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Search results for: complex zeros and poles, numerical computations, root finding algorithm, roots of complex equation, resonators, waveguide structures.
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Multimodal Genetic Algorithm with Phase Analysis to Solve Complex Equations of Electromagnetic Analysis
PublicationIn this contribution, a new genetic-algorithm-based method of finding roots and poles of a complex function of a complex variable is presented. The algorithm employs the phase analysis of the function to explore the complex plane with the use of the genetic algorithm. Hence, the candidate regions of root and pole occurrences are selected and verified with the use of discrete Cauchy's argument principle. The algorithm is evaluated...
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Analysis of nonlinear eigenvalue problems for guides and resonators in microwave and terahertz technology
PublicationThis dissertation presents developed numerical tools for investigating waveguides and resonators' properties for microwave and terahertz technology. The electromagnetics analysis requires solving complex eigenvalue problems, representing various parameters such as resonant frequency or propagation coefficient. Solving equations with eigenvalue boils down to finding the roots of the determinant of the matrix. At the beginning, one...
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Multimodal Particle Swarm Optimization with Phase Analysis to Solve Complex Equations of Electromagnetic Analysis
PublicationIn this paper, a new meta-heuristic method of finding roots and poles of a complex function of a complex variable is presented. The algorithm combines an efficient space exploration provided by the particle swarm optimization (PSO) and the classification of root and pole occurrences based on the phase analysis of the complex function. The method initially generates two uniformly distributed populations of particles on the complex...
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublicationIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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Numerical Test for Stability Evaluation of Analog Circuits
PublicationIn this contribution, a new numerical test for the stability evaluation of analog circuits is presented. Usually, if an analog circuit is unstable then the roots of its characteristic equation are localized on the right half-plane of the Laplace s- plane. Because this region is unbounded, we employ the bilinear transformation to map it into the unit disc on the complex plane. Hence, the existence of any root inside the unit disc...
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A New Approach to Stability Evaluation of Digital Filters
PublicationIn this paper, a new numerical method of evaluating digital filter stability is presented. This approach is based on novel root-finding algorithms at the complex plane using the Delaunay triangulation and Cauchy's Argument Principle. The presented algorithm locates unstable zeros of the characteristic equation with their multiplicities. The proposed method is generic and can be applied to a vast range of systems. Verification of...
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Dimensional Synthesis of Coupled-Resonator Pseudoelliptic Microwave Bandpass Filters with Constant and Dispersive Couplings
PublicationIn this paper, we propose a novel technique for the dimensional synthesis of coupled-resonator pseudoelliptic microwave filters with constant and dispersive couplings. The proposed technique is based on numerical simulations of small structures, involving up to two adjacent resonators, and it accounts for a loading effect from other resonators by replacing them with terminations coupled through appropriately scaled inverters. The...
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Inline Waveguide Filter With Compact Frequency-Dependent Coupling Producing Two Additional Poles and Three Transmission Zeros
PublicationThis work reports a compact frequency-dependent coupling (FDC) structure introduced in a rectangular waveguide, which allows to generate two additional in-band transmission poles and three transmission zeros (TZs). This serves to increase the order/selectivity of the waveguide bandpass filter in a compact inline topology, thus without the need for any additional space/volume or cross coupling. The proposed FDC consists of a partial-height...
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Testing Stability of Digital Filters Using Optimization Methods with Phase Analysis
PublicationIn this paper, novel methods for the evaluation of digital-filter stability are investigated. The methods are based on phase analysis of a complex function in the characteristic equation of a digital filter. It allows for evaluating stability when a characteristic equation is not based on a polynomial. The operation of these methods relies on sampling the unit circle on the complex plane and extracting the phase quadrant of a function...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublicationIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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Highly-Compact Dual-Band Bandpass Waveguide Filter Based on Cross-Shaped Frequency-Dependent Coupling
PublicationThis work reports the design of an original class of highly-compact dual-band bandpass filter based on dual-mode waveguide resonators inter-coupled through a novel type of frequency-dependent coupling (FDC). The devised FDC consists of a cross-shaped metallic structure placed in the broad wall of a rectangular waveguide. This FDC produces two additional poles and three extra transmission zeros (TZs). Specifically, each pole is...
