Problem In Frequency Domain Research Articles

Fast 3D Magnetotelluric Forward Modeling Based on a Regularization Approach in Spherical Coordinate

The earth’s curvature shouldn’t be ignored for the large-scale magnetotelluric (MT) modeling. A forward code of spherical coordinate MT method based on staggered grid finite difference method is developed. In addition, the forward problem is usually solved numerically, mostly based on iterative solution. Krylov subspace method is widely used to solve electromagnetic forward modeling problems in frequency domain. However, as the period increases, the convergence of these methods becomes significantly slower (especially for long-period MT data). We added a scaled grad-div operator to the double curl equation of the electric field to perform the nondivergence condition (CCGD). The results show that CCGD method is more efficient than other methods, which is an efficient method for our code.

Toward a certified greedy Loewner framework with minimal sampling

We propose a strategy for greedy sampling in the context of non-intrusive interpolation-based surrogate modeling for frequency-domain problems. We rely on a non-intrusive and cheap error indicator to drive the adaptive selection of the high-fidelity samples on which the surrogate is based. We develop a theoretical framework to support our proposed indicator. We also present several practical approaches for the termination criterion that is used to end the greedy sampling iterations. To showcase our greedy strategy, we numerically test it in combination with the well-known Loewner framework. To this effect, we consider several benchmarks, highlighting the effectiveness of our adaptive approach in approximating the transfer function of complex systems from a few samples.

Multiple-scattering frequency-time hybrid solver for the wave equation in interior domains

This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, (1) A multiple scattering strategy that decomposes a given interior time-domain problem into a sequence of limited-duration time-domain problems of scattering by overlapping open arcs, each one of which is reduced (by means of the Fourier transform) to a sequence of Helmholtz frequency-domain problems; (2) Boundary integral equations on overlapping boundary patches for the solution of the frequency-domain problems in point (1); (3) A smooth “Time-windowing and recentering” methodology that enables both treatment of incident signals of long duration and long time simulation; and, (4) A Fourier transform algorithm that delivers numerically dispersionless, spectrally-accurate time evolution for given incident fields. By recasting the interior time-domain problem in terms of a sequence of open-arc multiple scattering events, the proposed approach regularizes the full interior frequency domain problem—which, if obtained by either Fourier or Laplace transformation of the corresponding interior time-domain problem, must encapsulate infinitely many scattering events, giving rise to non-uniqueness and eigenfunctions in the Fourier case, and ill conditioning in the Laplace case. Numerical examples are included which demonstrate the accuracy and efficiency of the proposed methodology.

Wave resonances in the presence of current and the frequency and time-domain interconnection

The current work investigates the relationship between frequency and time domain problems associated with flexural gravity wave motion with oblique incidence and current. Different types of wave resonances such as buckling resonance, primary and secondary blocking resonance, Bragg resonance and interaction among them are discussed. Three propagating wave modes are observed between the primary and secondary blocking points, two of which are associated with positive group velocities and the third one is related to negative group velocities. Again, the Bragg resonance is analyzed for wave scattering problems. The complex porosity parameter is found to have a significant effect on the buckling and blocking resonance but does not affect Bragg resonance. The discontinuity of Bragg reflection is observed at primary and secondary blocking points and the peak values of Bragg reflection increase in the blocking zone. Again, we establish the interconnection between the frequency and time domain by deriving the time-domain solution from the frequency-domain solution and vice versa. The derivation of time-domain solutions using the dispersion relation and method of stationary phase is an intriguing finding. Wave energy and wave packets move faster in co-propagating waves than in counter-propagating waves and shallow water than in finite water depth. To validate the results, time-domain simulation and spectral methods are used.

