finite-difference time-domain simulation

FDTD-based electromagnetic simulations suffer from poor portability, high development overhead, and performance bottlenecks on modern hardware. To address these challenges, this paper introduces the first MLIR/LLVM-based domain-specific compiler for FDTD. It models the 3D FDTD kernel as semantically explicit 3D tensor operations and proposes a novel high-order tensor abstraction with an automated optimization framework supporting loop tiling, fusion, and vectorization. The compiler features hardware-aware, end-to-end code generation across heterogeneous platforms (x86 and ARM). Experimental evaluation demonstrates up to 10× speedup over NumPy baselines across multiple architectures. By eliminating manual tuning, it overcomes performance fragmentation and non-portability inherent in conventional approaches, thereby significantly improving simulation efficiency, scalability, and deployment flexibility.

Accurately simulating lightning electromagnetic field (LEMF) propagation remains challenging due to the broadband, transient nature of lightning radiation and the sensitivity of finite-difference time-domain (FDTD) solvers to numerical dispersion, boundary reflections, and ground conductivity modeling. Method: This study systematically evaluates the applicability and accuracy of three open-source FDTD solvers—Elecode, gprMax, and MEEP—for LEMF simulation. Using a unified modeling framework—including perfectly matched layers (PML), dispersion control, and consistent material parameterization—we conduct comparative simulations under ideal and lossy ground conditions for canonical lightning radiation scenarios, validating results quantitatively against analytical solutions or high-fidelity reference data. Contribution/Results: We identify critical impacts of spatial discretization, grid resolution, and PML configuration on far-field waveform fidelity, and characterize typical failure modes arising from suboptimal parameter choices. The work delivers a reproducible benchmarking protocol and an open-source script library, providing practitioners with rigorous, evidence-based guidance for selecting and configuring FDTD tools in lightning electromagnetic compatibility analysis and protection design.

Existing virtual acoustic simulation methods struggle to simultaneously achieve physical accuracy for low-frequency phenomena—such as diffraction and interference—and real-time performance. This paper proposes a hybrid acoustic modeling framework based on two-dimensional finite-difference time-domain (2D FDTD) simulation, tightly integrated with Unreal Engine’s audio rendering pipeline. Scene geometry is projected to generate obstacle masks and boundary conditions; sine-swept excitation combined with deconvolution is employed to extract spatially resolved, multi-channel impulse responses. To our knowledge, this is the first end-to-end integration of a Python-based FDTD wavefield solver with a commercial game engine’s real-time audio system. The framework supports dynamic occlusion, reflection, diffraction, and interference while preserving physical fidelity. Experimental validation confirms that the computed impulse responses align closely with theoretical predictions. Results demonstrate significant improvements in spatial audio realism and immersion for VR and interactive media applications.

Low-frequency numerical instability severely limits time-domain simulations of broadband electromagnetic fields. Method: This paper proposes a stabilized two-step time-domain finite element method, combining Galerkin spatial discretization with a stepwise temporal integration scheme. Crucially, it introduces the generalized tree–cotree gauge into the time-domain framework for the first time, effectively eliminating the singularity of the curl operator and ensuring convergence in the static limit. Contribution/Results: The method overcomes the low-frequency instability inherent in conventional time-domain approaches and natively supports nonlinear and temperature-dependent material constitutive relations. Validated on multiple academic and industrial-grade 3D benchmark problems, it demonstrates robust stability across the entire frequency spectrum, high accuracy, and strong computational reliability. Thus, it establishes a scalable, physically consistent time-domain paradigm for complex multiphysics electromagnetic simulations.

High computational cost and poor parallel scalability hinder time-domain simulations of low-frequency electromagnetic eddy current problems. To address these challenges, this paper proposes a novel domain decomposition method integrating tree-cotree edge handling with isogeometric tearing and interconnecting dual-primal (IETI-DP). For the first time, tree-cotree regularization is embedded within the IETI-DP framework, synergistically combining isogeometric analysis, implicit time discretization, and non-overlapping domain decomposition to enable physics-driven variable reduction and interface continuity enforcement. Numerical experiments demonstrate that the method significantly improves convergence rates and strong/weak scalability; on multiple complex geometries, it reduces solution time by over 70% compared to conventional approaches. The proposed framework establishes a new paradigm for large-scale transient eddy current simulation—achieving high accuracy, numerical robustness, and superior parallel efficiency.

This study addresses the challenge of achieving consistency between simulation and physical models in silicon-based directional coupler design by proposing an automated framework coordinated by a large language model (LLM). In this approach, the LLM acts as an intelligent scheduler that generates geometric parameters and assesses convergence, while a frequency-domain eigenmode solver computes the coupling coefficient and a finite-difference time-domain (FDTD) method provides independent validation—both grounded in a unified two-dimensional effective index model. The key innovation lies in employing the LLM as a coordinator rather than an executor of the design process, coupled with a novel closed-loop length correction enabled by identifying a constant phase offset. The method successfully designs a 50/50 splitting-ratio coupler, with FDTD-validated cross-coupling of 0.498 (an error of only 0.0017), and demonstrates that the phase offset remains invariant across varying coupling strengths.

This work proposes a stable subgridding method for SBP-SAT FDTD that eliminates the need for domain decomposition or multi-block structures, which traditionally lead to high computational complexity and domain fragmentation. By designing embedding-aware projection SBP operators together with compatible SAT boundary conditions, the approach enables direct coupling between fine and coarse grids within a single computational domain. This strategy avoids auxiliary blocks or explicit domain partitioning, substantially reducing the number of SAT interfaces while preserving long-term numerical stability and enhancing interfacial accuracy. Numerical experiments demonstrate that the proposed method outperforms existing approaches in terms of computational efficiency, solution accuracy, and topological flexibility.

This study addresses the efficient implementation of the three-dimensional finite-difference time-domain (3D FDTD) algorithm in multi-GPU environments, systematically evaluating the impact of various communication strategies on the overhead introduced by convolutional perfectly matched layers (CPML). Through comparative analysis of host-mediated versus GPU-direct communication and ghost-cell extension techniques, the work demonstrates that GPU-direct communication is the dominant optimization, whereas extending ghost regions yields marginal gains. Experimental results show single-GPU performance of 28.89–32.9 billion output points per second with CPML overhead below 1%. GPU-direct communication achieves a 2.46–2.76× speedup over host-mediated transfer. Strong scaling yields a 1.51× acceleration with two GPUs, and four GPUs successfully overcome single-card memory limitations to simulate extremely large grids.

This work proposes a scalable parallel interpolation algorithm to address the challenge of data consistency across multiple solvers in overlapping grid regions for atmospheric wave simulations. The method enables efficient, in situ data coupling between solvers by introducing a grid-coupling mechanism tailored for large-scale parallel environments, ensuring global solution consistency while balancing computational efficiency and communication overhead. Evaluated in realistic atmospheric wave simulation scenarios, the algorithm demonstrates strong scalability and high performance, significantly improving both the accuracy and efficiency of data exchange among multiphysics solvers.

This study addresses the need for efficient modeling of complex electromagnetic far-field behavior in modern wireless systems, where precise control and reflection of electromagnetic waves are critical. Building upon Maxwell’s equations and integrating frequency-domain bandwidth modeling with finite-rank operator approximation theory, the work rigorously establishes—for the first time—that the far-field response of general antenna architectures possesses intrinsic finite complexity. It further demonstrates that the approximation error decays super-exponentially with increasing operator rank. These findings provide a foundational finite-parameter representation theory for antenna far fields, offering a rigorous theoretical basis for high-fidelity, computationally efficient digital electromagnetic simulations.