An Object-oriented Finite Element Framework And Parallel Computing On GPU For Electromagnetic Forming

Electromagnetic forming technology is one of the important technical means to improve the difficult-to-formability of lightweight alloy materials.The electromagnetic forming process involves the intersection of thermodynamics,mechanics,electromagnetics and other disciplines.Finite element method as one of the numerical simulation techniques can effectively solve this complex process.The numerical simulation of electromagnetic forming is usually based on commercial finite element software,but with the rapid development of finite element technology,adding new elements,new materials and new algorithms to these closed-source commercial software has become a challenge.At the same time,low calculation efficiency and poor accuracy when solving large-scale and complex electromagnetic forming processes and discussing the influence of circuit parameters on forming performance.In order to solve the above problems,this article applies object-oriented programming technology to the finite element program design of multi-physics coupled of electromagnetic forming.Parallel computing based on graphics processing unit(GPU)for electromagnetic forming process is also discussed in this paper.The specific research work of this paper is as follows:1.Build a single-physics finite element analysis framework that supports smoothed finite element method based on object-oriented programming ideas.The general calculation process of finite element analysis is abstracted into input-output modules,finite element components,analysis modules and matrix vector operation modules.These main module classes are defined as abstract classes,which implement specific functions through inheritance class.Factory design patterns is adopt here that allows create inheritance class dynamicly at runtime to improve the scalability and flexibility of the program.By analyzing the commonalities between finite element method and smoothed finite element method,the Method class representing the numerical analysis method is established,and the FEMRule class and ESFEMRule class are derived.At the same time,the calculation of the element level is transferred to the subdomain level,and the Sub Domain base class representing the subdomain is established.2.Build a program framework for analyzing the coupling of electromagnetic forming multi-physics based on object-oriented programming technology.In order to realize multi-physics coupling,add the Problem base class to describe the problem to be analyzed.Its derived class EMFProblem class is composed of analysis classes representing each physical field,including EMModel,SMEModel and SMIModel classes.The EMFProblem class controls the overall calculation process and data transfer between each physical field of electromagnetic forming numerical analysis,while each analysis class completes the calculation of a single physical field.When using the same mesh to discrete the overlapping multiphysics,in order to avoid reading repeated elements when constructing analysis classes,a number of element and node sets are established in the entire problem domain,and the problem domain of each analysis class is composed of these sets.3.GPU-based parallel computing of electromagnetic forming multi-physics coupling.Aiming at the cyclic traversal of various levels in the electromagnetic forming calculation process,in order to reasonably utilize the computing resources and memory resources of the GPU,the corresponding thread mapping strategy and data storage format are introduced.On this basis,the correlation matrix and vector are calculated in parallel.Aiming at the "competitive writing" problem caused by matrix and vector assembly,atomic operations and parallel assembly at the subdomain level are converted into a parallel computing strategy at the degree of freedom level.Finally,the Jacobian preconditioning conjugate gradient method without matrix assembly is used to solve the linear equations.Numerical examples show that GPU parallel computing can significantly improve the computational efficiency of electromagnetic forming problems.