Toward Real-Time Finite-Element Simulation on GPU

In this paper, we introduce some parallel techniques on NVIDIA compute unified device architecture GPU for the finite-element method applied in the magnetic field computation. To ensure the load balance, each parallel thread performs the integration of one element. In the assembly step, we introduced a fast procedure based on the sorting and rearrangement of non-zero entries on the GPU global memory. Then, a reducing process is executed to obtain the resulting coefficient matrix in a sparse format. About the solving step, we use the conjugate gradient iterative solver with a variety of preconditioning techniques. Our implementation does not require any preprocessing on mesh, but takes advantage of the parallel computing power of GPU. In our test, this parallel strategy improved the performance 30 times faster on the assembly process and four times faster on the solving process.