Vector Finite Element Method Research Articles

2D Magnetotelluric Resistivity Structure Modeling Using Finite Element Method Based on Vector Triangular Grid and Its Application to Lembang Fault MT Data

Abstract Magnetotellurics is one of the geophysical exploration techniques that relies on the natural fluctuations of electromagnetic waves to delineate their influence on the Earth. The primary focus of this method is to reveal the structure of Earth’s subsurface with the value of resistivity. The application of numerical approaches in magnetotelluric modeling has proven to be an efficient method in various theoretical studies in the field of geophysics, particularly in the context of modeling two-dimensional structures. This research explains a 2D resistivity structure modeling using a vector finite element method. This approach utilizes the edges of elements as vector bases. The presented results include response values such as apparent resistivity and impedance phase at the surface. The study employs the standard model from COMMEMI as a reference to validate the modeling program. Furthermore, the results from this modeling program are compared with the outcomes of the modeling program developed by Weaver et al. The good results were obtained with error values for each model for layered and homogeneous Earth < 3%. Additionally, for the reference model COMMEMI, errors of 3.4393% and 1.4050% were obtained for TE and TM modes, respectively. Furthermore, apparent resistivity and impedance phase results closely approximated the reference values for the topography model. Subsequently, in the application to field data, specifically the Lembang Fault, errors were obtained for the TE and TM modes within the range of 1.16 – 9.16% for each MT data acquisition site.

Transient Electromagnetic Monitoring of the Cryolithozone: Mathematical Modeling

Abstract ––The paper presents theoretical results on mathematical modeling and numerical inversion of transient electromagnetic data for the monitoring of the state of the cryolithozone. Solutions to the direct and inverse problems are considered based on the vector finite element method, the Sumudu integral transform and the apparatus of artificial neural networks. We show the capability of spatial localization of thaw zones (taliks) with transient cross-borehole exploration systems in a geoelectric model that takes into account the dispersive properties of frozen rocks. The performance and accuracy of the developed algorithms are assessed.

Global mantle conductivity imaging using 3-D geomagnetic depth sounding with real earth surface conductivity constraint

The water content in the Earth's interior is of great significance for material circulation and the dynamic evolution of the planet. The water content in mantle minerals significantly affects their conductivities. By measuring the variations in conductivity within the Earth, we can infer the water content in the mantle and study the movement and processes of materials within the Earth. The geomagnetic depth sounding is a widely used method for imaging the mantle conductivity as it has large sounding depth. However, the ocean induction effects can seriously impact geomagnetic data that can't be well corrected using conventional methods. Here, we present a novel three-dimensional inversion method for geomagnetic depth sounding to overcome the ocean induction effects by directly adopt the real earth surface conductivity into the inverse model. In this method, the unstructured tetrahedral grids are used to represent the model in multi-scale and the vector finite-element method is adopted to accurately compute the geomagnetic responses. The synthetic model tests show that the earth surface conductivity has serious effect on the inversion results, but it can be well suppressed by directly modeling it in the inverse model. We further invert the data from 128 geomagnetic stations around the world and obtain a more accurate new model of global mantle conductivity.

Design of hexagonal shaped spectroscopy based biosensor for the detection of tuberculosis

A proposal has been made to identify tuberculosis cells using a novel compact sensor based on photonic crystal fiber: PCF in accordance with hexagonal spectroscopy. This proposed structure, which consists of a closely packed hexagonal air hole in the cladding region and a hollow-core area, possesses a very low loss of 6.30 × 10−8 dB/m and an exceptionally high sensitivity of up to 91.75 % (tuberculosis cell for 1.345). Numerous optical parameters have been identified and assessed, comprised of the numerical aperture, the V-parameter, or normalized frequency (Veff), and the effective area (Aeff). The operational wavelength range is defined as 0.80–3.0 THz. The numerical investigation of the properties of the proposed TB sensors is performed within the environment of COMSOL Multiphysics (Version 5.3) using FV-FEM stands for the full vector finite element method. PCF sensors composed of hexagonal lattice in a circular form with ZEONEX as the backdrop material is intended to boost the sensitivity response in comparison to the earlier works. Additionally, the sensor that is being displayed achieves a single modality throughout its whole operational wavelength range. This proposed sensor may play a significant role in identifying tuberculosis thanks to its superior sensitivity response and extremely minimal confinement loss. So, it is clearly seen that this sensor could be used to bio-medical sectors with process of terahertz (THz) wave pulse.

