinear low-frequency electrical circuits with pulsed excitation. The MPDEs are solved by a Galerkin approach and a conventional time discretization. Nonlinearities are efficiently accounted for by neglecting the high-frequency components (ripples) of the state variables and using only their envelope for the evaluation. It is shown that the impact of this approximation on the solution becomes increasingly negligible for rising frequency and leads to significant performance gains. [ABSTRACT FROM AUTHOR]

Electro-quasi-static (EQS) 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 (ODEs) 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 EQS system of ODE 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. [ABSTRACT FROM AUTHOR]

Uncertainty quantification plays an important role in biomedical engineering as measurement data are often unavailable and literature data show a wide variability. Using the state-of-the-art methods, one encounters difficulties when the number of random inputs is large. This is the case, e.g., when using composite Cole–Cole equations to model random electrical properties. It is shown that how the number of parameters can be significantly reduced by the Karhunen–Loève expansion. The low-dimensional random model is used to quantify uncertainties in the axon activation during deep brain stimulation. Numerical results for a Medtronic 3387 electrode design are given. [ABSTRACT FROM AUTHOR]

This paper focuses on the acceleration of the numerical linear algebra for solving large nonlinear electro-quasi-static problems in time domain as they occur in high-voltage applications utilizing nonlinear electric field stress grading materials. An algebraic multigrid (AMG) scheme is executed on multiple graphic processor units (GPUs) as a preconditioner for the conjugate gradients method. The speedup is further increased by exploiting the fact that the repeated solutions of almost similar systems must be obtained in the Newton–Raphson iterations of the implicit time-stepping scheme. A tailored update algorithm for the AMG preconditioner is proposed that significantly reduces the computational time due to a reduction of communication between GPUs and host. [ABSTRACT FROM AUTHOR]

Stern–Gerlach magnets are used to magnetically separate a beam of atoms or atom clusters. The design is difficult, since both the magnetic field gradient and its homogeneity should be maximized. This paper proposes the numerical optimization of the device’s pole-shoe shapes, starting from a reference geometry given in the literature. The main contributions of this paper are the generalization of a magnetic field–magnetic circuit coupling and the application of isogeometric analysis (IGA), which are shown to reduce the computational complexity and increase the accuracy. The field–circuit coupling significantly reduces the size of the field model part, in which the IGA’s spline-based framework enables a highly accurate evaluation of local field quantities, even across elements. [ABSTRACT FROM PUBLISHER]

In this contribution, a multi-graphic processing unit (GPU) implementation of Krylov sub-space methods with algebraic multi-grid preconditioners is proposed. It is used to solve large linear systems stemming from finite element or finite difference discretizations of elliptic problems as they occur, e.g., in electrostatics. The distribution of data across multiple GPUs and the effects on memory and speed are discussed when using an approach that preserves the effects of fine-grained parallelism with shared memory on the GPU while distributing data across multiple GPUs with minimal communication effort. [ABSTRACT FROM PUBLISHER]