Diakoptic Method Research Articles

A Lagrangian variational modular approach to thermodynamic systems

The diakoptical method developed by Kron (1963) has been known as a powerful tool in modeling and analyzing large-scale physical systems. The principal idea lies in the process of tearing and interconnection for a physical system, namely, one can reticulate the system into several subsystems, each of which is called a primitive system when it once torn apart from the original system. The original system can be regarded as an interconnected system via the interconnection structure, which is known to be modeled as a Dirac structure. This paper illustrates the idea of a Lagrangian variational modular approach by extending the case in mechanics done by Jacobs and Yoshimura (2014) to the case of thermodynamic systems, by following Gay-Balmaz and Yoshimura (2023), together with examples of non-simple thermodynamic systems with internal heat transfer and mechanical interactions.

DEVELOPMENT OF A MATHEMATICAL MODEL OF TRANSITIONAL PROCESSES IN THE ELECTRICAL NETWORK IN PHASE COORDINATES

Distribution electrical networks of great length are characterized by a high order of the system of equations of electromagnetic transients. To improve the efficiency of modelling such networks, it is necessary to develop formalized procedures that provide automation of both the solution and the formation of systems of equations using modern computer technology. To simplify the development of mathematical models, transformations are used to move from a real three-phase network to other coordinate systems, but this is achieved at the expense of additional restrictions. To solve the problems of choosing and increasing the efficiency of means for limiting currents and overvoltages during transient processes in electrical networks, it is necessary to have a model reflecting a number of features, both of the networks themselves, and of the transient processes occurring in them. This is implemented in a model based on the representation of network elements not by single-phase equivalents, but by equations in phase coordinates. These equations contain the parameters of the network elements (active resistances, own and mutual inductances and capacitances) and the parameters of its mode (currents, voltages, phase powers), corresponding to the real physical parameters of electrical systems. A mathematical model of electromagnetic transient processes in an electrical network in phase coordinates has been developed. Calculation of the transient process when using the implicit method and representing the three-phase elements at the integration step by discrete models makes it possible to reduce the solution of a system of differential equations to multiple formation and solution of a system of equations. The diakoptic method for studying complex systems was developed, which was used to develop a mathematical model of electromagnetic transient processes in a three-phase electrical network. The proposed form of representation of discrete models of three-phase multipoles allows one to formalize both the solution procedure and the procedure for drawing up equations of transient processes for three-phase circuits of electrical networks of arbitrary configuration. Prospects for further research are computational experiments to study electromagnetic transient processes during ground faults in electrical networks of arbitrary configuration with various neutral modes and means of limiting currents and overvoltages.

Analysis of heterogeneous information and diagnostics of complex technical systems based on methods of diakoptics and correlation analysis

The article is devoted to the investigation of the applicability of the correlation analysis for the processing of heterogeneous data obtained from complex technical systems. In this article, heterogeneous data is understood to mean heterogeneous data obtained from means of monitoring the state of individual objects. The proposed approach is proposed to be used to diagnose complex technical systems using the example of digital substations. For this purpose, an imitation model for power substation based on the method of diakoptics was developed. And all components of the system, regardless of their physical functioning principles, are represented in the form of electrical sub-models. The substitution schemes based on operational amplifiers are used. The model simulates the operation of measuring current and voltage transformers, power transformer, circuit breaker and relay protection. To test the proposed approach, we also considered an amplifier circuit based on three operational amplifiers. The calculation of the circuit is described, as well as the simulation of the circuit in the MicroCap environment. The simulation was carried out with the aim of realizing parametric and structural diagnostics on the basis of correlation analysis. The results of modeling the applicability of the proposed approach for both parametric and structural diagnostics is proved operability.

Volume Integral Equation-Based Diakoptic Method for Electromagnetic Modeling

A novel diakoptic method based on volume integral equation (VIE) modeling of subsystems is proposed for 3-D electromagnetic analysis. The theoretical foundation of the method is the surface and volume equivalence principles, as it combines the VIE and surface integral equation (SIE) formulations, in conjunction with the method of moments (MoM). The method breaks the original structure into a number of nonoverlapping closed-region subsystems that contain inhomogeneous dielectric materials and an open-region subsystem. Each subsystem is analyzed completely independently applying the double higher order large-domain Galerkin generalized MoM-VIE-SIE (VSIE) or MoM-SIE solvers. The final solution is obtained from diakoptic matrices expressing linear relations between the electric and magnetic equivalent surface current coefficients on diakoptic surfaces. The proposed VSIE-diakoptic method is validated, evaluated, and discussed in several characteristic examples. The examples demonstrate that the diakoptic method substantially increases the efficiency of the conventional MoM-VIE approach. When compared with the pure MoM-VIE double higher order technique, the diakoptic approach enables very considerable accelerations and memory savings, while fully preserving the accuracy of the analysis.

