Search Results (15)

As a foundation for numerical solvers in computational electromagnetics, particularly for multiphysics and electromagnetic compatibility applications, Jefimenko’s equations offer a generalized solution to Maxwell’s equations, enabling the direct computation of electromagnetic fields from time-dependent source distributions without the boundary-condition artifacts inherent to grid-based methods. However, the numerical integration of these equations is computationally intensive, typically scaling as $\mathcal{O}\left(N_{\mathrm{s}}{N}_{\mathrm{o}}\right)$ for $N_{\mathrm{s}}$ source points and $N_{\mathrm{o}}$ observation points. In this paper, we present JefiFast, a highly optimized graphics processing unit (GPU) implementation that significantly outperforms the state-of-the-art JefiGPU algorithm. We identify that previous implementations are strictly memory-bound due to inefficient global memory transactions and a lack of data reuse. JefiFast addresses these bottlenecks through four key optimizations: (i) a packed memory layout (PML) using an array-of-structures approach to ensure coalesced memory access for source densities and their derivatives; (ii) geometry-aware shared memory tiling strategies that maximize L2 (level-2) cache hit rates and on-chip data reuse; (iii) pre-computation of time derivatives to minimize redundant arithmetic operations; and (iv) a robust observation domain decomposition strategy that enables linear scaling across multiple GPUs. Benchmarks demonstrate that JefiFast achieves speedups ranging from $4.08$ times (for ${30}^3$ grids on a single NVIDIA V100 graphic processor) to $84.51$ times (for ${50}^3$ grids on 4 NVIDIA V100 processors) compared to the baseline. Notably, for a ${50}^3$ grid on a single GPU, JefiFast reduces execution time from about 51 min to just about 2.6 min ($19.54$ times speedup). These performance advances make high-resolution relativistic heavy-ion collision simulations feasible in near real-time. Full article

This study aims to address the acoustic resonance control problem of a three-dimensional nose landing gear (NLG) cavity. We propose a refined numerical approach based on an eigenvalue solver for the Helmholtz equation. A high-order finite element method (FEM) combined with perfectly matched layer (PML) boundary conditions was employed to accurately capture complex eigenmodes. The radiation damping characteristics of the system were then quantitatively characterized using the quality factor (Q-factor) and resonance frequency. Results indicate that the Helmholtz-type (0,0,0) mode dominates the cavity’s resonance response, with its frequency coinciding with the shear layer-driven Rossiter mode. This study reveals a strong coupling mechanism with the shear-layer-driven Rossiter mode at Mach 0.57, confirming that this interaction is the primary driver of cavity aeroacoustic tonal noise. Taking radiation damping as the core design parameter, a systematic sensitivity analysis was conducted on geometric modifications: aft door length, front door angle, cavity volume, and the introduction of a longitudinal gap. Key findings: shortening the aft door reduces the resonance peak by 8.5 dB; introducing a longitudinal gap with a 10% width reduces the Q-factor by approximately 50%; a combined control strategy (2.5% gap width and 6% cavity volume reduction) achieves 4.9 dB of noise attenuation. Finally, this study establishes a validated acoustic-damping control framework, providing quantitative design criteria and technical guidance for aeroacoustic noise control of NLG cavities. Full article

The simulation of wave propagation, such as soliton propagation, based on the Rosenau-KdV-RLW equation on unbounded domains requires a bounded computational domain. Therefore, a special boundary treatment, such as an absorbing boundary condition (ABC) or a perfectly matched layer (PML), is necessary to minimize the reflections of outgoing waves at the boundary, preventing interference with the simulation’s accuracy. However, the presence of higher-order partial derivatives, such as $u_{xxt}$ and $u_{xxxxt}$ in the Rosenau-KdV-RLW equation, raises challenges in deriving accurate artificial boundary conditions. To address this issue, we propose an artificial neural network (ANN) method that enables soliton propagation through the computational domain without imposing artificial boundary conditions. This method randomly selects training points from the bounded computational space-time domain, and the loss function is designed based solely on the initial conditions and the Rosenau-KdV-RLW equation itself, without any boundary conditions. We analyze the convergence of the ANN solution theoretically. This new ANN method is tested in three examples. The results indicate that the present ANN method effectively simulates soliton propagation based on the Rosenau-KdV-RLW equation in unbounded domains or over extended periods. Full article