Trefftz co-chain calculus

We are concerned with a special class of discretizations of general linear transmission problems stated in the calculus of differential forms and posed on {mathbb {R}}^n. In the spirit of domain decomposition, we partition {mathbb {R}}^n=Omega cup Gamma cup Omega _{+}, Omega a bounded Lipschitz polyhedron, Gamma :=partial Omega , and Omega _{+} unbounded. In Omega , we employ a mesh-based discrete co-chain model for differential forms, which includes schemes like finite element exterior calculus and discrete exterior calculus. In Omega _{+}, we rely on a meshless Trefftz–Galerkin approach, i.e., we use special solutions of the homogeneous PDE as trial and test functions. Our key contribution is a unified way to couple the different discretizations across Gamma . Based on the theory of discrete Hodge operators, we derive the resulting linear system of equations. As a concrete application, we discuss an eddy-current problem in frequency domain, for which we also give numerical results.

Deep learning-based LPI radar signals analysis and identification using a Nyquist Folding Receiver architecture

Nyquist Folding Receiver (NYFR) is a perceptron structure that realizes a low probability of intercept (LPI) signal analog to information. Aiming at the problem of LPI radar signal receiving, the time domain, frequency domain, and time-frequency domain problems of signals intercepted by NYFR structure are studied. Combined with the time-frequency analysis (TFA) method, a radar recognition scheme based on deep learning (DL) is introduced, which can reliably classify common LPI radar signals. First, the structure of NYFR and its characteristics in the time domain, frequency domain, and time and frequency domain are analyzed. Then, the received signal is then converted into a time-frequency image (TFI). Finally, four kinds of DL algorithms are used to classify LPI radar signals. Simulation results demonstrate the correctness of the NYFR structure, and the effectiveness of the proposed recognition method is verified by comparison experiments.

Efficient goal-oriented mesh refinement in 3-D finite-element modelling adapted for controlled source electromagnetic surveys

SUMMARY We developed a 3-D forward modelling code, which simulates controlled source electromagnetic problems in frequency domain using edge-based finite elements and a total electric field approach. To evaluate electromagnetic data acquired across complex subsurface structures, software performing accurate 3-D modelling is required, especially for incorporation in inversion approaches. Our modelling code aims at finding a good compromise between the necessary solution accuracy at the points of interest and the general problem size by using a goal-oriented mesh refinement strategy designed for models of variable electric conductivity and magnetic permeability. To formulate an improved error estimator suitable for controlled source electromagnetic problems, we developed literature approaches of mesh refinement further targeting three aspects. First, to generate a roughly homogeneously fine mesh discretization around all receiver sites, our new error estimator weights the adjoint source term by the approximate decay of the electric field with increasing distance from the primal source using the expression for a homogeneous half-space. This causes almost no additional computational cost. Second, the error estimator employed in the refinement approach can be optimized for models with pronounced conductivity and magnetic permeability contrasts as often encountered in, for example, mineral prospecting scenarios by optionally including terms that measure the continuity of the normal component of current flow and the tangential component of the magnetic field across interfaces of abutting elements. Third, to avoid amplitude-dependent over-refining of the mesh, we formulate our element-wise error estimators relative to the local amplitude of the electromagnetic field. In this work, we evaluate the implemented adaptive mesh refinement approach and its solution accuracy comparing our solutions for simple 1-D models and a model with 3-D anomalies to semi-analytic 1-D solutions and a second-order finite-element code, respectively. Furthermore, a feasibility study for controlled-source electromagnetic measurements across ferrous mineral deposits is conducted. The numerical experiments demonstrate that our new refinement procedure generates problem-specific finite-element meshes and yields accurate solutions for both simple synthetic models and realistic survey scenarios. Especially for the latter, characteristics of our code, such as the possibility of modelling extended sources as well as including arbitrary receiver distributions and detailed subsurface anomalies, are beneficial.