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Global Complex Roots and Poles Finding Algorithm in C × R Domain
PublicationAn algorithm to find the roots and poles of a complex function depending on two arguments (one complex and one real) is proposed. Such problems are common in many fields of science for instance in electromagnetism, acoustics, stability analyses, spectroscopy, optics, and elementary particle physics. The proposed technique belongs to the class of global algorithms, gives a full picture of solutions in a fixed region ⊂ C × R and...
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Self-Adaptive Mesh Generator for Global Complex Roots and Poles Finding Algorithm
PublicationIn any global method of searching for roots and poles, increasing the number of samples increases the chances of finding them precisely in a given area. However, the global complex roots and poles finding algorithm (GRPF) (as one of the few) has direct control over the accuracy of the results. In addition, this algorithm has a simple condition for finding all roots and poles in a given area: it only requires a sufficiently dense...
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Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis for Propagation and Radiation Problems
PublicationA flexible and effective algorithm for complex roots and poles finding is presented. A wide class of analytic functions can be analyzed, and any arbitrarily shaped search region can be considered. The method is very simple and intuitive. It is based on sampling a function at the nodes of a regular mesh, and on the analysis of the function phase. As a result, a set of candidate regions is created and then the roots/poles are verified...
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An Improvement of Global Complex Roots and Poles Finding Algorithm for Propagation and Radiation Problems
PublicationAn improvement of the recently developed global roots finding algorithm has been proposed. The modification allows to shorten the computational time by reducing the number of function calls. Moreover, both versions of the algorithms (standard and modified) have been tested for numerically defined functions obtained from spectral domain approach and field matching method. The tests have been performed for three simple microwave...
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Complex Root Finding Algorithm Based on Delaunay Triangulation
PublicationA simple and flexible algorithm for finding zeros of a complex function is presented. An arbitrary-shaped search region can be considered and a very wide class of functions can be analyzed, including those containing singular points or even branch cuts. The proposed technique is based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes. As a result, a set of candidate points...
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Efficient Complex Root Finding Algorithm for Microwave and Optical Propagation Problems
PublicationArticle relates to the use of innovative root finding algorithm (on a complex plane) to study propagation properties of microwave and optical waveguides. Problems of this type occur not only in the analysis of lossy structures, but also in the study of complex and leaky modes (radiation phenomena). The proposed algorithm is simple to implement and can be applied for functions with singularities and branch cuts in the complex plane...
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On root finding algorithms for complex functions with branch cuts
PublicationA simple and versatile method is presented, which enhances the complex root finding process by eliminating branch cuts and branch points in the analyzed domain. For any complex function defined by a finite number of Riemann sheets, a pointwise product of all the surfaces can be obtained. Such single-valued function is free of discontinuity caused by branch cuts and branch points. The roots of the new function are the same as the...
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Evaluation of propagation parameters of open guiding structures with the use of complex root finding algorithms
PublicationAn efficient complex root tracing algorithm is utilized for the investigation of electromagnetic wave propagation in open guiding structures. The dispersion characteristics of propagated and leaky waves are calculated for a couple of chosen waveguides. The efficiency of the root tracing algorithm is discuses and compared to a global root finding algorithm.
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Efficient Complex Root Tracing Algorithm for Propagation and Radiation Problems
PublicationAn efficient complex root tracing algorithm for propagation and radiation problems is presented. The proposed approach is based on a discretization of Cauchy’s Argument Principle and its generalization to the C × R space. Moreover, an engagement of the tracing process with a global root finding algorithm recently presented in the literature is performed. In order to confirm a validity and efficiency of the proposed technique, a...
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Multipath Complex Root Tracing
PublicationThe problem of multipath root tracing is being addressed in this communication. The self-adaptive complex root tracing algorithm, which was previously utilized for the investigation of various propagation and radiation problems, is analyzed here for the cases when the traced characteristic bifurcates. A procedure of multiroute detection is proposed and demonstrated on the coaxially loaded cylindrical waveguide example.
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A Self-Adaptive Complex Root Tracing Algorithm for the Analysis of Propagation and Radiation Problem
PublicationAn improved complex root tracing algorithm for radiation and propagation issues is proposed. The approach is based on a self-adaptive discretization of Cauchy’s argument principle for a C × R space and requires a reduced number of function calls in comparison to other procedures presented in the literature. A few different examples concerning propagation and radiation problems have been considered to verify the validity and efficiency...