Diakoptic Approach Combining Finite-Element Method and Method of Moments in Analysis of Inhomogeneous Anisotropic Dielectric and Magnetic Scatterers

A new diakoptic method combining the finite-element method and the method of moments is proposed for analysis of inhomogeneous anisotropic dielectric and magnetic scatterers. The method splits the original electromagnetic system into a number of closed-region finite-element method subsystems containing material complexities and an open-region method of moments subsystem, which are analyzed independently. The solution to the original problem is obtained from linear relations between coefficients in expansions of equivalent electric and magnetic surface currents on diakoptic boundary surfaces. Diakoptic electric sources and the magnetic field in finite-element method subsystems are connected using dual sets of higher-order hierarchical basis functions.

SOLVING WAVE PROPAGATION WITHIN FINITE-SIZED COMPOSITE MEDIA WITH LINEAR EMBEDDING VIA GREEN'S OPERATORS

The calculation of electromagnetic (EM) flelds and waves inside flnite-sized structures comprised of difierent media can beneflt from a diakoptics method such as linear embedding via Green's oper- ators (LEGO). Unlike scattering problems, the excitation of EM waves within the bulk dielectric requires introducing sources inside the struc- ture itself. To handle such occurrence, we have expanded the set of LEGO sub-domains | employed to formulate an EM problem | to deal with the inclusion of elementary sources. The corresponding sub- domains (bricks) play the role of \generators in the equivalent model. Moreover, if a source is \turned ofi, as it were, the enclosing brick can be utilized as a numerical \probe to sample the EM fleld. In this paper, we present the integral equations of LEGO modifled so as to accommodate generator/probe bricks. Numerical results are provided which demonstrate the validity and the e-ciency of the approach.

CONVERGENCE PROPERTIES OF A DIAKOPTICS METHOD FOR ELECTROMAGNETIC SCATTERING FROM 3-D COMPLEX STRUCTURES

Linear embedding via Green's operators (LEGO) is a diakoptics method that employs electromagnetic \bricks to formulate problems of wave scattering from complex structures (e.g., penetrable bodies with inclusions). In its latest version the LEGO integral equations are solved through the Method of Moments combined with adaptive generation of Arnoldi basis functions (ABF) to compress the resulting algebraic system. In this paper we review and discuss the convergence properties of the numerical solution in relation to the number of ABFs. Besides, we address the issue of setting the threshold for stopping the generation of ABFs in conjunction with the adaptive Arnoldi algorithm.

844 陰的なラグランジュ系による柔軟多体系のダイナミクスの定式化

The paper presents a modeling method of flexible multibody dynamics in the context of implicit Lagrangian systems. The main idea is based on a Diakoptical method originally developed by Kron, which reticulates required kinematical and dynamical relations into separate ones and then incorporate them into an interconnection of implicit Lagrangian systems. By using the idea, we first show how a flexible beam attached to a rigid base undergoing a large overall motion can be modeled as an interconnected implicit Lagrangian system, in which geometrically nonlinear couplings between flexible deformations and large overall motions are incorporated into a nonlinear finite element model. Lastly, some numerical results are shown in comparison with the model developed by Simo and Vu-Quoc.

Algorithms for Fast Simulation of Transformer Windings for Diagnostic Testing of Power Transformers

Accurate high-frequency simulation of power transformer windings often involves detailed turn-by-turn modeling of the winding structure. The most detailed models currently in existence use multiphase transmission systems with frequency-dependent losses. The conventional Electromagnetic Transients Program method of solving these systems involves eigenvalue decompositions for hyperbolic corrections as well as matrix inversions, both of which are prohibitively computationally expensive. This paper presents three optimized algorithms for improving the simulation speed of the most common circuit models by taking advantage of useful mathematical identities. A diakoptic method of splitting the system into series and shunt elements to exploit the sparsity of the shunt admittance system is also presented. The result is a significant speed increase, making the simulation of large systems more feasible and minimizing the need for circuit-reduction techniques.

A Comparative Study on the Induced Current Density in Humans Exposed to ELF Electric Fields

A comparison between two theoretical methods, recently adopted for evaluating induced currents in a human body, is here presented. In both cases, a vertical ELF electric field is assumed for the coupling to a standard human subject.Specifically, the diakoptic method (DM), applied to a homogeneous multi-sphere model of man with low partitioning degree, and the Boundary Element Method (BEM), applied to a non-homogeneous model with high partitioning degree, have been selected. The analytical and numerical formulations, respectively distinctive of the above methods, are carefully described and a number of data are reported and commentedupon.

Linear embedding via Green’s operators: A modeling technique for finite electromagnetic band-gap structures

We propose a modular electromagnetic modeling procedure for large finite electromagnetic band-gap (EBG) structures, called linear embedding via Green's operators. It is a diakoptic method based on the Huygens-Schelkunoff principle involving equivalent boundary current sources that electromagnetically characterize the enclosed domain of arbitrary shapes, as if it were a multiport system. In a cascade of embedding steps, separate reusable domains are combined to form larger domains. Device design often involves tuning local medium properties in a compact designated domain with a large environment. Through an additional embedding step the equivalent sources describing the environment can be transferred to the boundary of the designated domain, rendering subsequent design steps very fast. This two-stage optimization process is applied in the design of an EBG power splitter.