Seismic wave propagation in complex terrains, especially in the presence of air layers, plays a crucial role in accurate subsurface imaging. However, the influence of different boundary conditions on seismic wave propagation characteristics has not been fully explored. This study employs the finite element method (FEM) to simulate and analyze seismic wavefields under different boundary conditions, including perfectly matched layer (PML), Neumann free boundary conditions, and air layer conditions. First, the finite element solution for the 2D frequency-domain acoustic wave equation is introduced, and the correctness of the algorithm is validated using a homogeneous model. Then, both horizontal and undulating terrain interfaces are designed to investigate the kinematic and dynamic characteristics of the wavefields under different boundary conditions. The results show that PML boundaries effectively absorb seismic waves, prevent reflections, and ensure stable wave propagation, making them an ideal choice for simulating open boundaries. In contrast, Neumann boundaries generate significant reflected waves, particularly in undulating terrains, complicating the wavefield characteristics. Introducing an air layer alters the dynamics of the wavefield, leading to energy leakage and multi-path effects, which are more consistent with real-world seismic-geophysical models. Finally, the computational results using the Overthrust model under different boundary conditions further demonstrate that different boundary conditions significantly affect wavefield morphology. It is essential to select appropriate boundary conditions based on the specific simulation requirements, and boundary conditions with an air layer are most consistent with real seismic geological models. This study provides new insights into the role of boundary conditions in seismic numerical simulations and offers theoretical guidance for improving the accuracy of wavefield simulations in realistic geological scenarios. Full article

In order to analyze the ground vibration responses induced by the dynamic loads in a tunnel, this paper proposes a new simplified tunnel–soil model. Specifically, based on the basic theory of the thin-layer method (TLM), the basic solution of three-dimensional layered foundation soil displacement was derived in the cylindrical coordinate system. The perfectly matched layer (PML) boundary condition was applied to the TLM. Subsequently, a tunnel–soil dynamic interaction analysis model was established using the volume method (VM) in conjunction with the TLM-PML method. The displacement frequency response function of the foundation soil around the tunnel foundation was derived. Finally, a ground vibration test under an impact load in a tunnel was carried out. The test and calculated results were compared. The comparison results show that the ground vibration acceleration response values within 25 m from the load are similar. Compared with the test results, the theoretical calculation results exhibit a decreasing trend in the range of 40–80 Hz between 25 and 60 m, with the maximum reduction being approximately one order of magnitude. In addition, the experimental comparison demonstrates that the model can be used to analyze the ground vibrations caused by underground loads. Full article

The time-fractional Cattaneo (TFC) equation is a practical tool for simulating anomalous dynamics in physical diffusive processes. The existing numerical solutions to the TFC equation generally deal with the Dirichlet boundary conditions. In this paper, we incorporate the absorbing boundary condition as a complex-frequency-shifted (CFS) perfectly matched layer (PML) into the TFC equation. Then, we develop an adaptive-coefficient (AC) finite-difference frequency-domain (FDFD) method for solving the TFC with CFS PML. The corresponding analytical solution for homogeneous TFC equation with a point source is proposed for validation. The effectiveness of the developed AC FDFD method is verified by the numerical examples of four typical TFC models, including the different orders of time-fractional derivatives for both the homogeneous model and the layered model. The numerical examples show that the developed AC FDFD method is more accurate than the traditional second-order FDFD method for solving the TFC equation with the CFS PML absorbing boundary condition, while requiring similar computational costs. Full article

In the fields of structural and geotechnical engineering, improving the understanding of soil–structure interaction (SSI) effects is critical for earthquake-resistant design. Engineers and practitioners often resort to finite element (FE) software to advance this objective. Unfortunately, the availability of software equipped with boundary representation for absorbing scattered waves and ensuring consistent input ground motion prescriptions, which is necessary for accurately representing SSI effects, is currently limited. To address such limitations, the authors developed Seismo-VLAB (SVL v1.0-stable) an open-source software designed to perform SSI simulations. The methodology considers the integration of advanced techniques, including the domain decomposition method (DDM), perfectly matched layers (PMLs), and domain reduction method (DRM), in addition to parallel computing capabilities to accelerate the solution of large-scale problems. In this work, the authors provide a detailed description of the implementation for addressing SSI modeling, validate some of the SVL’s features needed for such purpose, and demonstrate that the coupled DRM–PML technique is a necessary condition for accurately solving SSI problems. It is expected that SVL provides a significant contribution to the SSI research community, offering a self-contained and versatile alternative. The software’s practical application in analyzing SSI and directionality effects on 3D structures under seismic loading demonstrates its capability to model real-world earthquake responses in structural engineering. Full article