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Efficient model order reduction for FEM analysis of waveguide structures and resonators
PublicationAn efficient model order reduction method for three-dimensional Finite Element Method (FEM) analysis of waveguide structures is proposed. The method is based on the Efficient Modal Order Reduction (ENOR) algorithm for creating macro-elements in cascaded subdomains. The resulting macro-elements are represented by very compact submatrices, leading to significant reduction of the overall number of unknowns. The efficiency of the model...
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Role of public space in designing complex urban structures
PublicationThe aim of this article is to present the main assumptions about design studios as held in the Faculty of Architecture at Gdańsk University of Technology (FA-GUT), Gdańsk, Poland, adapted to the development of key competencies in the urban planning of complex urban structures. One of these competencies is the design of public spaces. The main goal of the studios was to deliver knowledge of the role of public spaces in the design...
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FPGA computation of magnitude of complex numbers using modified CORDIC algorithm
PublicationIn this work we present computation of the magnitude of complex numbers using a modified version of the CORDIC algorithm that uses only five iterations. The relationship between the computation error and the number of CORDIC iterations are presented for floating-point and integer arithmetics. The proposed modification of CORDIC for integer arithmetic relies upon the introduction of correction once basic computations are performed...
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Inline Waveguide Filter With Transmission Zeros Using a Modified-T-Shaped-Post Coupling Inverter
PublicationThis letter reports the design techniques for a class 2 of inline waveguide bandpass filters with sharp-rejection capabil3 ities at the lower stopband based on a novel nonlinear-frequency4 variant-coupling (NFVC) structure. The proposed NFVC consists 5 of a modified-T-shaped metallic post (MTP) that is placed at the 6 center of the waveguide broad wall with its open arms lying 7 along the waveguide width. The engineered NFVC structure 8...
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Numerical analysis of the ostiomeatal complex aeration using the CFD method
PublicationWe aimed to analyse ostiomeatal complex (OMC) aeration using the computational fluid dynamics (CFD) method of simulation based on human craniofacial computed tomography (CT) scans. The analysis was based on CT images of 2 patients: one with normal nose anatomy and one with nasal septal deviation (NSD). The Reynolds-Average Simulation approach and turbulence model based on linear eddy viscosity supplemented with the two-equation...
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Rectangular Waveguide Filters Based on Deformed Dual-Mode Cavity Resonators
PublicationIn this paper, a novel design for rectangular waveguide filters with deformed dual-mode (DM) cavity resonators is demonstrated. The new resonant cavity shape is a result of applying shape deformation to the basic rectangular cavity to enable its dual-mode operation. Internal coupling between the two orthogonal cavity modes is realized by geometry deformation, eliminating the need for additional coupling elements. The designs are...
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Improved magnitude estimation of complex numbers using alpha max and beta min algorithm
PublicationThe paper presents an improved algorithm for calculating the magnitude of complex numbers. This problem, which is a special case of square rooting, occurs for example, in FFT processors and complex FIR filters. The proposed method of magnitude calculation makes use of the modified alpha max and beta min algorithm. The improved version of the algorithm allows to control the maximum magnitude approximation error by using an adequate...
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Simplified Map-based Selection of Optimal Spindle Speeds When Milling Complex Structures
PublicationIn the paper a method for selecting optimal spindle speeds for complex structures during milling operations is presented. It is based on the selection of the spindle speed in accordance with a simple equation resulting from the minimisation of vibration energy, which leads to the minimisation of the work of cut-ting forces presented in previous elaborations by the authors [1]. Optimal spindle speeds are obtained for many points...
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Miniaturized Inline Bandpass Filters Based on Triple-Mode Integrated Coaxial-Waveguide Resonators
PublicationThis work presents a design technique to implement miniaturized cross-coupled bandpass filters in inline physical configurations based on triple-mode resonators. Triple-mode resonances are obtained by using integrated coaxial-waveguide cavity resonators. They consist of two coaxial conducting posts placed in the sidewalls of a rectangular waveguide cavity. In the proposed triplet, a transmission zero (TZ) can be positioned at any...
