arXiv subjects

Lukas Jelinek

Publications and source records attributed to Lukas Jelinek.

At least 37 records · Page 2Linked to original sources

arXiv2023

Optimal Inverse Design Based on Memetic Algorithms -- Part 1: Theory and Implementation

A memetic framework for optimal inverse design is proposed by combining a local gradient-based procedure and a robust global scheme. The procedure is based on method-of-moments matrices and does not demand full inversion of a system matrix. Fundamental bounds are evaluated for all optimized metrics in the same manner, providing natural stopping criteria and quality measures for realized devices. Compared to density-based topology optimization, the proposed routine does not require filtering or thresholding. Compared to commonly used heuristics, the technique is significantly faster, still preserving a high level of versatility and robustness. This is a two-part paper in which the first part is devoted to the theoretical background and properties, and the second part applies the method to examples of varying complexity.

math.OC↗

arXiv2023

Energy Stored by Radiating Systems

Though commonly used to calculate Q-factor and fractional bandwidth, the energy stored by radiating systems (antennas) is a subtle and challenging concept that has perplexed researchers for over half a century. Here, the obstacles in defining and calculating stored energy in general electromagnetic systems are presented from first principles as well as using demonstrative examples from electrostatics, circuits, and radiating systems. Along the way, the concept of unobservable energy is introduced to formalize such challenges. Existing methods of defining stored energy in radiating systems are then reviewed in a framework based on technical commonalities rather than chronological order. Equivalences between some methods under common assumptions are highlighted, along with the strengths, weaknesses, and unique applications of certain techniques. Numerical examples are provided to compare the relative margin between methods on several radiating structures.

physics.class-ph↗

arXiv2022

Performance Bounds of Magnetic Traps for Neutral Particles

Knowledge of the fundamental limitations on a magnetic trap for neutral particles is of paramount interest to designers as it allows for the rapid assessment of the feasibility of specific trap requirements or the quality of a given design. In this paper, performance limitations are defined for convexity of magnetic trapping potential and bias field using a local approximation in the trapping center. As an example, the fundamental bounds are computed for current supporting regions in the form of a spherical shell, a cylindrical region, and a box. A Pareto-optimal set considering both objectives is found and compared with known designs of the Baseball trap and Ioffe-Pritchard trap. The comparison reveals a significant gap in the performance of classical trap designs from the fundamental limitations. This indicates a possibility of improved trap designs and modern techniques of shape synthesis are applied in order to prove their existence. The topologically optimized traps perform almost two times better as compared to conventional designs. Last, but not least, the developed framework might serve as a prototype for the formulation of fundamental limitations on plasma confinement in a wider sense.

physics.comp-ph↗

arXiv2022

Characteristic Mode Decomposition Using the Scattering Dyadic in Arbitrary Full-Wave Solvers

Characteristic modes are formulated using the scattering dyadic, which maps incident plane waves to scattered far fields generated by an object of arbitrary material composition. Numerical construction of the scattering dyadic using arbitrary full-wave electromagnetic solvers is demonstrated in examples involving a variety of dielectric and magnetic materials. Wrapper functions for computing characteristic modes in method-of-moments, finite-difference time domain, and finite element solvers are provided as supplementary material.

cs.CE↗

arXiv2022

Iterative Calculation of Characteristic Modes Using Arbitrary Full-wave Solvers

An iterative algorithm is adopted to construct approximate representations of matrices describing the scattering properties of arbitrary objects. The method is based on the implicit evaluation of scattering responses from iteratively generated excitations. The method does not require explicit knowledge of any system matrices (e.g., stiffness or impedance matrices) and is well-suited for use with matrix-free and iterative full-wave solvers, such as FDTD, FEM, and MLFMA. The proposed method allows for significant speed-up compared to the direct construction of a full transition matrix or scattering dyadic. The method is applied to the characteristic mode decomposition of arbitrarily shaped obstacles of arbitrary material distribution. Examples demonstrating the speed-up and complexity of the algorithm are studied with several commercial software packages.

physics.comp-ph↗

arXiv2021

Method of Moments and T-matrix Hybrid

Hybrid computational schemes combining the advantages of a method of moments formulation of a field integral equation and T-matrix method are developed in this paper. The hybrid methods are particularly efficient when describing the interaction of electrically small complex objects and electrically large objects of canonical shapes such as spherical multi-layered bodies where the T-matrix method is reduced to the Mie series making the method an interesting alternative in the design of implantable antennas or exposure evaluations. Method performance is tested on a spherical multi-layer model of the human head. Along with the hybrid method, an evaluation of the transition matrix of an arbitrarily shaped object is presented and the characteristic mode decomposition is performed, exhibiting fourfold numerical precision as compared to conventional approaches.