Understanding the effect of vortexes on sound propagation is of great significance in the field of target detection and acoustic imaging. A prediction algorithm of the two-dimensional vortex scattering is realized based on a finite-difference frequency-domain (FDFD) numerical scheme with perfectly matched layers (PML). Firstly, the governing equation for flow–sound interaction is given based on the perturbation theory, and the FDFD program is built. Subsequently, the mesh independence is verified, and the result has a good convergence when the mesh corresponds to over 15 nodes per wavelength. Then, computational parameters of the PML are discussed to achieve better absorbing boundary conditions. Finally, the results of this algorithm are compared with previous literature data. Results show that for different cortex scattering cases, the absorption coefficient should vary linearly with the density of the medium and the incident wave frequency. When the thickness of the PML boundary is greater than 2.5 times the wavelength, the PML boundary can absorb the scattering sound effectively. This provides a reliable algorithm for the numerical study of the effect of vortexes on sound propagation. Full article

In this paper, the combined compact difference scheme (CCD) and the combined supercompact difference scheme (CSCD) are used in the numerical simulation of the shear-wave equation. According to the Taylor series expansion and shear-wave equation, the fourth-order discrete scheme of the displacement field is established; then, the CCD and CSCD schemes are used to calculate the spatial derivative of the displacement field. Additionally, the accuracy, dispersion, and stability of the CCD and CSCD are analyzed, and numerical simulation analyses are carried out using 1D uniform models. Lastly, based on the processing of artificial boundary reflection using PML boundary conditions, shear-wave reverse-time migrations are carried out using synthetic data. The results show that (1) CCD and CSCD have smaller truncation errors, higher simulation precision, and lower numerical dispersion than other normal difference schemes; (2) CCD and CSCD can use the coarse grid and larger time step to calculate, with less memory and high computational efficiency; (3) finally, the result of the shear-wave reverse-time migration of the 2D synthetic data model show that the reverse-time migration imaging is clear, and the proposed method for shear-wave reverse-time migration is practical and effective. Full article

Waveguide-like transmission line (WLTL) structures, including rectangular waveguides, circular waveguides, and coaxial lines, have been widely used in microwave engineering. Determining how to efficiently model WLTLs has become vital for the design of various WLTL-based devices. In this paper, a circuit-based wave port boundary condition (CWPBC) is developed and applied in the discontinuous Galerkin time-domain (DGTD) method to accurately simulate these structures for the first time. In the CWPBC, modal voltages and currents of a WLTL are defined, and circuits based on modal voltages and currents are introduced. By co-simulating the modal circuit and the WLTL modeled using the DGTD method, various modal fields can be excited in the WLTL, and at the same time, the WLTL can be terminated without reflections. No extra costs or approximations are used in the proposed CWPBC, and there is no requirement of either the extension of the computational domains widely used in perfectly matched layer (PML) termination or the longitudinal field continuity used in the reported DGTD method. The proposed method can easily obtain the postprocessing parameters, including S-parameters and port power. Numerical results, including rectangular waveguide filters, circular waveguide horns, and coaxial-fed electromagnetic bandgaps (EBG), are given to validate the effectiveness of the proposed CWPBC. Full article

In this article, an efficient Z-transform-based finite-difference time-domain (Z-FDTD) is developed to implement and analyze electromagnetic scatterings in the 3D biaxial anisotropy. In terms of the Z-transform technique, we first discuss the conversion relationship between time- or frequency-domain derivative operators and the corresponding Z-domain operator, then build up the Z-transform-based iteration from the electric flux D converted to the electric field E based on dielectric tensor ε (and from the magnetic flux B converted to the magnetic field H in line with permeability tensor μ) by combining the constitutive formulations about the biaxial anisotropy. As a result, the iterative process about the Z-FDTD implementation can be smoothly carried out by means of combining with the Maxwell’s equations. To our knowledge, it is inevitably necessary for the absorbing boundary condition (ABC) to be considered in the electromagnetic scattering; hence, we utilize the unsplit-field complex-frequency-shifted perfectly matched layer (CFS-PML) to truncate the Z-FDTD’s physical region, and then capture time- and frequency-domain radiation with the electric dipole. In the 3D simulations, we select two different biaxial anisotropic models to validate the proposed formulations by using the popular commercial software COMSOL. Moreover, it is certain that those results are effective and available for electromagnetic scattering problems under the oblique incidence executed by the Z-FDTD method. Full article

