arXiv subjects

Shunchuan Yang

Publications and source records attributed to Shunchuan Yang.

At least 19 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↗

arXiv2024

RIMformer: An End-to-End Transformer for FMCW Radar Interference Mitigation

Frequency-modulated continuous-wave (FMCW) radar plays a pivotal role in the field of remote sensing. The increasing degree of FMCW radar deployment has increased the mutual interference, which weakens the detection capabilities of radars and threatens reliability and safety of systems. In this paper, a novel FMCW radar interference mitigation (RIM) method, termed as RIMformer, is proposed by using an end-to-end Transformer-based structure. In the RIMformer, a dual multi-head self-attention mechanism is proposed to capture the correlations among the distinct distance elements of intermediate frequency (IF) signals. Additionally, an improved convolutional block is integrated to harness the power of convolution for extracting local features. The architecture is designed to process time-domain IF signals in an end-to-end manner, thereby avoiding the need for additional manual data processing steps. The improved decoder structure ensures the parallelization of the network to increase its computational efficiency. Simulation and measurement experiments are carried out to validate the accuracy and effectiveness of the proposed method. The results show that the proposed RIMformer can effectively mitigate interference and restore the target signals.

eess.SP↗

arXiv2023

A Transient Electrical-Thermal Co-Simulation Method with LTS for Multiscale Structures

In this article, an efficient transient electricalthermal co-simulation method based on the finite element method (FEM) and the discontinuous Galerkin time-domain (DGTD) method is developed for electrical-thermal coupling analysis of multiscale structures. Two Independent meshes are adopted by the steady electrical analysis and the transient thermal simulation to avoid redundant overhead. In order to enhance the feasibility and efficiency of solving multiscale and sophisticated structures, a local time stepping (LTS) technique coupled with an interpolation method is incorporated into the co-simulation method. Several numerical examples from simple structures to complex multiscale PDN structures are carried out to demonstrate the accuracy and efficiency of the proposed method by comparing with the COMSOL. Finally, two practical numerical examples are considered to confirm the performance of the proposed method for complex and multiscale structures.

math.NA↗

arXiv2022

An SIE Formulation with Triangular Discretization and Loop Analysis for Parameter Extraction of Arbitrarily Shaped Interconnects

A surface integral equation (SIE) formulation under the magneto-quasi-static assumption is proposed to efficiently and accurately model arbitrarily shaped interconnects in packages. Through decently transferring all electromagnetic quantities into circuit elements, the loop analysis is used to carefully construct matrix equations with an independent and complete set of unknowns based on graph theory. In addition, an efficient preconditioner is developed, and the proposed formulation is accelerated by the pre-corrected Fast Fourier Transform (pFFT). Four practical examples, including a rectangular metallic interconnect, bounding wire arrays, interconnects in a real-life circuit and the power distribution network (PDN) used in packages, are carried out to validate its accuracy, efficiency and scalability. Results show that the proposed formulation is accurate, efficient and flexible to model complex interconnects in packages.

cs.CE↗

arXiv2022

Nonconformal Domain Decomposition Method Based on the Hybrid SIE-PDE Formulation for Flexible Transverse Magnetic Analysis

A nonconformal domain decomposition method based on the hybrid surface integral equation partial differential equation (SIE-PDE) formulation is proposed to solve the transverse magnetic electromagnetic problems. In the hybrid SIE-PDE formulation, an equivalent model with only the electric current density is first constructed, and then is embedded into the inhomogeneous Helmholtz equation as an excitation. A connection matrix, which couples the interfaces of the SIE and PDE domains, is carefully designed to support nonconformal meshes. Since meshes in each domain are independently generated, it is much more efficient and flexible to model multiscale and complex structures compared with the original hybrid SIE-PDE formulation with conformal meshes. The proposed formulation is efficient, flexible and easy to implement. Its accuracy, efficiency and flexibility are validated by three numerical examples.

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↗

arXiv2022

A SBP-SAT FDTD Subgridding Method Using Staggered Yee's Grids Without Modifying Field Components

A summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-domain (FDTD) subgridding method is proposed to model geometrically fine structures in this paper. Compared with our previous work, the proposed SBP-SAT FDTD method uses the staggered Yee's grid without adding or modifying any field components through field extrapolation on the boundaries to make the discrete operators satisfy the SBP property. The accuracy of extrapolation keeps consistency with that of the second-order finite-difference scheme near the boundaries. In addition, the SATs are used to weakly enforce the tangential boundary conditions between multiple mesh blocks with different mesh sizes. With carefully designed interpolation matrices and selected free parameters of the SATs, no dissipation occurs in the whole computational domain. Therefore, its long-time stability is theoretically guaranteed. Three numerical examples are carried out to validate its effectiveness. Results show that the proposed SBP-SAT FDTD subgridding method is stable, accurate, efficient, and easy to implement based on existing FDTD codes with only a few modifications.