Powerful numerical method for analysis of electromagnetic scattering from multiple 3D coated targets buried under rough surface

ABSTRACT In this work, an efficient numerical method is proposed for three-dimensional (3D) electromagnetic scattering from multiple coated targets buried under a two-dimensional dielectric rough surface. In the proposed method, the interior region of each coated target is regarded as an independent subregion. The field within each coated target is modeled by 3D vector finite element method (FEM). The multiple scattering interactions between the buried targets and between targets and rough surface are considered by the electric field integral equation and the Poggio–Miller–Chang–Harrington–Wu integral equations, respectively. The fields inside and outside the targets are coupled together via boundary conditions on the boundary of each target. To improve the calculation efficiency and reduce the memory requirement, the fast multipole technique is used in our method. The presented method is numerically validated by comparing it with method of moments and conventional FEM-boundary integral method (BIM). The results indicate that, compared with traditional FEM-BIM, our method has significant advantages in computational efficiency and memory requirements.

Influence of Magnetic Polarization on Diagrams of Inductive and Electromagnetic Logs

Abstract ––We present the results of the study of the effect of induced magnetic polarization of clay beds under the influence of an external harmonic electromagnetic field (frequencies 70 and 875 kHz). A two-stage numerical modeling procedure is proposed. At the first stage we determine the effective relative magnetic permeability of a synthetic sample with inclusions of clay particles. In this case a 3D heterogeneous mesh sample is generated. Then we numerically model a spatial distribution of an electric field. The electromotive force (EMF) induced in the measuring coil is calculated from this distribution. Relative magnetic permeability is determined by comparison with EMF of homogeneous samples with different values of magnetic permeability. It has been found that during the electric field excitation by an alternating current coil, the effect of induced magnetic polarization appears in the sample with clay particles. Its manifestation is that the effective magnetic permeability becomes complex. At the second stage we calculate the EMF diagram of the three-coil logging probe in the macro-model ‘clay cap – reservoir’. Magnetic permeability of the clay cap is given by a complex value. In the generated logs, extremes appear in the vicinity of the bottom of the clay cap; they do not correspond to the distribution of electrical conductivity and magnetic permeability in the given model. They can be incorrectly interpreted when analyzing real logs into individual formations. Numerical modeling at all stages is performed by the Vector Finite Element Method on a consistent adaptive tetrahedral partition and the first-order Webb vector basis.

Broadband dispersion compensation and high birefringence photonic crystal fiber for CWDM/DWDM networks

In this study, we propose a new design based on photonic crystal fibers (PCFs) for broadband dispersion compensation in telecommunication networks. The proposed design has a hexagonal structure arrangement of air-holes rings of different diameters between the silica core and the cladding. The PCF properties like effective area, nonlinearity, dispersion slope, confinement loss, and birefringence are reported and discussed. For the best performance we present three designs A, B and C. Simulation results show that the three designs cover the six-telecommunication optical bands O-, E-, S-, C-, L- and U- bands (wavelengths ranging from 1260 to 1675 nm). Design A achieves a large negative dispersion value of about − 1716 ps/(nm.km) with relative dispersion slope equals to that of conventional single-mode optical fibers (SMFs) of about 0.0036 nm−1, which makes it very suitable for long-haul DWDM transmission systems. With a little modification in the core, designs B and C achieve much higher confinement ability and achieve a very large birefringence value for polarization mode dispersion and sensing applications. Design C is engineered to have exact opposite dispersion of SMF with zero dispersion at the wavelength 1310 nm, which makes it a promising design in CWDM transmission system. The numerical values have been investigated using the full vector finite element method.

