Complex physical phenomena can be numerically simulated by mathematical techniques. Usually, these techniques are based on discretization of partial differential equations that govern these phenomena. Hence, these simulations enable the solution of large-scale systems. The parallelization of algorithms of numerical simulation, i. e., their adaptation to parallel processing architectures, is an aim to reach in order to hinder exorbitant execution times. The parallelism has been imposed at the level of processor architectures and graphics cards are now used for purposes of general calculation, also known as "General-Purpose computation on Graphics Processing Unit (GPGPU)". The clear benefit is the excellent performance/price ratio. This thesis addresses the design of high-performance applications for simulation of electrical machines. We provide a methodology based on Model Driven Engineering (MDE) to model an application and its execution architecture in order to generate OpenCL code. Our goal is to assist specialists in algorithms of numerical simulations to create a code that runs efficiently on GPGPU architectures. To ensure this, we offer a compilation model chain that takes into account several aspects of the OpenCL programming model. In addition, to get a code fairly efficient compared to a code developed manually, we provide model transformations that analyze some levels of optimizations based on the characteristics of the architecture (e. g. memory issues). As an experimental validation, the methodology is applied to the creation of an application that solves a linear system resulting from the Finite Element Method (FEM) for simulation of electrical machines. In this case, we show, among other things, the ability of the methodology of scaling by a simple modification of the number of available GPU devices.