physics.comp-ph↗

arXiv2021

Fundamental Bounds to Time-Harmonic Quadratic Metrics in Electromagnetism: Overview and Implementation

Fundamental bounds on quadratic electromagnetic metrics are formulated and solved via convex optimization. Both dual formulation and method-of-moments formulation of the electric field integral equation are used as key ingredients. The trade-off between metrics is formulated as a multi-objective optimization resulting in Pareto-optimal sets. Substructure fundamental bounds are also introduced and formulated as additional affine constraints. The general methodology is demonstrated on a few examples of minimal complexity and all examples are supported with freely available MATLAB codes contained in the developed package on fundamental bounds.

physics.comp-ph↗

arXiv2021

Unified Theory of Characteristic Modes: Part II -- Tracking, Losses, and FEM Evaluation

This is the second component of a two-part paper dealing with a unification of characteristic mode decomposition. This second part addresses modal tracking and losses and presents several numerical examples for both surface- and volume-based method-of-moment formulations. A new tracking algorithm based on algebraic properties of the transition matrix is developed, achieving excellent precision and requiring a very low number of frequency samples as compared to procedures previously reported in the literature. The transition matrix is further utilized to show that characteristic mode decomposition of lossy objects fails to deliver orthogonal far fields and to demonstrate how characteristic modes can be evaluated using the finite element method.

physics.class-ph↗

arXiv2021

Unified Theory of Characteristic Modes: Part I -- Fundamentals

A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition matrices, the latter of which was used in early definitions of characteristic modes and is uniquely defined for all scattering scenarios. This also makes it possible to extend the known application domain of characteristic mode decomposition to any other frequency-domain solver capable of generating transition matrices, such as finite difference or finite element methods. The formulation of characteristic modes using a transition matrix allows for the decomposition of induced currents and scattered fields from arbitrarily shaped objects, providing high numerical dynamics and increased stability, removing the issue of spurious modes, and offering good control of convergence. This first part of a two-part paper introduces the entire theory, extensively discusses its properties and offers its basic numerical validation.

physics.class-ph↗

arXiv2021

Fundamental Bounds on the Performance of Monochromatic Passive Cloaks

Fundamental bounds on the performance of monochromatic scattering-cancellation and field-zeroing cloaks made of prescribed linear passive materials occupying a predefined design region are formulated by projecting field quantities onto a sub-sectional basis and applying quadratically constrained quadratic programming. Formulations are numerically tested revealing key physical trends as well as advantages and disadvantages between the two classes of cloaks. Results show that the use of low-loss materials with high dielectric contrast affords the highest potential for effective cloaking.

physics.optics↗

arXiv2020

Excitation of Orthogonal Radiation States

A technique of designing antenna excitation realizing orthogonal states is presented. It is shown that a symmetric antenna geometry is required in order to achieve orthogonality with respect to all physical quantities. A maximal number of achievable orthogonal states and a minimal number of ports required to excite them are rigorously determined from the knowledge of an antenna's symmetries. The number of states and number of ports are summarized for commonly used point groups (a rectangle, a square, etc.). The theory is applied to an example of a rectangular rim where the positions of ports providing the best total active reflection coefficient, an important metric in multi-port systems, are determined. The described technique can easily be implemented in existing solvers based on integral equations.

eess.SP↗

arXiv2020

Finding Optimal Total Active Reflection Coefficient and Realized Gain for Multi-port Lossy Antennas

A numerically effective description of the total active reflection coefficient and realized gain are studied for multi-port antennas. Material losses are fully considered. The description is based on operators represented in an entire-domain port-mode basis, i.e., on matrices with favorably small dimensions. Optimal performance is investigated and conditions on optimal excitation and matching are derived. The solution to the combinatorial problem of optimal ports' placement and optimal feeding synthesis is also accomplished. Four examples of various complexity are numerically studied, demonstrating the advantages of the proposed method. The final formulas can easily be implemented in existing electromagnetic simulators using integral equation solver.