Fiber design and performance analyses for optical multiplexing: terahertz optical communications

Multiplexing is the process of combining multiple signals at a single channel. Orbital Angular Momentum (OAM) is one of the main multiplexing techniques for optical data transmissions. This paper examines and suggests a hollow core with four layers of semilunar air-hole-shaped circular photonic crystal fiber (PCF) capable of transmitting terahertz (THz) OAM information-carrying modes. By using the full vector finite element method (FEM), OAM multiplexing is analyzed for the proposed fiber. All the THz OAM-based factors are analyzed at a frequency band ranging from 400 GHz to 800 GHz. For the first time, some important PCF factors such as effective refractive index difference (ERID), dispersion profile (DP), OAM purity, confinement loss (CL), effective mode area (ERA), and numerical aperture (NA) are quantitatively discussed with applications. The proposed design supports 50 OAM modes with ERID up to 10−3. The PCF has a CL of approximately 10–10 dB cm−1 and the lowest dispersion profile is 0.3581 ps/THz/cm. Furthermore, the OAM purity is around 97%. Nonetheless, the proposed design can be used in THz-OAM transmission and high optical fiber communications.

3-D forward modeling of shale gas fracturing dynamic monitoring using the borehole-to-ground transient electromagnetic method

The borehole-ground transient electromagnetic method enhances the detection range and resolution by placing the transmitter electrode within the borehole, allowing for close-proximity excitation of subsurface targets and compensating for the shortcomings of traditional ground-based methods. Utilizing an unstructured vector finite element method combined with a second-order backward Euler variable time-stepping difference scheme and the MUMPS solver, we have achieved three-dimensional forward modeling simulation of the transient electromagnetic field for a borehole-ground electric source. Based on the validation of its accuracy, we analyzed the effectiveness of this method for dynamic monitoring of shale gas reservoir fracturing. Through forward modeling, we examined the characteristics of the radial electric field response during shale gas reservoir fracturing monitoring and evaluated the effectiveness of the borehole-ground TEM method in dynamic monitoring of shale gas reservoirs. The research results indicate that this method can meet the requirements for reservoir fracturing dynamic monitoring and has a promising application prospect.

Photonic crystal fiber sensors to excite surface plasmon resonance based on elliptical detection channels are used for highly sensitive magnetic sensing

To improve the detection performance of fiber optic magnetic field sensors a new photonic crystal fiber (PCF) based on surface plasmon resonance (SPR) was designed and investigated. The designed sensor uses an elliptical detection channel, and the modal transmission characteristics and magnetic field sensing characteristics of this fiber optic sensor are analyzed using the full vector finite element method (FVFEM). In addition, the effect of the detection channel on the detection accuracy at different curvatures was investigated. Compared with previous optical fiber magnetic field (MF) sensors, the designed sensor meets the requirements of both refractive index (RI) and MF measurements, and the MF sensitivity, RI sensitivity, and amplitude sensitivity (AS) of the sensor reach 0.739 nm/Oe, 12043.8 nm/RIU, and 754.88RIU−1, respectively. The designed sensor expands the application range of optical fiber sensors and reduces the cost. It has great potential for application in complex environments.

High-sensitivity dual U-shaped PCF-SPR refractive index sensor for the detection of gas and liquid analytes.

