In recent years, high performance scientific computing on graphics processing units (GPUs) have gained widespread acceptance. These devices are designed to offer massively parallel threads for running code with general purpose. There are many researches focus on finite element method with GPUs. However, most of the works are specific to certain problems and applications. Some works propose methods for finite element assembly that is general for a wide range of finite element models. But the

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... lopment of finite element code is dependent on the hardware architectures. It is usually complicated and error prone using the libraries provided by the hardware vendors. In this paper, we present architecture and implementation of finite element assembly for partial differential equations (PDEs) based on symbolic computation and runtime compilation technique on GPU. User friendly programming interface with symbolic computation is provided. At the same time, high computational efficiency is achieved by using runtime compilation technique. As far as we know, it is the first work using this technique to accelerate finite element assembly for solving PDEs. Experiments show that a one to two orders of speedup is achieved for the problems studied in the paper.