An improved model of man for ESD applications

Human-generated ESD current waveshapes are predicted under contact discharge and arc discharge conditions. The uncertainties connected to man's posture and proximity to the victim are carefully examined. The adopted human body model is devised to be composed of 11 elemental blocks and treated by the diakoptic method in analogy with network theory. The set of given leakage capacitances, in conjunction with the resistances and inductances as serial parameters, forms a complex RLC network. The assembly includes the grounded or ungrounded victim and image elements due to the presence of the plane and a nearby vertical wall. A PSPICE software allows the discharge scenario to be evaluated. New insight into the complex charge transfer is thus gained, which is combined with arc discharge performances. This careful analytical interpretation of the ESD phenomenon could contribute to in-progress standardization.

Analysis of open microstrip structures by using diakoptic method of lines combined with periodic boundary conditions

This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch current excited by plane wave. Impedance matrix elements are computed by using fast Fourier transform(FFT), and reduced equation is solved by using diakoptic technique. Consequently, the computing time is reduced significantly. The convergence property of simulating open structure by using PBC and the comparison of the computer time between using PBC and usual absorbing boundary condition (ABC) show the validity of the method proposed in this paper. Finally, the resonant frequency of a microstrip patch is computed. The numerical results obtained are in good agreement with those published.

96/06103 Novel network diakoptics method for parallel solving the decoupled load flow of a power system

96/06103 Novel network diakoptics method for parallel solving the decoupled load flow of a power system

Novel network diakoptics method for parallel solving the decoupled load flow of a power system

In this paper a novel network diakoptics method and a parallel algorithm are presented for solving the decoupled load flow of a power system. Using the novel network diakoptics method, the power system is broken down into several smaller components. Within each of these components the decoupled load flow solution can be solved using parallel computing and the results combined to yield the solution of the total system. An application of the bordered block diagonal form is developed to solve the decoupled load flow program based on a multi-processor which consists of a number of transputers. The results show that the proposed method is adequate for parallel processing on the decoupled load flow solution.

Application of clustering and factorisation tree techniques for parallel solution of sparse network equations

Through the use of diakoptical techniques it is possible to solve the network equations for a power system using a parallel computer architecture. Traditional parallel solution techniques give an unimpressive return on investment as more processors are applied to the problem owing to unacceptably large sequential sections of the algorithm and ill-balanced computational loads. The paper analyses the diakoptical method using the factorisation tree as a tool. New algorithms are proposed for network splitting, node ordering and load balancing between processors. This, in connection with a novel recursively parallel solution algorithm, gives improved speedup over the conventional parallel solution method. Simulation results are presented which confirm the usefulness of the method.

Fast sequential FDTD diakoptics method using the system identification technique

The sequential finite-difference time-domain (FDTD) diakoptics method is accelerated by a system identification technique. The time-domain convolution in diakoptics is replaced by a difference equation with a small number of coefficients. Hence, the memory size is also reduced. The validity of this method is confirmed by comparison with simulated results from Microwave SPICE. The accuracy of this fast algorithm is also demonstrated by the analysis of cascaded circuit modules.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of disk‐loaded antenna with matching posts by diakoptic theory

AbstractAs equipment becomes smaller and lighter, the antenna needs to become smaller and planarized. One of the analysis methods for the small antenna with a complex configuration is the Diakoptic (DK) method which is a type of moment method. By means of the DK method, an analysis is carried out for a disk‐loaded monopole antenna (DLA) with matching posts which is a planar antenna suitable for mobile communication. In the analysis, the current distribution on the disk is approximated with a single current distribution function to reduce the computational amount and time. The effectiveness of the analysis is demonstrated by comparing the analysis results for the cases with one and two matching posts with the experimental data.

A comparison between the time‐domain and the frequency‐domain diakoptic methods of solving field problems by transmission‐line modelling

AbstractThe nature and significance of time‐domain approximations needed for a diakoptic solution using transmission‐line modelling (TLM) are examined. Truncation, filtering and repeated convolution of time responses result in severe restrictions in the accuracy of time‐domain diakoptics. The frequency‐domain diakoptic method has several advantages, including speed and simplicity, and warrants further study.

Modified diakoptic theory of antennas

The diakoptic theory of antennas, suggested by Goubau, is an independent approach to the numerical analysis of multi-element antennas of complex configuration. Based on physical reasoning, the theory is designed to be amenable to efficient computer evaluation. However, as an intermediate step, the theory involves hypothetical current sources with one terminal only, which violate the current continuity condition, so that Maxwell's equations cannot be applied without precautions. Here, a modified version of the diakoptic theory is presented which avoids this complication by a simple change in the basic approach while otherwise it preserves most features of Goubau's original theory. In addition, the modified version starts with a well-established, rigorous impedance matrix formulation of the problem and allows one to readily establish the relationships with the method of moments. Thus, it may facilitate understanding the diakoptic method.