A dual U-shaped photonic crystal fiber (PCF) biochemical sensor based on surface plasmon resonance (SPR) is designed for the simultaneous detection of gas and liquid analytes, and the properties are analyzed by the full vector finite element method (FEM). SPR is excited by placing gold nanowires on the inner surface of the U-shaped device. In this technique, the traditional metal deposition process can be replaced, subsequently reducing the difficulty and complexity of actual production and improving the phase matching between the basic mode and plasmonic modes. To improve the detection properties, the structural parameters of the sensor including the air hole diameter, spacing, gold nanowire diameter, and polishing depth are optimized, and to better evaluate and analyze the sensing properties, the wavelength and amplitude modulation inquiry method is adopted. The results show that the maximum wavelength sensitivity (WS), amplitude sensitivity (AS), minimum resolution (R), and optimal FOM are 35,000nm/RIU, 438.08R I U -1, 2.86×10-6 R I U, and 165.16R I U -1, respectively. In addition, the sensor can detect analyte RIs between 1.00 and 1.36 for gas and liquid analytes simultaneously. Owing to the simple structure, low cost, and ambient-condition monitoring, the sensor has large potential in a myriad of applications including sewage treatment, food safety, humoral regulation, environmental and biological monitoring, and medical diagnosis.

Design and simulation of photonic crystal fiber for highly sensitive chemical sensing applications

Abstract Photonic crystal fibers (PCF) have demonstrated promising capabilities for liquid sensing applications owing to their distinctive optical properties. This work presents a numerical investigation of a PCF sensor optimized for discriminating water, ethanol, and benzene samples. In the proposed configuration, there are five concentric rings of air holes in the cladding arranged in a hybrid lattice structure, while the core contains only one air hole. The optical properties of the sensor, such as refractive index, power fraction, relative sensitivity, confinement loss, effective area, and nonlinearity, were assessed through a comprehensive analysis utilizing the full vector Finite Element Method within the COMSOL Multiphysics software. All these properties have been meticulously examined through numerical investigation across a broader range of wavelengths spanning from 0.8 to 2.2 µm. The suggested model has high sensitivity, minimal confinement loss, and an exceptional nonlinear coefficient value. At a wavelength of 1.3 µm, the suggested PCF exhibits greater sensitivity of 96.84, 98.12, and 100% for water, ethanol, and benzene, respectively, and nonlinear coefficients of 13.98 W−1 km−1 for water, 13.93 W−1 km−1 for ethanol, and 14.85 W−1 km−1 for benzene, with decreased confinement loss. The created model can be utilized in several research areas, particularly in chemical sensing and bio-sensing, as well as their respective applications.

Highly sensitive plasmonic-grating PCF biosensor for cancer cell detection

Highly sensitive biosensor based on D-shaped photonic crystal fiber (PCF) with plasmonic grating is introduced and analyzed. The suggested structure is tested using four different grating structures (rectangular, triangular, circular, or elliptical) on the polished surface of the D-shaped PCF. The sensing operation depends on surface plasmon resonance mechanism where the analyte refractive index (RI) is utilized to control the coupling between the core mode and surface plasmon mode via phase matching phenomenon. Rhodium is employed as a plasmonic material to induce the SPMs. The resonance (i.e., phase matching) wavelength is a function of the analyte RI. The geometrical parameters of the proposed structure are optimized using full vectorial finite element method to enhance the sensor sensitivity. The proposed biosensor can be utilized in the detection of different cancerous Basel, Breast and Cervical cells. The performance of the reported biosensor is investigated in terms of sensitivity, linear response, and fabrication tolerance. The reported biosensor has high sensitivities of 19,750 nm/RIU, 20,428 nm/RIU and 20,041 nm/RIU for the detection of Basel, Breast and Cervical cancer cells, respectively. The presented biosensor is a good candidate for biological sample detection and organic chemical sensing.

