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In this article, a highly efficient hp -adaptive scheme has been developed for the discontinuous Galerkin time-domain (DGTD) method. In order to achieve the ${h}$ - and ${p}$ -adaptive behaviors, a hierarchical octree-based recursive meshing procedure has been introduced. In the hp -adaptive scheme, the transformation method of the basis function is developed to convert the fields between the parent element and the child elements and between the higher- and the lower-order bases. Instead of the time-consuming field update process according to the governing equations, the error based on modified reference solutions can be rapidly and accurately calculated in the ${h}$ - and ${p}$ -adaptions by using the proposed transformation, thus flexibly manipulating the hp -adaptive procedure. Some 3-D radiation and scattering examples are given to demonstrate the good accuracy and high efficiency of the proposed hp -adaptive DGTD method. [ABSTRACT FROM AUTHOR]

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 letter, an improved approach for the estimation of time step bound in the discontinuous Galerkin time-domain (DGTD) method has been developed. Different from the widely used energy-based technique, the spectral radius of the system matrix in the proposed method is used to analytically derive the stability condition of the DGTD method. In order to accelerate the solution of the time step bound, the spectral radius of the local system instead of the global spectral radius is solved, and thus, the proposed elementwise estimation scheme is suitable for the practical large-scale problems. The numerical examples demonstrate that the maximal time step estimated by the proposed method is up to 0.95 times as large as the accurate one and up to 3.83 times as large as the one determined by the widely used energy technique. [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]

This letter develops a nodal discontinuous Galerkin time-domain method based on wave equation (NDGTD-WE) to accurately solve the electromagnetic problems. The governing equation of the NDGTD-WE method has been formulated by using interior penalty numerical flux and the nodal basis functions have been used to expand the unknown electric field. In order to reduce the memory usage of the NDGTD-WE method, a low storage scheme has been developed by transforming the integral in the global element to that in the reference element and meanwhile calculating the nodal bases in the global element in terms of the modal bases in the reference element. The wave sources of the NDGTD-WE method in free space and waveguide have been derived. Numerical examples show good performance of the proposed NDGTD-WE including low memory and good accuracy. [ABSTRACT FROM AUTHOR]

In this article, a graphic processing unit (GPU)-based acceleration implementation of a hybrid discontinuous Galerkin time domain method based on Maxwell’s equations and Helmholtz vector wave equation (HDGTD) has been developed. The computational domain is discretized by tetrahedrons and the resultant meshes are categorized into two regions solved by Maxwell’s equations and Helmholtz vector wave equation, respectively. The hierarchical vector basis functions are used to expand the unknowns in the HDGTD method, and a universal matrix technique is proposed to decompose the geometry-dependent matrices in each tetrahedron into the summation of universal matrices defined in barycentric coordinates, thus giving rise to a great decrease of the memory usage. A local time stepping (LTS) method based on a simple interpolation is introduced in the proposed HDGTD method to achieve highly efficient solution of multiscale problems. Two kinds of compute unified device architecture (CUDA)-based mapping techniques, i.e., 1-D and 2-D blocks, are implemented to achieve a tradeoff between the parallel speedup and the memory usage. With the 1-D block mapping, over 590 times speedup can be achieved, and in the case of the 2-D block mapping, over 150 times acceleration and 13 times memory reduction are obtained. Some practical complex examples are given to demonstrate a good performance of the proposed parallel method. [ABSTRACT FROM AUTHOR]