Search

In this communication, a novel message passing interface (MPI) parallel algorithm for nodal discontinuous Galerkin time-domain (NDGTD) method has been developed. A unified MPI + MPI technique has been introduced for extreme parallelism on a large-scale computer cluster. Through the data transmission between CPU nodes using MPI persistent nonblocking two-side communication and the direct data connection between processors in the same node via MPI shared memory windows, a two-layered parallel architecture is implemented to minimize the communication. To further accelerate the solution of the multiscale problems, the local time stepping (LTS) technique has been employed in the NDGTD method. A fast time step estimation method has been presented in this communication. With high overlap between the information transmission and the data calculation, the proposed MPI + MPI scheme overcomes the degradation of the parallel efficiency of the pure MPI technique in the scenario of the LTS technique and the large-scale CPU cores. Up to 94% parallel efficiency in 6400 CPU cores is achieved for the average single-core loading about 1700 finite elements, and 18 times acceleration for time step estimation can be obtained with the fourth-order basis function. Three practical complex examples are given to demonstrate a good performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, penalty factor threshold and time step bound in discontinuous Galerkin time method based on vector wave equation (DGTD-WE) method are well estimated. Based on the semidiscrete form of the DGTD-WE method, properties of the system matrices are studied and the stability condition related to the penalty factor is derived. By decomposing the global system matrices of the DGTD-WE method into the local ones and developing an efficient iteration procedure, the lower bound threshold of the penalty factor is well estimated to guarantee the positive semidefinite property of the global system matrices. With the calculated penalty factor, the maximum time step is analytically determined by approximating spectral radius of the local system matrix. Both the penalty factor bound and the maximal time step are computed element-wise instead of a global system matrix operation, and thus, the proposed method can be efficiently applied into the large-scale meshes with different types of the basis functions and boundary conditions. Numerical examples are presented to demonstrate the validity and good performance of the proposed methods. [ABSTRACT FROM AUTHOR]