Transient Electromagnetic Monitoring of Permafrost: Mathematical Modeling Based on Sumudu Integral Transform and Artificial Neural Networks

Due to the ongoing global warming on the Earth, permafrost degradation has been extensively taking place, which poses a substantial threat to civil and industrial facilities and infrastructure elements, as well as to the utilization of natural resources in the Arctic and high-latitude regions. In order to prevent the negative consequences of permafrost thawing under the foundations of constructions, various geophysical techniques for monitoring permafrost have been proposed and applied so far: temperature, electrical, seismic and many others. We propose a cross-borehole exploration system for a high localization of target objects in the cryolithozone. A novel mathematical apparatus for three-dimensional modeling of transient electromagnetic signals by the vector finite element method has been developed. The original combination of the latter, the Sumudu integral transform and artificial neural networks makes it possible to examine spatially heterogeneous objects of the cryolithozone with a high contrast of geoelectric parameters, significantly reducing computational costs. We consider numerical simulation results of the transient electromagnetic monitoring of industrial facilities located on permafrost. The formation of a talik has been shown to significantly manifest itself in the measured electromagnetic responses, which enables timely prevention of industrial disasters and environmental catastrophes.

Highly sensitive temperature sensor based on nematic liquid crystal channel waveguide on silicon

This paper presents a highly sensitive hybrid plasmonic liquid crystal channel-based temperature sensor. The proposed structure has V-groove waveguide channel infiltrated with nematic liquid crystal (NLC) material of type E7 and coated by a gold (Au) layer to excite the surface plasmon resonance at the metal/dielectric interface. The NLC refractive indices depend on the temperature which affects the resonance wavelength where coupling occurs between the core and surface plasmon modes. The full vectorial finite element method is employed to evaluate the sensing performance of the reported sensor. The numerical results show that the suggested sensor can achieve an average temperature sensitivity of 24.5 nm/°C over a temperature range from 15 to 40 °C. The obtained wavelength sensitivity is higher than those of most similar temperature sensors based on silica-silicon or silicon-on-insulator technology in literature. In addition, the average amplitude sensitivity and figure of merit of the presented sensor are 0.135 °C− 1 and 0.43 °C− 1, respectively. Moreover, the introduced structure is complementary metal-oxide-semiconductor compatible with simple design and good fabrication tolerance of ± 5% where the temperature sensitivity is better than 23 nm/°C.

Vectorial finite element method for neutron transport solving with preconditioning GMRES acceleration

This work proposed a vectorial finite element method (VFEM) for solving neutron transport equation with high accuracy and convergence. The Streamline Upwind Petrov–Galerkin method is used to establish the VFEM for accuracy, and the traditional discrete-ordinate neutron transport equation is organized in vectorial form for high stability and convergence. To further improve the convergence efficiency of VFEM, the preconditioning GMRES is introduced for solving the VFEM linear system, and different preconditioners are imposed, including the Jacobian and Block-Jacobian. Numerical results showed that the proposed VFEM has high accuracy and adaptability for multi-group and multi-dimensional neutron transport simulation. Further performance analyses showed that the proposed VFEM has higher efficiency than the traditional finite element method, while the application of preconditioning GMRESs can further improve the convergence efficiency. This work can provide an innovative and effective unstructured-mesh neutron transport solution format, and provide a valuable reference for further improvement of other numerical methods.

Optimization of ultrathin polarization insensitive metamaterial absorbers using trust region algorithm based on Co-kriging model

In this paper, a trust region optimization algorithm integrated with a co-kriging surrogate-model is newly formulated to optimize compact ultrathin wideband metamaterial absorbers with high absorption. The reported algorithm is linked with the full vectorial finite element method to simulate and optimize the studied absorbers. In order to show the power of the suggested algorithm, the geometrical parameters of a previous metamaterial absorber (MA) with L-shaped resonators are optimized to achieve high absorption (over 90 %) over a frequency band from 13.8 GHz to 24.5 GHz covering most of KU and K bands. Then, a novel design of L-shaped MA with triangular resonators is optimized, analyzed and fabricated with high absorption (above 90 %) through a large frequency band from 11.9 GHz to 22 GHz covering the entire KU-band and most of the K-band. The reported design is also robust against the variations of the incident angle (above 80 % up to 50°) for both transverse electric (TE) and transverse magnetic (TM) polarized modes. Therefore, the proposed algorithm could be used efficiently for the design and optimization of metamaterial absorbers.

