Conference Agenda

Asynchronous linear solvers and preconditioners have gained significant attention as effective strategies to mitigate synchronization bottlenecks in computational processes, particularly prevalent in the field of computational electromagnetics (CEM). These solvers and preconditioners have been demonstrated to enhance the efficiency of solving large-scale linear systems, which are frequently encountered in CEM applications, such as modeling electromagnetic wave propagation and scattering. In this study, we introduce a mixed-precision randomized preconditioner implemented on GPUs, alongside a generalized row-based randomized asynchronous linear solver designed to leverage GPU capabilities. Reduced-precision preconditioners are well established for their ability to accelerate computations while maintaining convergence properties, making them particularly suitable for the large, sparse systems characteristic of CEM problems. This approach offers a promising pathway to address the computational challenges inherent in high-frequency electromagnetic simulations and large-scale system analyses.

Matrix-free finite element methods (FEM) combined with tensor product basis functions have garnered significant attention as effective strategies to address the memory bandwidth limitations inherent in classical FEM formulations. By avoiding the explicit storage of global matrices and leveraging the efficiency of tensor product structures, these approaches substantially reduce memory requirements and computational overhead. This capability is particularly advantageous in high-dimensional problems and large-scale simulations, including computational electromagnetics, where memory constraints often pose critical challenges. In this study, we aim to explore the effect of modern hardware acceleration in this framework. By benchmarking performance and analyzing the scalability of these methods on contemporary high-performance computing platforms, we seek to uncover insights into their potential for solving increasingly complex problems in computational electromagnetics and beyond.

This paper demonstrates a strategy to solve large-scale parallel finite-element time-domain (FETD) with a performance analysis on heterogeneous computer architectures. Scalability is demonstrated by speedup studies of a 3D metallic body illuminated by an electromagnetic plane wave with more than 4 billion degrees of freedom on a computer system with an Intel Xeon CPU and NVIDIA RTX GPU. This work is significant because in the domain of finite element analysis in computational electromagnetics (CEM) with complex geometry we demonstrate on a parallel large-scale computing platform local machine—the HP Z8 G5 workstation an approach to address principal constraints in CEM involving memory bandwidth and capacity, which affect FETD efficiency and precision.

The Finite Element method is widely used to study and design electromagnetic devices. This method is very accurate but often requires huge computational time even during the post processing step where quantities of interest are calculated. In this communication we propose to apply the K-Means method in order to reduce the computational time of the iron losses distribution in a postprocessing stage. Indeed, the iron losses distribution calculation relies only on the calculation on only few elements of mesh and not on all elements like in the standard method. The proposed method is tested on a nonlinear magnetic example based on a linear actuator showing a good agreement between the iron losses distribution obtained by the standard and the proposed methods.

Simulations of particle beam dynamics in electron accelerators need to account for both internal space charge effects and transient electromagnetic waves scattered at chamber walls. Commonly, these effects are treated separately using very different simulation techniques. We present a coupling procedure to account for both effects simultaneously by using a scattered field formulation. Here, we combine two field solvers optimized to simulate either the internal beam dynamics assuming free space or the transient electromagnetic wave propagation. Furthermore, in this paper we extend the approach to account for synchrotron radiation wakefields.

In the paper, we show that volume integral operators discretized in Discontinuous Galerkin can be interpreted in tensor representations and we give the idea for a new assembly strategy. A numerical example illustrates the compression and the computational time obtained.

In this paper, we present the use of the Finite Volume Method to compute the non-linear behaviour of superconductor material. In this approach, curl-curl operator is discretised using the diamond scheme, and we solve H-formulation of electromagnetic problem in superconductor material. An example of a 2D cable with six superconducting filaments is proposed to show efficiency of this approach.

In this paper, we present implementation of a DDFV solver on massively parallel architecture to compute electromagnetic field. This work is based on using three standard scientific libraries, Metis for mesh partitioning, MPI to manage process communications and PETSc for linear algebra operations, on multi-core supercomputers. Discrete basis renumbering technique is also implemented to reduce synchronization slow down and memory bandwidth limitation. A 2D example consisting in solving a system of few millions DOF on a supercomputer with 480 cores is proposed to show efficiency of our implementation.

This work addresses the development of reliable surrogates for electromagnetic problems with uncertainties, by introducing a new sampling approach for the computation of polynomial-chaos (PC) expansions via least squares. The proposed scheme adopts a sequential framework, enabling the development of an adaptive algorithm that promotes denser sample concentrations at areas with significant variance density of the quantity of interest. At the same time, a subset of samples is selected via a distance-based criterion, to ensure that the overall sample set preserves adequate space-filling properties. In this way, experimental designs balancing two different selection criteria are constructed, and their impact on the efficiency of PC computations is demonstrated herein via a number of tests.

While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. The Multi-Level Monte Carlo method reduces the overall computational effort, but is unable to reduce the time to solution in a sufficiently parallel computing environment. In this work, we propose a Uncertainty Quantification method combining Multi-Level Monte Carlo sampling and Parallel-in-Time integration for select samples, exploiting remaining parallel computing capacity to accelerate the computation. As a first numerical test, the method is applied to an electric induction machine model, where a speedup of around 27.2% compared to Multi-Level Monte Carlo sampling is observed.

The virtual element method have the ability in handling meshes with polygonal elements and thus offers greater flexibility than the finite element method for meshing complex geometries. We propose here to apply the method to a transient induced current problem and apply it to the case of an axisymmetric magnetic core.