arXiv subjects

Hanhong Liu

Publications and source records attributed to Hanhong Liu.

4 recordsLinked to original sources

arXiv2026

A Stable SBP-SAT FDTD Subgridding Method Without Region Split

A provably stable summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-domain (FDTD) subgridding method without region split is proposed. By designing projection SBP operators tailored for embedded topological features and deriving the corresponding SAT boundary conditions, this approach guarantees long-time stability through discrete energy analysis. Unlike conventional SBP-SAT FDTD subgridding techniques that rely on aligned or multi-block configurations, the proposed method enables a direct coupling between an internal refined region and a single surrounding coarse-grid domain without introducing auxiliary blocks or causing domain fragmentation. Numerical results validate the efficiency, accuracy, and topological flexibility of the proposed method. Compared with existing multi-block SBP-SAT methods, this method effectively reduces computational complexity by minimizing SAT boundary conditions and improves calculation accuracy near grid interfaces.

cs.CE↗

arXiv2022

Towards the Development of A Three-Dimensional SBP-SAT FDTD Method: Theory and Validation

To enhance the scalability and performance of the traditional finite-difference time-domain (FDTD) methods, a three-dimensional summation-by-parts simultaneous approximation term (SBP-SAT) FDTD method is developed to solve complex electromagnetic problems. It is theoretically stable and can be further used for multiple mesh blocks with different mesh sizes. This paper mainly focuses on the fundamental theoretical aspects upon its three-dimensional implementation, the SAT for various boundary conditions, and the numerical dispersion properties and the comparison with the FDTD method. The proposed SBP-SAT FDTD method inherits all the merits of the FDTD method, which is matrix-free, easy to implement, and has the same level of accuracy with a negligible overhead of runtime (0.13\%) and memory usage (1.2\%). Four numerical examples are carried out to validate the effectiveness of the proposed method.

cs.CE↗

arXiv2021

An Unconditionally Stable Conformal LOD-FDTD Method For Curved PEC Objects and Its Application to EMC Problems

The traditional finite-difference time-domain (FDTD) method is constrained by the Courant-Friedrich-Levy (CFL) condition and suffers from the notorious staircase error in electromagnetic simulations. This paper proposes a three-dimensional conformal locally-one-dimensional FDTD (CLOD-FDTD) method to address the two issues for modeling perfectly electrical conducting (PEC) objects. By considering the partially filled cells, the proposed CLOD-FDTD method can significantly improve the accuracy compared with the traditional LOD-FDTD method and the FDTD method. At the same time, the proposed method preserves unconditional stability, which is analyzed and numerically validated using the Von-Neuman method. Significant gains in Central Processing Unit (CPU) time are achieved by using large time steps without sacrificing accuracy. Two numerical examples include a PEC cylinder and a missile are used to verify its accuracy and efficiency with different meshes and time steps. It can be found from these examples, the CLOD-FDTD method show better accuracy and can improve the efficiency compared with those of the traditional FDTD method and the traditional LOD-FDTD method.

cs.CE↗

arXiv2021

A Stable FDTD Subgridding Scheme with SBP-SAT for Transient Electromagnetic Analysis

We proposed a provably stable FDTD subgridding method for accurate and efficient transient electromagnetic analysis. In the proposed method, several field components are properly added to the boundaries of Yee's grid to make sure that the discrete operators meet the summation-by-parts (SBP) property. Then, by incorporating the simultaneous approximation terms (SATs) into the finite-difference time-domain (FDTD) method, the proposed FDTD subgridding method mimics the energy estimate of the continuous Maxwell's equations at the semi-discrete level to guarantee its stability. Further, to couple multiple mesh blocks with different mesh sizes, the interpolation matrices are also derived. The proposed FDTD subgridding method is accurate, efficient, easy to implement and be integrated into the existing FDTD codes with only simple modifications. At last, three numerical examples with fine structures are carried out to validate the effectiveness of the proposed method.

cs.CE↗