Comparative analysis of computational schemes for FEM modeling of 3D time-domain geoelectromagnetic fields excited by a horizontal grounded-wire source

Two mathematical formulations are considered for calculating the time-domain electromagnetic fields excited by a horizontal grounded-wire source in a 3D geological medium. The first of them is formulated for a vector potential (A-formulation), the second one is formulated for the electric field strength (E-formulation). Both formulations are also considered when using the primary-secondary field approach (PSFA), where the primary field is calculated in a horizontally layered medium. The calculation of 3D non-stationary fields is performed using the vector finite element method (FEM). For time discretization, both two-point and three-point implicit schemes are considered. As the initial field, we used the stationary field of the direct current, the corresponding mathematical formulations are also presented using the PSFA. To verify computational schemes, a comparison with the results of other authors is given. For the problems of marine electrical exploration, we present a comparison of two formulations, analyze the effectiveness of PSFA and the use of a three-point implicit scheme instead of a two-point one. The results of computational experiments have shown that when using both formulations, the use of PSFA and the three-point implicit scheme “with backward overstepping” (instead of the two-point implicit scheme) can reduce computational costs by more than an order. In this case, both formulations give solutions that are close to each other in accuracy and computational costs. However, the implementation of the E-formulation using the PSFA requires certain thoroughness and in some cases can lead to a sharp deterioration in the numerical solution accuracy at late times. This is due to the fact that when using the vector FEM, the numerical solution can lead to a nonzero constant field, which is the gradient of some scalar function.

Structure optimization of large-solid-core photonic crystal fibers based on Ge\(_{20}\)Sb\(_{5}\)Se\(_{75}\) for optical applications

This paper presents a new design of Ge20Sb5Se75 large-solid-core photonic crystal fiber (PCF) with a 1st-ring-removed square lattice. Using the full vector finite element method for anisotropic perfectly matched layers, we numerically examine the dispersion characteristics of the PCF in the wavelength range spanning from 1.5 µm to 6.0 µm. The results reveal that photonic crystal fibers exhibit a variety of dispersion properties, including all-normal and anomalous dispersion, featuring one or two zero dispersion wavelengths (ZDWs). We propose two designs with optimal dispersion characteristics based on our numerical simulations. These designs have small lattice constants (Ʌ = 1.0 µm; Ʌ = 1.5 µm) and low fill factors (d/Ʌ = 0.3; d/Ʌ = 0.35). Furthermore, these selected fibers offer high nonlinearity and low confinement loss, making them excellent candidates for a wide range of optical applications.

Cancer cell detection by plasmonic dual V-shaped PCF biosensor

In this paper, a highly sensitive plasmonic photonic crystal fiber (PCF) biosensor is reported for cancer cell detection. The modal analysis of the reported biosensor is performed using the full vectorial finite element method. The suggested PCF sensor has dual V-shaped groves to enhance the sensor sensitivity where two gold nano-rods are mounted on the etched surfaces. The main idea of the optical sensors is to track the electromagnetic coupling between the leaky core mode and the surface plasmon mode (SPM) at the metal/dielectric interface. When the SPM and one of the fundamental core modes are phase-matched, strong coupling occurs. Therefore, maximum confinement loss is achieved for the core-guided mode at the resonance wavelength, which depends on the analyte refractive index (RI). The V-shaped groove enhances the core/SPM coupling where high RI sensitivity of 24,000 nm/RIU is achieved along the RI range from 1.38 to 1.39, with a resolution of 2.703×10−6RIU. The potential of using the suggested RI sensor for cancer cell detection is then demonstrated. In this context, high sensitivities of 23,700 nm/RIU, 8,208 nm/RIU, and 14,428.6 are obtained for basal, cervical, and breast cancer cells with resolutions of 4.22×10−6RIU, 12.18×10−6RIU, and 6.93×10−6RIU, respectively. The achieved sensitivity and resolution are higher than those of the recently reported cancer biosensors. Moreover, the developed label-free biosensor is safer than other chemical and surgical techniques.