A dual-channel propagation controlled photonic crystal fiber (PCF)-based plasmonic sensor was presented to detect multiple analytes simultaneously. Plasmonic micro-channels were placed on the outer surface of the PCF, which facilitates an easy sensing mechanism. The sensor was numerically investigated by the finite element method (FEM) with the perfectly matched layer (PML) boundary conditions. The proposed sensor performances were analyzed based on optimized sensor parameters, such as confinement loss, resonance coupling, resolution, sensitivity, and figure of merit (FOM). The proposed sensor showed a maximum wavelength sensitivity (WS) of 25,000 nm/refractive index unit (RIU) with a maximum sensor resolution (SR) of 4.0 × 10⁻⁶ RIU for channel 2 (Ch-2), and WS of 3000 nm/RIU with SR of 3.33 × 10⁻⁵ RIU for channel 1 (Ch-1). To the best of our knowledge, the proposed sensor exhibits the highest WS compared with the previously reported multi-analyte based PCF surface plasmon resonance (SPR) sensors. The proposed sensor could detect the unknown analytes within the refractive index (RI) range of 1.32 to 1.39 in the visible to near infrared region (550 to 1300 nm). In addition, the proposed sensor offers the maximum Figure of Merit (FOM) of 150 and 500 RIU⁻¹ with the limit of detection (LOD) of 1.11 × 10⁻⁸ RIU²/nm and 1.6 × 10⁻¹⁰ RIU²/nm for Ch-1 and Ch-2, respectively. Due to its highly sensitive nature, the proposed multi-analyte PCF SPR sensor could be a prominent candidate in the field of biosensing to detect biomolecule interactions and chemical sensing. Full article

This paper proposes a Photonic Crystal Fiber (PCF) refractive index sensor model based on the surface plasmon resonance effect. The proposed PCF model also uses the full vector finite element method to transfer the structure under the anisotropic Perfect Matching Layer (PML) boundary condition. Numerical calculations were carried out on the sensor characteristics. The calculation results show that the elliptical air hole on the left side of the PCF core is coated with a gold-nano film which serves as a Surface Plasmon Resonance (SPR) sensing channel to detect the refractive index of liquid materials. Compared with other structures, the resonant peak generated by the excited SPR effect from the elliptical sensing channel has a high sensitivity to the change of the refractive index of the liquid to be measured. With the help of this attribute, it is relatively easy to adjust the sensitivity. The refractive index range of this structure is within 1.43–1.49 and the sensitivity is up to 12,719.97 nm·RIU⁻¹. The linearity is good; R² = 0.99927, which is very suitable for liquid sensing. Full article

This paper proposes an efficient technique to solve the electromagnetic scattering problem, in the near zone of scatterers illuminated by external fields. The technique is based on a differential formulation of the Helmholtz equation discretized in terms of a finite element method (FEM). In order to numerically solve the problem, it is necessary to truncate the unbounded solution domain to obtain a bounded computational domain. This is usually done by defining fictitious boundaries where absorbing conditions are imposed, for example by applying the perfect matching layer (PML) approach. In this paper, these boundary conditions are expressed in an analytical form by using the Dirichlet-to-Neumann (DtN) operator. Compared to classical solutions such as PML, the proposed approach based on the DtN: (i) avoids the errors related to approximated boundary conditions; (ii) allows placing the boundary in close proximity to the scatterers, thus, reducing the solution domain to be meshed and the related computational cost; (iii) allows dealing with objects of arbitrary shapes and materials, since the shape of the boundary independent from those of the scatterers. Case-studies on problems related to the scattering from cable bundles demonstrate the accuracy and the computational advantage of the proposed technique, compared to existing ones. Full article

In this paper, we numerically demonstrate a two-layer circular lattice photonic crystal fiber (PCF) biosensor based on the principle of surface plasmon resonance (SPR). The finite element method (FEM) with circular perfectly matched layer (PML) boundary condition is applied to evaluate the performance of the proposed sensor. A thin gold layer is deposited outside the PCF structure, which acts as the plasmonic material for this design. The sensing layer (analyte) is implemented in the outermost layer, which permits easy and more practical fabrication process compared to analyte is put inside the air holes. It is demonstrated that, at gold layer thickness of 40 nm, the proposed sensor shows maximum sensitivity of 2200 nm/RIU using the wavelength interrogation method in the sensing range between 1.33–1.36. Besides, using an amplitude interrogation method, a maximum sensitivity of 266 RIU⁻¹ and a maximum sensor resolution of 3.75 × 10⁻⁵ RIU are obtained. We also discuss how phase matching points are varied with different fiber parameters. Owing to high sensitivity and simple design, the proposed sensor may find important applications in biochemical and biological analyte detection. Full article