Solution of large-scale 3D controlled-source electromagnetic modeling problem using efficient iterative solvers

With geophysical surveys evolving from traditional 2D to 3D models, the large volume of data adds challenges to inversion, especially when aiming to resolve complex 3D structures. An iterative forward solver for the controlled-source electromagnetic (CSEM) method requires less memory than that for a direct solver; however, it is not easy to iteratively solve an ill-conditioned linear system of equations arising from finite-element discretization of Maxwell’s equations. To solve this problem, we have developed efficient and robust iterative solvers for frequency- and time-domain CSEM modeling problems. For the frequency-domain problem, we first transform the linear system into its equivalent real-number format, and then introduce an optimal block-diagonal preconditioner. Because the condition number of the preconditioned linear equation system has an upper bound of [Formula: see text], we can achieve fast solution convergence when applying a flexible generalized minimum residual solver. Applying the block preconditioner further results in solving two smaller linear systems with the same coefficient matrix. For the time-domain problem, we first discretize the partial differential equation for the electric field in time using an unconditionally stable backward Euler scheme. We then solve the resulting linear equation system iteratively at each time step. After the spatial discretization in the frequency domain, or space-time discretization in the time domain, we exploit the conjugate-gradient solver with auxiliary-space preconditioners derived from the Hiptmair-Xu decomposition to solve these real linear systems. Finally, we check the efficiency and effectiveness of our iterative methods by simulating complex CSEM models. The most significant advantage of our approach is that the iterative solvers we adopt have almost the same accuracy and robustness as direct solvers but require much less memory, rendering them more suitable for large-scale 3D CSEM forward modeling and inversion.

Three-dimensional full-wave transient analysis of switches and faults using a method of moments solution of the electric field integral equation

Three-dimensional full-wave electromagnetic transient (EMT) analysis of switches and faults is shown to be possible in the time domain (TD) from numerical solutions of Maxwell's equations in the frequency domain (FD). The electric field integral equation is solved by the method of moments for the initial fault or switch condition (open/closed). The problem is then cast into subsequent FD problems based on the principle of superposition. At each stage, the FD solution is converted into TD and modified by appropriate functions selected to enforce the desired switch operation (closing/opening) in the next stage. This is also applicable to applying and clearing faults at desired times. In order to navigate between the TD and FD solutions, the fast Fourier transforms are applied and a systematic procedure for obtaining a numerically convergent solution is introduced. For slow transients, results exhibit excellent agreement with simulations obtained from an EMT-type program. However, when faster transients are considered (e.g. in gas-insulated substations), the proposed method is shown to provide more realistic results than those computed by the conventional EMT simulations.

Research on a new diagnosis index for fixed-point rub-impact of rotor system

A model for a rotor system simulated with finite element method and a test bench are established in this paper. The fixed-point rub-impact fault on rotor system is studied (There are six clearances to be discussed). It is found that the nonlinear compositions are contained in the output responses by analyzing these vibration signals of the rotor system with fixed-point rub-impact, which implies that a nonlinear term appears in the system. In order to extract these compositions, a nonlinear method, named weighted contribution rate of nonlinear output frequency response functions (WNOFRFs), is adopted for analyzing the mechanism of these nonlinear problems in frequency domain. Furthermore, the Clenshaw-Curtis numerical integration method and the minimum mutual entropy principle (MMEP) are used to extract the fault diagnosis index J for identifying the fixed-point rub-impact fault of the system. At last, according to the simulation and experiment research, WNOFRFs can improve these higher-order nonlinear characteristics. And these findings prove that the index J has certain advantages compared with other indexes in the diagnosis of the rotor rub-impact fault.

A Causality-Constrained Frequency-Domain Least-Squares Filter Design Method for Crosstalk Cancellation

Crosstalk cancellation filters play a crucial role when reproducing binaural signals over loudspeakers. Least-squares design methods for crosstalk cancellation filters are commonly formulated either in the time domain or in the frequency domain. While the time-domain problem is too complex to be solved in a dynamic real-time setup, the frequency-domain problem is computationally cheap. However, it yields circular convolution artifacts, which degrade the performance. Using a unified framework, we derive a causality-constrained frequency-domain least-squares problem, which itself is an unconstrained problem. Our method does not yield circular convolution artifacts since the impulse responses are causal by construction. This construction is based on the fact that the real part and the imaginary part of a causal signal's spectrum are related via Hilbert transform. By approximating the Hilbert transform, we reduce the proposed method's computational complexity. The complexity reduces by two to three orders of magnitude while the performance remains close to that of the time-domain solution. We provide a detailed complexity analysis and compare our method to three state-of-the-art methods on a large dataset. Our investigations reveal that the causality-constrained method enables a flexible tradeoff between computational complexity and performance figures.