eess.SP↗

arXiv2020

Trade-offs in absorption and scattering by nanophotonic structures

Trade-offs between feasible absorption and scattering cross sections of obstacles confined to an arbitrarily shaped volume are formulated as a multi-objective optimization problem solvable by Lagrangian-dual methods. Solutions to this optimization problem yield a Pareto-optimal set, the shape of which reveals the feasibility of achieving simultaneously extremal absorption and scattering. Two forms of the trade-off problems are considered involving both loss and reactive material parameters. Numerical comparisons between the derived multi-objective bounds and several classes of realized structures are made. Additionally, low-frequency (electrically small, long wavelength) limits are examined for certain special cases.

physics.optics↗

arXiv2020

A Role of Symmetries in Evaluation of Fundamental Bounds

A problem of the erroneous duality gap caused by the presence of symmetries is solved in this paper utilizing point group theory. The optimization problems are first divided into two classes based on their predisposition to suffer from this deficiency. Then, the classical problem of Q-factor minimization is shown in an example where the erroneous duality gap is eliminated by combining solutions from orthogonal sub-spaces. Validity of this treatment is demonstrated in a series of subsequent examples of increasing complexity spanning the wide variety of optimization problems, namely minimum Q-factor, maximum antenna gain, minimum total active reflection coefficient, or maximum radiation efficiency with self-resonant constraint. They involve problems with algebraic and geometric multiplicities of the eigenmodes, and are completed by an example introducing the selective modification of modal currents falling into one of the symmetry-conformal sub-spaces. The entire treatment is accompanied with a discussion of finite numerical precision, and mesh grid imperfections and their influence on the results. Finally, the robust and unified algorithm is proposed and discussed, including advanced topics such as the uniqueness of the optimal solutions, dependence on the number of constraints, or an interpretation of the qualitative difference between the two classes of the optimization problems.

physics.comp-ph↗

arXiv2019

Modal Tracking Based on Group Theory

Issues in modal tracking in the presence of crossings and crossing avoidances between eigenvalue traces are solved via the theory of point groups. The von Neumann-Wigner theorem is used as a key factor in predictively determining mode behavior over arbitrary frequency ranges. The implementation and capabilities of the proposed procedure are demonstrated using characteristic mode decomposition as a motivating example. The procedure is, nevertheless, general and can be applied to an arbitrarily parametrized eigenvalue problems. A treatment of modal degeneracies is included and several examples are presented to illustrate modal tracking improvements and the immediate consequences of improper modal tracking. An approach leveraging a symmetry-adapted basis to accelerate computation is also discussed. A relationship between geometrical and physical symmetries is demonstrated on a practical example.

physics.comp-ph↗

arXiv2019

Optimal Planar Electric Dipole Antenna

Considerable time is often spent optimizing antennas to meet specific design metrics. Rarely, however, are the resulting antenna designs compared to rigorous physical bounds on those metrics. Here we study the performance of optimized planar meander line antennas with respect to such bounds. Results show that these simple structures meet the lower bound on radiation Q-factor (maximizing single resonance fractional bandwidth), but are far from reaching the associated physical bounds on efficiency. The relative performance of other canonical antenna designs is compared in similar ways, and the quantitative results are connected to intuitions from small antenna design, physical bounds, and matching network design.

physics.class-ph↗

arXiv2019

Inversion-Free Evaluation of Nearest Neighbors in Method of Moments

A recently introduced technique of topology sensitivity in method of moments is extended by the possibility of adding degrees-of-freedom (reconstruct) into underlying structure. The algebraic formulation is inversion-free, suitable for parallelization and scales favorably with the number of unknowns. The reconstruction completes the nearest neighbors procedure for an evaluation of the smallest shape perturbation. The performance of the method is studied with a greedy search over a Hamming graph representing the structure in which initial positions are chosen from a random set. The method is shown to be effective data mining tool for machine learning-related applications.

physics.comp-ph↗

arXiv2019

Shape Synthesis Based on Topology Sensitivity

A method evaluating the sensitivity of a given parameter to topological changes is proposed within the method of moments paradigm. The basis functions are used as degrees of freedom which, when compared to the classical pixeling technique, provide important advantages, one of them being impedance matrix inversion free evaluation of the sensitivity. The devised procedure utilizes port modes and their superposition which, together with only a single evaluation of all matrix operators, leads to a computationally effective procedure. The proposed method is approximately one hundred times faster than contemporary approaches, which allows the investigation of the sensitivity and the modification of shapes in real-time. The method is compared with known approaches and its validity and effectiveness is verified using a series of examples. The procedure can be implemented in up-to-date EM simulators in a straightforward manner. It is shown that the iterative repetition of the topology sensitivity evaluation can be used for gradient-based topology synthesis. This technique can also be employed as a local step in global optimizers.

physics.comp-ph↗