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↗

arXiv2021

A Hybrid SIE-PDE Formulation Without Boundary Condition Requirement for Transverse Magnetic Electromagnetic Analysis

A hybrid surface integral equation partial differential equation (SIE-PDE) formulation without the boundary condition requirement is proposed to solve the transverse magnetic (TM) electromagnetic problems. In the proposed formulation, the computational domain is decomposed into two overlapping domains: the SIE and PDE domains. In the SIE domain, complex structures with piecewise homogeneous media, e.g., highly conductive media, are included. An equivalent model for those structures is constructed by replacing them with the background medium and introducing a surface equivalent electric current density on an enclosed boundary to represent their electromagnetic effects. The remaining computational domain and homogeneous background medium replaced domain consist of the PDE domain, in which inhomogeneous or non-isotropic media are included. Through combining the surface equivalent electric current density and the inhomogeneous Helmholtz equation, a hybrid SIE-PDE formulation is derived. It requires no boundary conditions, and is mathematically equivalent to the original physical model. Through careful construction of basis functions to expand electric fields and the equivalent current density, the discretized formulation is made compatible with the SIE and PDE domain interface. The accuracy and efficiency are validated through two numerical examples. Results show that the proposed SIE-PDE formulation can obtain accurate results, and significant performance improvements in terms of CPU time and memory consumption compared with the FEM are achieved.

math.NA↗

arXiv2021

An Adaptive Interpolation Scheme for Wideband Frequency Sweep in Electromagnetic Simulations

An adaptive interpolation scheme is proposed to accurately calculate the wideband responses in electromagnetic simulations. In the proposed scheme, the sampling points are first carefully divided into several groups based on their responses to avoid the Runge phenomenon and the error fluctuations, and then different interpolation strategies are used to calculate the responses in the whole frequency band. If the relative error does not satisfy the predefined threshold in a specific frequency band, it will be refined until the error criteria is met. The detailed error analysis is also presented to verify the accuracy of the interpolation scheme. At last, two numerical examples including the antenna radiation and the filter simulation are carried out to validate its accuracy and efficiency.

cs.CE↗

arXiv2021

Vector Single-Source Surface Integral Equation for TE Scattering From Cylindrical Multilayered Objects

A single-source surface integral equation (SS-SIE) for transverse electric (TE) scattering from cylindrical multilayered objects is proposed in this paper. By incorporating the differential surface admittance operator (DSAO) and recursively applying the surface equivalence theorem from innermost to outermost boundaries, an equivalent model with only electric current density on the outermost boundary can be obtained. In addition, an integration approach is proposed, where the small argument expansion of the Hankel function is used to evaluate the singular and nearly singular integrals. Compared with other SIEs, such as the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation, the computational expenditure is reduced for multilayered structures because only a single source is needed on the outermost boundary. As shown in the numerical results, the proposed method generates only 19% of unknowns, uses 26% of memory, and requires 29% of the CPU time of the PMCHWT formulation.

cs.CE↗

arXiv2021

Single-Source SIE for Two-Dimensional Arbitrarily Connected Penetrable and PEC Objects with Nonconformal Meshes

We proposed a simple and efficient modular single-source surface integral equation (SS-SIE) formulation for electromagnetic analysis of arbitrarily connected penetrable and perfectly electrical conductor (PEC) objects in two-dimensional space. In this formulation, a modular equivalent model for each penetrable object consisting of the composite structure is first independently constructed through replacing it by the background medium, no matter whether it is surrounded by the background medium, other media, or partially connected objects, and enforcing an equivalent electric current density on the boundary to remain fields in the exterior region unchanged. Then, by combining all the modular models and any possible PEC objects together, an equivalent model for the composite structure can be derived. The troublesome junction handling techniques are not needed and non-conformal meshes are intrinsically supported. The proposed SS-SIE formulation is simple to implement, efficient, and flexible, which shows significant performance improvement in terms of CPU time compared with the original SS-SIE formulation and the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation. Several numerical examples including the coated dielectric cuboid, the large lossy objects, the planar layered dielectric structure, and the partially connected dielectric and PEC structure are carried out to validate its accuracy, efficiency and robustness.