90 Years of Galbrun’s Equation: An Unusual Formulation for Aeroacoustics and Hydroacoustics in Terms of the Lagrangian Displacement

The field of aeroacoustics has gained much attention since the well-known acoustic analogies were first published in the 1950s. In parallel, the continuous growth of computational resources has enabled researchers and engineers to investigate phenomena involving flow-induced noise or sound propagation effects related to arbitrary velocity fields. To describe the latter mentioned physical processes, Galbrun utilized a mixed Eulerian–Lagrangian framework to describe perturbations of the underlying fluid dynamics. While less known compared to the more common linearized Euler equations, Galbrun’s equation provides an original framework. Since its publication in 1931, a number of scholars have further developed the approach first proposed by Galbrun. This paper provides a review of the existing literature dedicated to the use of Galbrun’s equation by highlighting possible advantages of the underlying theory as well as difficulties when utilizing numerical methods for solving problems in time or frequency domain. Furthermore, this work intents to serve as a companion for researchers interested in the field of aeroacoustics and hydroacoustics associated with Galbrun’s equation.

Review of truncation techniques for full and half space acoustic problems

Many acoustic problems involve modeling radiation or scattering phenomena, including transducer characterization and design, sonar applications, or studying the human HRTF. In all cases open non-reflecting conditions or truncation techniques need to be set up when using numerical simulation methods. Several methods exist to model the open domain depending on the used numerical technique. In this contribution we will present and study the performance of several of these methods under various conditions. This includes radiation boundary conditions, perfectly matched layers, hybrid finite element (FEM) and boundary element (BEM) setups, as well as other sponge or absorbing layer methods. These will be applied to both frequency domain and time domain problems. Of particular interest will also be the application of the truncation techniques to half space scattering problems encountered in the analysis of absorption or transmission characteristics. In these setups oblique angles of incidence exist, which leads to numerical challenges.

Sensor attack detection for cyber‐physical systems based on frequency domain partition

This study is concerned with the attack detection (AD) problems in finite frequency domain for cyber-physical systems with sensor attack. The frequency domain is divided into three frequency domains of low, medium and high, multiple AD filters are designed to work simultaneously. The attack detectionAD problem is transformed into a multi-objective optimisation schemes for each finite frequency domain. Finally, the experimental results of networked motion control system are given to verify the effectiveness and superiority of proposed method.

Application of POD and PGD for Efficient Parameter Sweeping in Frequency-Domain Full-Wave Problems

Full-wave solutions of Maxwell’s equations defined on a wide-range parametric space can be necessary for modeling and design of high-frequency electronic systems. Model order reduction (MOR) techniques can be used to develop efficient solvers for accelerating the parameter sweeping process. In this article, we implement two MOR methods for solving parametric full-wave problems. One is the well-known proper orthogonal decomposition (POD) method and the other is a more recent and novel method, which is proper generalized decomposition (PGD). The two methods are applied on a wave propagation problem in both frequency domain and frequency-permittivity domain. Results show that both POD and PGD can model the field changes in the parametric space accurately. The efficiency and behavior of the reduction modes of both methods are compared and discussed.

Inverse Scattering Based on Proper Solution Space

This paper is concerned with an inverse scattering problem in frequency domain, when the scattered field is governed by the Helmholtz equation. The algorithm is iterative in nature. It introduces a new approach which we refer to as proper solution space. It assumes an initial guess for the unknown function and obtains corrections to the guessed value. The updating stage is accomplished by generating a set of functions that satisfy some of the required boundary conditions. We refer to this space as proper solution space. The correction to the assumed value can then be obtained by imposing the remaining boundary conditions. A number of numerical examples are used to study the applicability and effectiveness of the new approach.

