Space-time grids for electromagnetic field computation using finite integration method

A finite integration method on 3D and 4D space-time grids is studied for electromagnetic wave computation, where a non-uniform time-step distribution is naturally introduced. A dual grid based on the Hodge duality and the Lorentz metric is introduced to provide a simple constitutive equation for electromagnetic variables. An improved space-time grid shape is proposed to suppress unphysical wave-reflection.

Thrombin is a serine protease involved in blood coagulation. Since thrombin inhibitors appear to be effective in the treatment and prevention of thrombotic and embolic disorders, considerable attention has been focused on the structure and interactions of the enzyme. In this work, we calculated the relative free energies of hydration of the new thrombin inhibitor candidates, p‐substituted derivatives of benzamidine, a well‐known noncovalent thrombin inhibitor. We used molecular dynamics and the finite difference thermodynamic integration (FDTI) algorithm within the Discover program of MSI. We have shown that the orthogonality problem that occurs in the calculation of intraperturbed‐group contributions to the free energy is treated adequately by the FDTI method. We have also shown that problems of singularity and convergence in free energy calculations can be properly solved using this method. To conclude, the calculated free energies of hydration gave the following order of solvation for the candidates: p‐(2‐oxo‐1‐propyl)benzamidine > p‐methylbenzamidine > p‐ethylbenzamidine > p‐(1‐propyl)benzamidine > benzamidine. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

This paper introduces a new algorithm for the automatic synthesis of SPICE-ready equivalent circuits of complex multiport lumped interconnect structures. The method is named time-domain vector fitting (TD-VF) due to its analogy to the well-known vector fitting algorithm, which operates in the frequency domain. The TD-VF computes a rational approximation of the transfer matrix for the structure under modeling using as raw data its transient port responses to suitable excitations. These include, e.g., the case of transient port scattering responses as typically obtained by full-wave electromagnetic solvers based on the finite-differences time-domain (FDTD) or finite integration (FIT) methods. The TD-VF algorithm works entirely in the time domain, without requiring any knowledge of the frequency-domain responses. This allows direct processing of possibly truncated transient responses, therefore allowing for short full-wave simulations. This paper shows that the accuracy level achievable by TD-VF is excellent. Hence, passivity can be enforced a posteriori using the spectral properties of associated Hamiltonian matrices. Several examples of package, connectors, and discontinuities are provided as illustration.

Summary form only given. Numerical analysis of electromagnetic scattering has been widely studied in the past. The method of moments (MoM) is suitable to simulate scattering from an object in an open region. In order to solve problems with complicated geometries and materials, the finite element method (FEM) is preferred. However, when solving unbounded problems with FEM, the use of absorbing boundary conditions or perfectly matched layers will result in truncation errors. To combine the advantages of both MoM and FEM, the finite element-boundary integral (FE-BI) method was developed and widely used (J. M. Jin, The Finite Element Method in Electromagnetics, Second Edition. New York: Wiley, 2002). This algorithm is not only able to deal with highly complicated geometry and material, but also able to eliminate the truncation error. However, since the MoM has O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2)</sup> computational and storage complexities, the computational cost of the BI-related algorithm is still prohibitively high when solving large-scale scattering problems. To alleviate this problem, the multilevel fast multipole algorithm (MLFMA) has been incorporated into the FE-BI method (J. Liu and J. M. Jin, IEEE Trans. Antennas Propag., vol. 51, pp.1157-1167, Jun. 2003). Another important technique to accelerate the computation is to resort to parallel computers. Recently, the graphics processing unit (GPU), as one of many-core computing systems, has received intensive attention from the scientific computing community due to its low price, a massive number of processors, and the resulting high computational efficiency. In this work, we discuss the GPU implementation of the FE-BI algorithm for solving electromagnetic scattering problems. First, the assembly of the BI-related matrix is parallelized on GPU by NVIDIA's compute unified device architecture (CUDA). A massive number of threads are assigned to carry out the assembly, and each thread computes one element in the BI-related matrix. Second, both the direct and iterative solvers are implemented on GPU. For the direct solver, the Intel's math kernel library (MKL) is used for LU decomposition, and the CUSPARSE (a set of basic linear algebra subroutines used for handling sparse matrices) is employed to speedup forward and backward substitutions. For the iterative solver, the high performance CUDA Basic Linear Algebra Subprograms (BLAS) is utilized for the matrix-vector multiplication and the vector-vector multiplication. Extensive numerical experiments are conducted to validate the implementation and demonstrate the achievable computational speedup.

In order to solve the thickness dependence of plasma absorption of electromagnetic waves and further reduce the backward radar scattering cross section (RCS) of the target, we designed a novel composite structure of a metasurface and plasma. A metasurface with three absorption peaks is designed by means of an equivalent circuit based on an electromagnetic resonance type metamaterial absorber. The reflection and absorption of the composite structure are numerically and experimentally verified. The finite integration method was used to simulate a composite structure of finite size to obtain the RCS. The experimental measurements of electromagnetic wave reflection were conducted by a vector network analyzer (Keysight N5234A) and horn antennas, etc. The research showed that the absorption capacity of this composite structure was substantially improved compared to either the plasma or the metasurface, and it is more convenient for application due to its low plasma thickness requirement and easy fabrication.