cs.CE↗

arXiv2020

Formulation of Single-Source Surface Integral Equation for Electromagnetic Analysis of Composite Penetrable Objects

This paper presents a new single-source surface integral equation (SS-SIE) to model composite penetrable objects. In the proposed formulation, the surface electric and magnetic fields on all interior boundaries are first eliminated through combining integral solutions inside each object. Then, by enforcing the surface electric fields in the original and equivalent configurations are equal to each other, an equivalent model with only the electric current density on the outermost boundaries is derived. Compared with other SIEs, like the PMCHWT formulation, all unknowns are residing on the outermost boundaries in the proposed formulation and therefore, less count of unknowns can be obtained. Finally, two numerical examples are carried out to validate the effectiveness of the proposed SS-SIE.

cs.CE↗

arXiv2020

Investigation of Numerical Dispersion with Time Step of The FDTD Methods: Avoiding Erroneous Conclusions

It is widely thought that small time steps lead to small numerical errors in the finite-difference time-domain (FDTD) simulations. In this paper, we investigated how time steps impact on numerical dispersion of two FDTD methods including the FDTD(2,2) method and the FDTD(2,4) method. Through rigorously analytical and numerical analysis, it is found that small time steps of the FDTD methods do not always have small numerical errors. Our findings reveal that these two FDTD methods present different behaviors with respect to time steps: (1) for the FDTD(2,2) method, smaller time steps limited by the Courant-Friedrichs-Lewy (CFL) condition increase numerical dispersion and lead to larger simulation errors; (2) for the FDTD(2,4) method, as time step increases, numerical dispersion errors first decrease and then increase. Our findings are also comprehensively validated from one- to three-dimensional cases through several numerical examples including wave propagation, resonant frequencies of cavities and a practical electromagnetic compatibility (EMC) problem.

cs.CE↗

arXiv2020

Towards a Unified Approach to Electromagnetic Analysis by Objects Embedded in Multilayers

In this paper, an efficient and accurate unified approach is proposed to solve transverse magnetic scattering problems by multilayer embedded objects. In the proposed approach, an equivalent current density is derived when the equivalent theorem is recursively applied on each boundary from inner to exterior regions. Then, the objects are replaced by the background medium and the equivalent electric current density enforced on the outermost boundary remains fields in the exterior region unchanged. Therefore, the scattering problems by the multilayer embedded objects can be solved with the electric field integral equation (EFIE). Compared with other two-region formulations (TRFs), like the PMCHWT, CTF, the proposed approach shows significant benefits: only the surface electric current density instead of both the electric and magnetic current densities is required to model the complex objects. Furthermore, the single electric current density is only enforced on the outermost boundary of objects. Therefore, the overall count of unknowns can be significantly reduced, especially when the number of boundaries between different homogeneous media is large. At last, several numerical experiments are performed to validate the accuracy and efficiency of the proposed approach.

cs.CE↗

arXiv2019

An Accurate Edge-based FEM for Electromagnetic Analysis with Its Applications to Multiscale Structures

This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of accuracy and numerical stability for mesh distortion compared with the traditional FEM. Unlike the traditional FEM, the computational domain in ES-FEM is divided into nonoverlapping smoothing domains associated with each edge of elements, triangles in two dimensional domain and tetrahedrons in three dimensional domain. Then, the gradient smoothing technique (GST) is used to smooth the gradient components in the stiff matrix of the FEM. Several numerical experiments are carried out to validate its accuracy and numerical stability. Numerical results show that the ES-FEM can obtain much more accurate results and is almost independent of mesh distortion.

cs.CE↗

arXiv2019

A Surface Integral Formulation for Scattering Modeling by 2D Penetrable Objects

In this paper, we proposed a single-source surface integral formulation to accurately solve the scattering problems by 2D penetrable objects. In this method, the objects are replaced by their surrounding medium through enforcing a surface equivalent electric current to ensure fields exactly the same as those in the original scattering problem. The equivalent electric current is obtained through emitting the equivalent magnetic current by enforcing that the electric fields in the original and equivalent problems equal to each other. Through solving the Helmholtz equation inside objects by the scalar second Green theorem, we could accurately model arbitrarily shaped objects. Then, we solve the exterior scattering problems through the combined integral equation (CFIE) with the equivalent electric current. The proposed formulation only requires a single electric current source to model penetrable objects. At last, two numerical experiments are carried out to validate its accuracy, stability and capability of handling non-smoothing objects.

cs.CE↗