Coupling Nonlinear Magneto‐Thermal Problems in Frequency Domain with the Mechanical Field

AbstractThis paper investigates a computationally efficient strategy for simulating induction heating processes, using a multiharmonic ansatz and harmonic balancing for the solution of the nonlinear magnetic eddy current problem in frequency domain. In order to increase the flexibility of the meshing procedure and decrease the number of degrees of freedom, a methodology for nonconforming interfaces and Nédéléc edge elements is presented. The verification of the proposed method is carried out by comparison to the conform (conforming mesh) solution. Furthermore, the results from the eddy current problem are used to simulate the temperature distrubution in a thin steel sheet and compute the resulting stresses.

Convolution quadrature methods for time-domain scattering from unbounded penetrable interfaces.

This paper presents a class of boundary integral equation methods for the numerical solution of acoustic and electromagnetic time-domain scattering problems in the presence of unbounded penetrable interfaces in two spatial dimensions. The proposed methodology relies on convolution quadrature (CQ) schemes and the recently introduced windowed Green function (WGF) method. As in standard time-domain scattering from bounded obstacles, a CQ method of the user's choice is used to transform the problem into a finite number of (complex) frequency-domain problems posed, in our case, on the domains containing unbounded penetrable interfaces. Each one of the frequency-domain transmission problems is then formulated as a second-kind integral equation that is effectively reduced to a bounded interface by means of the WGF method-which introduces errors that decrease super-algebraically fast as the window size increases. The resulting windowed integral equations can then be solved by means of any (accelerated or unaccelerated) off-the-shelf Nyström or boundary element Helmholtz integral equation solvers capable of handling complex wavenumbers with large imaginary part. A high-order Nyström method based on Alpert's quadrature rules is used here. A variety of CQ schemes and numerical examples, including wave propagation in open waveguides as well as scattering from multiple layered media, demonstrate the capabilities of the proposed approach.

An improved H∞ filtering for Markovian jump system with time-varying delay based on finite frequency domain

In traditional analysis of system performance, Markovian jump system is often considered in the full frequency domain. However, some unknown factors, such as noise interference, often act on a specific frequency domain, so there is a big defect in putting the system analysis in the full frequency domain. In this paper, the finite frequency domain is introduced into the Markovian jump system. By using generalized KYP lemma, the system is divided into three frequency bands: low, medium and high. The disturbance in different frequency domain is analyzed and the H∞ filter is designed. In addition, in dealing with inequality relations, the improved Wirtinger inequality method is used, and the Projection lemma is used in dealing with filter coupling terms, and time-varying delay problem in finite frequency domain is also considered. Finally, some examples are given to illustrate the effectiveness of our methods and the specific parameters and convergence graph of the finite frequency domain filter are obtained.

On impedance conditions for circular multiperforated acoustic liners

BackgroundThe acoustic damping in gas turbines and aero-engines relies to a great extent on acoustic liners that consists of a cavity and a perforated face sheet. The prediction of the impedance of the liners by direct numerical simulation is nowadays not feasible due to the hundreds to thousands repetitions of tiny holes. We introduce a procedure to numerically obtain the Rayleigh conductivity for acoustic liners for viscous gases at rest, and with it define the acoustic impedance of the perforated sheet.ResultsThe proposed method decouples the effects that are dominant on different scales: (a) viscous and incompressible flow at the scale of one hole, (b) inviscid and incompressible flow at the scale of the hole pattern, and (c) inviscid and compressible flow at the scale of the wave-length. With the method of matched asymptotic expansions we couple the different scales and eventually obtain effective impedance conditions on the macroscopic scale. For this the effective Rayleigh conductivity results by numerical solution of an instationary Stokes problem in frequency domain around one hole with prescribed pressure at infinite distance to the aperture. It depends on hole shape, frequency, mean density and viscosity divided by the area of the periodicity cell. This enables us to estimate dissipation losses and transmission properties, that we compare with acoustic measurements in a duct acoustic test rig with a circular cross-section by the German Aerospace Center in Berlin.ConclusionsA precise and reasonable definition of an effective Rayleigh conductivity at the scale of one hole is proposed and impedance conditions for the macroscopic pressure or velocity are derived in a systematic procedure. The comparison with experiments show that the derived impedance conditions give a good prediction of the dissipation losses.