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An algorithm for enhancing macromodeling in finite element analysis of waveguide components
PublicationAn algorithm for enhancing the finite element method with local model order reduction is presented. The proposed technique can be used in fast frequency domain simulation of waveguide components and resonators. The local reduction process applied to cylindrical subregions is preceded by compression of the number of variables on its boundary. As a result,the finite element large system is converted into a very compact set of linear...
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A Stabilized Complex LOBPCG Eigensolver for the Analysis of Moderately Lossy EM Structures
PublicationThis letter proposes a stabilized locally optimal block preconditioned conjugate gradient method for computing selected eigenvalues for complex symmetric generalized non-Hermitian eigenproblems. Effectiveness of the presented approach is demonstrated for a moderately lossy dual-mode dielectric resonator, modeled using finite-element method with higher order elements
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Nested Space Mapping Technique for Design and Optimization of Complex Microwave Structures with Enhanced Functionality
PublicationIn this work, we discuss a robust simulation-driven methodology for rapid and reliable design of complex microwave/RF circuits with enhanced functionality. Our approach exploits nested space mapping (NSM) technology, which is dedicated to expedite simulation-driven design optimization of computationally demanding microwave structures with complex topologies. The enhanced func-tionality of the developed circuits is achieved by means...
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Implementation of magnitude calculation of complex numbers using improved alpha max plus beta min algorithm
PublicationThe paper presents the hardware implementation of the improved alpha max plus beta min algorithm for calculating the magnitude of complex numbers. This version of the algorithm requires the general division which is performed using a noniterative multiplicative division algorithm. We analyze in detail the division algorithm, its error and the impact of finite word-length signal representations on the assumed total computation error....
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Application of the Monte Carlo algorithm for solving volume integral equation in light scattering simulations
PublicationVarious numerical methods were proposed for analysis of the light scattering phenomenon. Important group of these methods is based on solving the volume integral equation describing the light scattering process. The popular method from this group is the discrete dipole approximation (DDA). DDA uses various numerical algorithms to solve the discretized integral equation. In the recent years, the application of the Monte Carlo (MC)...
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Instantaneous complex frequency for pipeline pitch estimation
PublicationIn the paper a pipeline algorithm for estimating the pitch of speech signal is proposed. The algorithm uses instantaneous complex frequencies estimated for four waveforms obtained by filtering the original speech signal through four bandpass complex Hilbert filters. The imaginary parts of ICFs from each channel give four candidates for pitch estimates. The decision regarding the final estimate is made based on the real parts of...
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Zero-pole approach to computer aided design of in-line siw filters with transmission zeros
PublicationThis paper presents a design of a new type of in-line pseudo-elliptic filters implemented in substrate integrated waveguide(SIW) technology. To realize transmission zeros in in-line topology,frequency-dependent couplings were used. Such dispersive couplingswere implemented as shorted stubs. The design process startswith the generation of a suitable starting point. To this end, anapproximation of SIW as a rectangular waveguide is...
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Human voice modification using instantaneous complex frequency
PublicationThe paper presents the possibilities of changing human voice by modifying instantaneous complex frequency (ICF) of the speech signal. The proposed method provides a flexible way of altering voice without the necessity of finding fundamental frequency and formants' positions or detecting voiced and unvoiced fragments of speech. The algorithm is simple and fast. Apart from ICF it uses signal factorization into two factors: one fully...
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3-D finite-difference time-domain modelling of ground penetrating radar for identification of rebars in complex reinforced concrete structures
PublicationThis paper presents numerical and experimental investigations to identify reinforcing bars using the ground penetrating radar (GPR) method. A novel element of the paper is the inspection of different arrangements of reinforcement bars. Two particular problems, i.e. detection of few adjacent transverse bars and detection of a longitudinal bar located over or under transverse reinforcement, have been raised. An attention was also...
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The Syntheses and Crystal Structures of the First Disiloxane-1,3-dithiol and Its Cadmium Complex.
PublicationThe new silicon–sulfur compound: disiloxane-1,3-dithiol was obtained from silicon disulfide and 2,6-diisopropylphenol in a reaction catalyzed by imidazole or 4-(dimethylamino)pyridine (DMAP). Crystal structure of disiloxane–1,3-dithiol reveals a close-to-linear Si–O–Si angle and a mutual trans position of the two hydrosulfido groups. The compound forms a chelating mononuclear complex with cadmium ions.
