Paata Tsereteli

A partitioned MoM scheme is suggested to effectively handle series of geometries having a predominant common part. This scheme is based on a partitioned calculation and inversion of unvarying (basis) and differing (additional) parts of impedance matrices to quickly obtain solutions to EM problems on a series of geometries. The suggested scheme was validated to compare characteristics of 2 types of AM antennas mounted in a rear window of the realistic car model. Next, this scheme was applied to develop optimization strategy to solve vehicle antenna engineering EMC problems. An advantage of a new MoM scheme in sufficiently decreasing calculation time is illustrated, and its potential for solution of complicated automotive and other vehicle EMC problems is outlined. 

Investigations of vehicle glass antenna are the important part of EMC simulations in automotive industry. Hybrid FEM/MoM approach can be considered as one of the ways of direct solution. MoM techniques are very efficient for solving open radiation problems with long thin wires and conducting surfaces. FEM is very well suited for modeling inhomogeneous dielectric bodies. Thus, the conjugation of the MoM with the FEM exploits the benefits from both methods.

Automotive antenna design is a sophisticated process, related to both specific features of antennas itself, and their installation and operation in the complex electromagnetic (EM) environment of an automobile. Modern automobiles include a number of antenna solutions (AM/ FM radio, remote control systems, satellite services, etc.), operating simultaneously in the presence of car body, harness and electronic equipment. Design of them becomes even more complicated, when conformal and hidden antenna solutions are applied. These solutions encompass integrated glass antennas or active antennas, in combination with amplifiers, radio/ TV receivers and other network devices. Moreover, parametric tuning is required at all stages of development, making the complete chain of antenna design rather laborious and complex. These problems can be overcome using computer simulations with numerical analysis. However, accurate modelling of complicated models requires a combined usage of both traditional and special methods and techniques, including adaptive and hybrid ones, and special means for a fast and optimized numerical solution. Though different computational methods are used, the Method of Moments (MoM) (Harrington, 1968) is the most popular method in automotive antenna design. This chapter describes the recent enhancements (Bogdanov & Jobava, 2003; Bogdanov et al. 2004a, Bogdanov et al., 2004b; Jobava et al., 2005; Bogdanov et al., 2009; Bogdanov et al., 2010a; Bogdanov et al., 2010b) of the traditional MoM, offering a set of up-to-date methods and techniques, whose application provides an accurate and effective solution of EM problems related to modern automotive antenna simulations. After description of methods or techniques, application examples are presented. These examples include comparisons to other methods and experimental data. All the calculations are performed using the MoMbased code “TriD” (Bogdanov et al., 2010c) being a core of the program packages “EMC Studio” (EMCoS, 2010a) and “EMCoS Antenna VirtualLab” (EMCoS, 2010b).

The nonstationary problem for system of parabolic equations with first order boundary conditions is considered. The three-layer factorized scheme, whose solution does not require the inversion of the matrix, is constructed. The obtained algorithms can be effectively used on multiprocessing computing systems. For the difference scheme, the a priori estimation on layer in norm of some grid space is obtained, on the basis of which the convergence of its solution to the solution of the initial problem is proved.

Mathematical models of immune mediated disorders provide an analytic framework in which we can address specific questions concerning disease immune dynamics and the choice of treatment. Such models are actively reported in the field of tumor immunology and immunotherapy by de Phillis et al [2, 3]. Herein, we present a novel mathematical model that describes the immunopathogenesis and the targeted immunotherapy of rheumatoid arthritis using non-linear differential equations. Of importance, based on this model, the software that solves the Cauchy problem for this system and visualizes the obtained solution is developed. Solutions are obtained for the case of each individual patient to decipher the disease progress and the absence of disease.

The model based investigation of immune mediated disorders is a complex and evolving field. We herein report about further development of the mathematical model of rheumatoid arthritis. We improved previously reported model (Odisharia et al. in Vekua Inst Appl Math 31:107–110, 2017, [1]) by providing treatment component. Tocilizumab is considered as a drug for treatment. The model explores the functional dynamics of cartilage destruction during disease progression, in which a model deciphers the interactions between B and T lymphocytes. Coefficients of model equations allow the adaptation of the model to an individual case of patients that is its advantage. These coefficients can be calculated automatically based on the results of blood clinical analysis. Developed software simulates treatment process which will help in process of choosing optimal treatment scheme.

