Parallel Sparse Matrix Solver on the GPU Applied to Simulation of Electrical Machines

Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which need speed-up on their solution. This paper examines the parallelism of sparse matrix solver on the graphics processors. More specifically, we implement the conjugate gradient technique with input matrix stored in CSR, and Symmetric CSR and CSC formats. This method is one of the most efficient iterative methods available for solving the finite-element basis functions of Maxwell's equations. The GPU (Graphics Processing Unit), which is used for its implementation, provides mechanisms to parallel the algorithm. Thus, it increases significantly the computation speed in relation to serial code on CPU based systems

Automatic Multi-GPU Code Generation applied to Simulation of Electrical Machines

The electrical and electronic engineering has used parallel programming to solve its large scale complex problems for performance reasons. However, as parallel programming requires a non-trivial distribution of tasks and data, developers find it hard to implement their applications effectively. Thus, in order to reduce design complexity, we propose an approach to generate code for hybrid architectures (e.g. CPU + GPU) using OpenCL, an open standard for parallel programming of heterogeneous systems. This approach is based on Model Driven Engineering (MDE) and the MARTE profile, standard proposed by Object Management Group (OMG). The aim is to provide resources to non-specialists in parallel programming to implement their applications. Moreover, thanks to model reuse capacity, we can add/change functionalities or the target architecture. Consequently, this approach helps industries to achieve their time-to-market constraints and confirms by experimental tests, performance improvements using multi-GPU environments.Comment: Compumag 201

Two Guaranteed Equilibrated Error Estimators for Harmonic Formulations in Eddy Current Problems

International audienceIn this paper, two guaranteed equilibrated error estimators are proposed and compared for the 3D harmonic magnetodynamic problem of Maxwell's system. This system is recasted in the classical A − ϕ potential formulation or, equivalently , in the T − Ω potential formulation, and it is solved by the Finite Element method. The first equilibrated estimator presented is built starting from these two complementary problems, the other one is built starting from the A − ϕ numerical solution uniquely by a flux reconstruction technique. The equivalence between errors and estimators is established. Afterwards, an analytical benchmark test illustrates the obtained theoretical results and a physical benchmark test shows the efficiency of these two estimators

Parallel Direct Solver for the Finite Integration Technique in Electrokinetic Problems

International audienceThe finite integration technique allows the simulation of real-world electromagnetic field problems with complex geometries. It provides a discrete reformulation of Maxwell's equations in their integral form suitable for numerical computing. The resulting matrix equations of the discretized fields can be used for efficient numerical simulations on modern computers and can be exploited to use a parallel computing. In fact, by reordering the unknowns by the nested dissection method, it is possible to directly construct the lower triangular matrix of the Cholesky factorization with many processors without assembling the matrix system. In this paper, a parallel algorithm is proposed for the direct solution of large sparse linear systems with the finite integration technique. This direct solver has the advantage of handling singularities in the matrix of linear systems. The computational effort for these linear systems, often encountered in numerical simulation of electromagnetic phenomena by finite integration technique, is very significant in terms of run-time and memory requirements. Many numerical tests have been carried out to evaluate the performance of the parallel direct solver. Index Terms—Finite element methods, finite integration technique, linear systems, numerical analysis, parallel algorithms

Residual-based a posteriori estimators for the A/phi magnetodynamic harmonic formulation of the Maxwell system

International audienceThis paper is devoted to the derivation of an a posteriori residual-based error estimator for the A/phi magnetodynamic harmonic formulation of the Maxwell system. The weak continuous and discrete formulations are established, and the well-posedness of both of them is addressed. Some useful analytical tools are derived. Among them, an ad-hoc Helmholtz decomposition is proven, which allows to pertinently split the error. Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally efficient. Finally, numerical tests confirm the theoretical results

Solution of Large Stochastic Finite Element Problems – Application to ECT-NDT

Version éditeur disponible à cette adresse : http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6514633This paper describes an efficient bloc iterative solver for the Spectral Stochastic Finite Element Method (SSFEM). The SSFEM was widely used to quantify the effect of input data uncertainties on the outputs of finite element models. The bloc iterative solver allows reducing computational cost of the SSFEM. The method is applied on an industrial Non Destructive Testing (NDT) problem. The numerical performances of the method are compared with those of the Non-Intrusive Spectral Projection (NISP).This work has been supported by the pole MEDEE (EU and Nord Pas de Calais region

Stochastic Non Destructive Testing simulation: sensitivity analysis applied to material properties in clogging of nuclear power plant steam generators

La version éditeur de cette publication est disponible à l'adresse suivante : http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6514684A Non destructive Testing (NDT) procedure is currently used to estimate the clogging of tube support plates in French nuclear power plant steam generators. A stochastic approach has been applied to Finite Element electromagnetic field simulation to evaluate the impact of material properties uncertainties on the monitoring signal. The Polynomial Chaos Expansion method makes it possible to easily derive the Sobol decomposition which measures how much the variability of each input parameter affects the model outputThis work has been supported by the pole MEDEE (EU and Nord Pas de Calais Region

Iterative Solvers for Singular Symmetric Linear Systems in Low Frequency Electromagnetics

International audienceIn this paper, several methods based on Krylov methods are proposed to solve the singular linear systems from finite element method. Indeed, in the magnetostatic case, for A-formulation the system to solve is singular but it is auto-gauged by Krylov methods. However, due to the computation of residual vector all the methods (CG, MRTR, SQMR, MINRES) do not present the same behavior. Moreover, these methods are applied to eddy current problem. The numerical behavior are compared and analyzed

Constrained optimization of the brushless DC motor using the salp swarm algorithm

This paper presents an algorithm and optimization procedure for the optimization of the outer rotor structure of the brushless DC (BLDC) motor. The optimization software was developed in the Delphi Tiburón development environment. The optimization procedure is based on the salp swarm algorithm. The effectiveness of the developed optimization procedurewas compared with genetic algorithm and particle swarmoptimization algorithm. The mathematical model of the device includes the electromagnetic field equations taking into account the non-linearity of the ferromagnetic material, equations of external supply circuits and equations of mechanical motion. The external penalty function was introduced into the optimization algorithm to take into account the non-linear constraint function