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Substrate-integrated waveguide (SIW) filter design using space mapping
PublicationIn this paper, we present a fast technique for an automated design of microwave filters in substrate integrated wave (SIW) technology. The proposed methodology combines the space mapping technique with a cost function defined using the location of complex zeros and poles of filter’s transfer and reflection function and uses a rectangular waveguide as a surrogate model. The effectiveness of the proposed technique is presented with...
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Low-Loss 3D-Printed Waveguide Filters Based on Deformed Dual-Mode Cavity Resonators
PublicationThis paper introduces a new type of waveguide filter with smooth profile, based on specially designed dual-mode (DM) cavity resonators. The DM cavity design is achieved by applying a shape deformation scheme. The coupling between the two orthogonal cavity modes is implemented by breaking the symmetry of the structure, thus eliminating the need for additional coupling elements. The modes operating in the cavity are carefully analyzed...
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Properties and interpretation of Instantaneous Complex Frequency
PublicationThe concept of Instantaneous Complex Frequency (ICF) was first defined by Lindon and developed mainly in works of two authors S. Hahn and M. Rojewski. Although it is not widely used in signal analysis, ICF was already used as a complex signal representation in the verification of handwritten signatures, pitch estimation, symbol timing recovery in PSK receiver and in detection of anomalies in data transmission. It should be noted,...
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Balance error generated by numerical diffusion in the solution of Muskingum equation
PublicationIn the paper the conservative properties of the lumped hydrological models with variable parameters are discussed. It is shown that in the case of the non-linear Muskingum equation the mass balance is not satisfied. The study indicates that the mass balance errors are caused by the improper form of equation and by the numerical diffusion which is generated in the solution. It has been shown that the classical way of derivation...
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The Design of Cavity Resonators and Microwave Filters Applying Shape Deformation Techniques
PublicationThis article introduces shape deformation as a new approach to the computer-aided design (CAD) of high-frequency components. We show that geometry deformation opens up new design possibilities and offers additional degrees of freedom in the 3-D modeling of microwave structures. Such design flexibility is highly desirable if the full potential of additive manufacturing (AM) is to be exploited in the fabrication of RF and microwave...
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An MOR Algorithm Based on the Immittance Zero and Pole Eigenvectors for Fast FEM Simulations of Two-Port Microwave Structures
PublicationThe aim of this article is to present a novel model-order reduction (MOR) algorithm for fast finite-element frequency-domain simulations of microwave two-port structures. The projection basis used to construct the reduced-order model (ROM) comprises two sets: singular vectors and regular vectors. The first set is composed of the eigenvectors associated with the poles of the finite-element method (FEM) state-space system, while...
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Numerical Characterization of Thresholds for the Focusing 1d Nonlinear Schrödinger Equation
PublicationThe focusing nonlinear Schrödinger equation arises in various physical phenomena and it is therefore of interest to determine mathematical conditions on the initial data that guarantee whether the corresponding solution will blow up in finite time or exist globally in time. We focus on solutions to the mass‐supercritical nonlinear Schrödinger equation (1) in 1D case. In particular, we investigate numerical thresholds between blow...
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A Novel Trust-Region-Based Algorithm with Flexible Jacobian Updates for Expedited Optimization of High-Frequency Structures
PublicationSimulation-driven design closure is mandatory in the design of contemporary high-frequency components. It aims at improving the selected performance figures through adjustment of the structure’s geometry (and/or material) parameters. The computational cost of this process when employing numerical optimization is often prohibitively high, which is a strong motivation for the development of more efficient methods. This is especially...
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Multi-criterion, evolutionary and quantum decision making in complex systems
PublicationMulti-criterion, evolutionary and quantum decision making supported by the Adaptive Quantum-based Multi-criterion Evolutionary Algorithm (AQMEA) has been considered for distributed complex systems. AQMEA had been developed to the task assignment problem, and then it has been applied to underwater vehicle planning as another benchmark three-criterion optimization problem. For evaluation of a vehicle trajectory three criteria have...