A partitioned MoM scheme is suggested for electromagnetically treating assemblies of geometries having a substantial common part. This scheme is applied to compare and optimize the characteristics of various antennas installed on an airplane surface. The effectiveness of the suggested scheme to decrease CPU time efficiently is. demonstrated. The perspectives of the new scheme for the solution of various EM and EMC problems in vehicle design are outlined.

Solving modern problems of electromagnetic compatibility (EMC) in large systems involving electronic equipment (such as ships, planes, automobiles), in view of the complexity of the problems, demands enormous computing capacities and machine resources. Actually, solving many problems is impossible on standard personal computers/workstations. Therefore, the construction of high-efficiency cluster systems, allowing uniting in common use the resources of a group of personal computers, is very important. However, in order to exploit the computing power offered by a cluster of personal computers, efficient parallel implementations of 3D electromagnetic solvers, i.e. method of moments (MoM) solvers, using the message-passing paradigm have to be developed. We describe our experience with a parallel MoM solver, TriD (F.G. Bogdanov et al., 2003), for large-scale EMC problems.

The aim of this work is development of robust model suitable for analysis of automobile glass antennas. The model is based on FEM/MOM (Finite Element Method combined with Method of Moments) considerations for effective and accurate solution and reflects the latest improvements and modifications to EMAP5 [l],[2],[3]. Appropriate changes on pre-processing stage are performed in order to reflect data flow peculiarities in the automotive industry. Performance of the solver is improved because of usage sophisticated matrix solver. Some examples are provided to demonstrate the capability of modeling and to compare calculation time with those obtained original EMAP5.

Solving modern problems of electromagnetic compatibility (EMC) in large systems involving electronic equipment (such as ships, planes, automobiles), in view of the complexity of the problems, demands enormous computing capacities and machine resources. Actually, solving many problems is impossible on standard personal computers/workstations. Therefore, the construction of high-efficiency cluster systems, allowing uniting in common use the resources of a group of personal computers, is very important. However, in order to exploit the computing power offered by a cluster of personal computers, efficient parallel implementations of 3D electromagnetic solvers, i.e. method of moments (MoM) solvers, using the message-passing paradigm have to be developed. We describe our experience with a parallel MoM solver, TriD (F.G. Bogdanov et al., 2003), for large-scale EMC problems.

Based on the recent enhancements of the traditional MoM, a combined set of the advanced methods, techniques and special means is proposed to provide an accurate and effective simulation of EM/EMC automotive antenna problems.

In this paper effective acceleration technique for solving of electrically large EMC problems is described. It is known that for solving of large linear systems iterative solvers are very practical. The main problems for solution of such problems are related to large memory requirement for matrix and poor convergence of iterative solver. For solution of these problems the following techniques are applied: ACA (Adaptive Cross Approximation) technique for matrix compression and SPAI (Sparse Approximate Inverse) preconditioner to speed up convergence of iterative solver. For solving linear system BICGSTAB (Biconjugate Gradient Stabilised) solver is used. The advantages of considered solution are demonstrated using several numerical experiments.

The state-of-art computer architecture is based on multi core processor technology. Nowadays processors contain even more than ten cores. On the other hand new technologies have emerged that enable using GPU in general propose computing. Moreover, GPUs have become easier to program, which allows developers to effectively exploit their computational power. Currently, major chip manufacturers are developing next generation microprocessor designs that integrate multi core CPU and GPU components. Thus, it has become essential to develop algorithms that effectively use both, CPU and GPU opportunities. This paper describes one of that such hybrid GPU algorithms that is used in EMC problem solution.

The mixed problem with first order boundary conditions for system of differential equations, which describes dynamics of homogeneous and isotropic elastic body in case of flat deformation is considered. The numerical solution of this problem, as a rule, requires essential computing resources. One of the methods of abbreviation of time of the solution is the use of parallel algorithms. In this paper for solving of stated problem is constructed three-layer factorized difference scheme. For the numerical solution of the received difference equations the algorithm, which can be used effectively for parallel computing systems, is offered. The pseudocode of this algorithm is given.

This paper describes the application of ACA (Adaptive Cross Approximation) algorithm for acceleration of MoM solution of large scale radiation problems. System of linear equations is solved using iterative solution and ACA is used to reduce required memory for matrix storage and speed up matrix-vector-product operation. To demonstrate applicability and performance of described technique, two numerical experiments are presented: a) calculation of radiation pattern of Magellan spacecraft high gain reflector antenna operating at 3GHz and b) calculation of radiation pattern of Wi-Fi antenna mounted on the roof of the vehicle, operating at 5.9GHz frequency. We show that ACA calculation is much faster than direct solution, while accuracy is quite acceptable.