In this paper, the program system using the finite sound ray integration method was extended to permit the calculation of echo-diagrams up to 300 ms even for the room shapes having more than 900 wall surfaces. From echodiagrams, acoustical criteria for liveness and spatial impression were derived for three auditoriums. The measured criteria and caluculated criteria were found to be high correlated. Not only the correlation coefficients of D ; R, C, RI and RR values were high, but also the calculated values closely approximated to the measured values. Successively, authors developed two different methods to simulate the attenuation by air absorption in the computer simulation system based on the finite sound ray integration. The first method was to convolute the air absorption for each and every sound ray. The second was to convolute the air absorption to the calculated impulse response corresponding to the arrival time of sound. The latter yielded the more practical results by the short calculation time.

Eigenmode Solution of 2-D and 3-D Electromagnetic Cavities Containing Absorbing Materials Using the Jacobi–Davidson Algorithm

It is announced that the Maxwell equations can be solved on unstructured grids using finite integration methods. Numerical experiments show that next to the finite-volume method, a discretization technique can be defined based on ‘finite-surface’ integration.

In this contribution a novel finite element method for the system of first order Maxwell equations in the time domain is introduced. It is based on both a primal and a dual set of finite elements. The resulting discrete curl operators are equivalent to those from basis free methods such as the finite integration method, the discrete exterior calculus, and the Yee-cell method. Using a finite element approach leads to a natural discretisation of the permittivity and permeability operators. Because of the symmetry of the resulting linear system and the particular choice of discretisation, this method, when used in conjunction with a Crank-Nicholson time stepping scheme, conserves the electromagnetic energy exactly.

Based on the recently developed finite integration method (FIM) for solving one and two dimensional ordinary and partial differential equations, this paper extends FIM to both stationary and transient heat conduction inverse problems for anisotropic and functionally graded materials with high degree of accuracy. Lagrange series approximation is applied to determine the first order of integral and differential matrices, which are used to form the system equation matrix for two and three dimensional problems. Singular Value Decomposition (SVD) is applied to solve the ill-conditioned system of algebraic equations obtained from the integral equation, boundary conditions and scattered temperature measurements. The convergence and accuracy of this method are investigated with two examples for anisotropic media and functionally graded materials.

Detection of hydrocarbon in sea bed logging (SBL) is still a very challenging task for deep target reservoirs. The response of electromagnetic (EM) field from marine environment is very low and it is very difficult to predict deep target reservoirs below 2500 m from the sea floor. Straight antennas at 0.125 Hz and 0.0625 Hz are used for the detection of deep target hydrocarbon reservoirs below the seafloor. The finite integration method (FIM) is applied on 3D geological seabed models. The proposed area of the seabed model (16 km ×16 km) was simulated by using CST (computer simulation technology) EM studio. The comparison of different frequencies for different target depths was done in our proposed model. Total electric and magnetic fields were applied instead of scattered electric and magnetic fields, due to its accurate and precise measurements of resistivity contrast at the target depth up to 3000 m. From the results, it was observed that straight antenna at 0.0625 Hz shows 50.11% resistivity contrast at target depth of 1000 m whereas straight antenna at 0.125 Hz showed 42.30% resistivity contrast at the same target depth for the E-field. It was found that the E-field response decreased as the target depth increased gradually by 500 m from 1000 m to 3000 m at different values of frequencies with constant current (1250 A). It was also investigated that at frequency of 0.0625 Hz, straight antenna gave 7.10% better delineation of hydrocarbon at 3000 m target depth. It was speculated that an antenna at 0.0625 Hz may be able to detect hydrocarbon reservoirs at 4000 m target depth below the seafloor. This EM antenna may open a new frontier for oil and gas industry for the detection of deep target hydrocarbon reservoirs below the seafloor.

This paper introduces a novel hybrid shifted Gegenbauer integral–pseudospectral (HSG-IPS) method to solve the time-fractional Benjamin–Bona–Mahony–Burgers (FBBMB) equation with high accuracy. The approach transforms the equation into a form with only a first-order derivative, which is approximated using a stable shifted Gegenbauer differentiation matrix (SGDM), while other terms are computed with precise quadrature rules. By integrating advanced techniques such as the shifted Gegenbauer pseudospectral method (SGPS), fractional derivative and integral approximations, and barycentric integration matrices, the HSG-IPS method achieves spectral accuracy. Numerical results show it reduces average absolute errors (AAEs) by up to 99.99% compared to methods like Crank–Nicolson linearized difference scheme (CNLDS) and finite integration method using Chebyshev polynomial (FIM-CBS), with computational times as low as 0.04–0.05 s. The method’s stability is improved by avoiding ill-conditioned high-order derivative approximations, and its efficiency is boosted by precomputed matrices and Kronecker product structures. Robust across various fractional orders, the HSG-IPS method offers a powerful tool for modeling wave propagation and nonlinear phenomena in fractional calculus applications.

In this paper, the human body absorption of electromagnetic energy emitted by a dipole antenna operating at the current mobile phone technology frequencies is investigated. The specific absorption rate within a realistic anatomical model comprising of the metallic implant was evaluated. The research was carried out using electromagnetic numerical modeling based on the Finite Integration method. The primary objective was to compare levels of absorbed electromagnetic energy as a function of the antenna distance and mobile phone carrier frequency. The effect of implants presence was also studied. The results show that SAR varies with respect to the antenna distance as well as to the considered mobile phone technology standard. However, the antenna shift in the tens of millimeters provides significant SAR decrease below the safety limit. The presence of metallic implant in superficial tissue layers causes significant SAR increase, particularly for PM implant while the SAR enhancement for needle implant was negligible.

Reconstruction of inaccessible boundary value in a sideways parabolic problem with variable coefficients—Forward collocation with finite integration method

Surface-enhanced Raman scattering by hierarchical CuS microflowers: Charge transfer and electromagnetic enhancement