S. Coco

Finite element iterative solution of skin effect problems in open boundaries

The paper proposes an iterative procedure, called current iteration, for the finite element solution of two-dimensional steady-state skin effect problems in open boundaries. In the procedure a fictitious boundary is introduced enclosing all the conductors. On it, the magnetic vector potential is first guessed and then iteratively updated according to the current density computed in the conductors. Conditions are obtained implying convergence to the exact solution of the unbounded problem whatever the initial guess. The choice of the fictitious boundary and the selection of the relaxation parameter in such a way that computational efficiency is obtained are discussed. The greatest advantage of the procedure is its ease of implementation in a pre-existing finite element code for bounded problems. An axisymmetric version of the procedure is also described since implementation only involves minor changes as compared with the 2-D one. Examples are provided in order to clarify and validate the procedure and compare it with other techniques.

Shape Optimization of Multistage Depressed Collectors by Parallel Evolutionary Algorithm

In this paper a novel parallel meta-heuristic algorithm called MeTEO is presented, applied to the shape optimization of multistage depressed collectors, simulated by means of a Finite Element collector and electron gun simulator, COLLGUN, which uses the Constructive Solid Geometry for the description of the device shape. METEO is a hybrid algorithm composed by three different heuristics: FSO (Flock of Starlings Optimization), PSO (Particle Swarm Optimization), and BCA (Bacterial Chemotaxis Algorithm); it performs the optimization using both the topological and the metric rules and offers a natural parallel implementation that allows speeding up the whole process of optimization by the fitness modification (FM).

COCA: a novel 3-D FE simulator for the design of TWT's multistage collectors

In this paper, the simulator COCA, a novel fully three-dimensional (3-D) finite-element (FE) tool for the design of multistage depressed TWTs collectors is illustrated. COCA has been developed at the University of Catania under an ESA/ESTEC project. The complete simulator consists of three main modules: a fully 3-D deterministic/neural FE mesh generator, an FE Vlasov solver coupled with an electron trajectory tracer taking into account also external magnetic fields, and a postprocessing module for result restitution, including secondary electron emission effects. All the functions are interactively managed and executed by means of an especially developed user-friendly graphical user interface which controls all the various aspects of a simulation session. The results of a simulation test performed on an asymmetric collector are also reported showing excellent agreement with available measured data. The COCA simulator provides the user with flexible and effective tools to design, test, optimize, and verify innovative asymmetrical geometries for TWT collectors.

A theoretical study of charge iteration

Charge iteration is an iterative procedure for the finite element computation of unbounded electrical fields, created by voltaged conductors. It makes use of a fictitious boundary, enclosing all the conductors, on which the electrical potential is first guessed and then iteratively improved according to the charge lying on the conductor surfaces. Highlights the theoretical foundations of the procedure outside any numerical context. From this useful insight, obtains a model which can aid the user in utilization of the numerical version of the procedure.

A neural network approach for the differentiation of numerical solutions of 3-D electromagnetic problems

An innovative approach employing a neural network (NN) is presented to compute accurately derivatives and differential operators (such as Laplacian, gradient, divergence, curl, etc.) of numerical solutions of three-dimensional electromagnetic problems. The adopted NN is a multilayer perceptron, whose training is performed off-line by using a class of suitably selected polynomial functions. The desired degree of accuracy can be chosen by the user by selecting the appropriate order of the training polynomials. The on-line utilization of the trained NN allows us to obtain accurate results with a negligible computational cost. Comparative examples of differentiation performed both on analytical functions and finite element solutions are given in order to illustrate the computational advantages.

COCA: a novel 3D FE simulator for the design of TWTs multistage collectors

Specialized 3D numerical simulators are required to carry out the design process of asymmetrical high-efficiency TWT collectors. A Finite-Element (FE) approach has the advantage of flexibility in the treatment of realistic collector geometries, allowing an easy utilization of irregular meshes and mesh adaptation in the discretization process. In this way the user can fit better the discretized model to the design objectives. In this paper the present release of the simulator COCA, a novel 3D FE tool for the design of multistage depressed TWTs collectors is illustrated. COCA has been developed at the University of Catania under an ESA/ESTEC project. The complete simulator consists of three main modules: a dedicated fully 3D FE mesh generator, a 3D FE Vlasov solver, including space-charge effects, with an integrated electron trajectory tracer and a post-processing module for result restitution. The tool has been specifically conceived to provide the TWT designer with a flexible and easy-to-use environment through a friendly Graphical User Interface (GUI). In fact all the simulator functions are interactively managed and executed by using the GUI window, where several menus foresee all the actions necessary to create, modify and simulate a collector. Several examples of 3D simulations of asymmetric collectors have been performed to test the simulator; the results of the tests based on geometries available in literature are in excellent agreement with the reported measured data.

TWT magnetic focusing structure optimization by parallel evolutionary algorithm

Purpose – The purpose of this paper is to present the application of a novel hybrid algorithm, called MeTEO (Metric‐Topological‐Evolutionary‐Optimization), based on the combination of three heuristics inspired by artificial life to the solution of optimization problems of a real electronic vacuum device.Design/methodology/approach – The Particle Swarm Optimization (PSO), the Flock‐of‐Starlings Optimization (FSO) and the Bacterial Chemotaxis Algorithm (BCA) were adapted to implement a novel meta‐heuristic MeTEO the FSO has been powerfully employed for exploring the whole space of solutions, whereas the PSO is used to explore local regions where FSO had found solutions, and BCA to refine the solutions found by PSO, thanks its better performances in local search.Findings – The optimization of the focusing magnetic field of a Travelling Wave Tubes (TWT) collector is presented in order to show the effectiveness of MeTEO, in combination with COLLGUN FE simulator and equivalent source representation. The optimiz...

Charge iteration for N-dimensional unbounded electrical field computations

An N-dimensional finite element iterative procedure is presented for the computation of electrostatic fields in unbounded domains. The procedure is based on successive evaluations of the potential on a fictitious boundary enclosing all the conductors of the problem, according to the charge lying on their surface. For simplex Lagrangian elements the charge is computed by resorting to universal matrices. The main advantage of this procedure lies in its simplicity of implementation, because practically no extra software is needed as compared with that required for bounded domain problems. A simple example of computation of a 3-D electrostatic unbounded problem is presented. >

Axisymmetric unbounded electrical field computation by charge iteration

An iterative procedure is presented for the finite-element computation of axisymmetric electrostatic fields in unbounded domains. In the procedure the original unbounded problem is solved by using successive evaluations of the potential on a fictitious boundary enclosing all the conductors of the problem, according to the charge lying on their surface. For simplex Lagrangian elements universal matrices are used for a fast and efficient computation of this charge. The main advantage of this procedure lies in its ease of implementation in a standard bounded problem finite-element code and in the accuracy of the computed results. >

Bacterial chemotaxis shape optimization of electromagnetic devices

In this paper, a bacterial chemotaxis shape optimization algorithm is presented for the optimal design of electromagnetic devices. The bacterial chemotaxis algorithm exploits the conceptual analogy between bacteria and mesh nodes, improving the devices performance by moving the specific mesh nodes/bacteria defining the shape in the same way the bacteria move toward regions presenting better life conditions. Validation tests are also presented in order to show the performance of the developed shape optimizer.