On the domain decomposition method preconditioning of surface integral equation formulations solved by GMRES

In this communication, the performance of the generalized minimum residual method (GMRES) preconditioned by a domain decomposition method (DDM) scheme embedded in a surface integral equation (SIE) formulation is studied. In realistic large multiscale problems, the individual subdomain solutions, which in a DDM scheme acts as the preconditioners, have to be obtained by the Krylov subspace iterative processes with a decisive influence on the outcome of the overall iterative process that deals with subdomains’ mutual couplings. The convergence and accuracy of the global solution, as well as the degree of correlation between them, are studied for the left-, right-, and flexible-right-preconditioned GMRES to draw conclusions which maximize the efficiency in the application of the SIE-DDM implementation to challenging problems.Agencia Estatal de Investigación | Ref. PID2020-116627RB-C21Agencia Estatal de Investigación | Ref. PID2020-116627RB-C22Universidade de Vigo/CISU

Accurate EMC engineering on realistic platforms using an integral equation domain decomposition approach

This article investigates the efficiency, accuracy and versatility of a surface integral equation (SIE) multisolver scheme to address very complex and large-scale radiation problems including multiple scale features, in the context of realistic electromagnetic compatibility (EMC)/electromagnetic interference (EMI) studies. The tear-and-interconnect domain decomposition (DD) method is applied to properly decompose the problem into multiple subdomains attending to their material, geometrical, and scale properties, while different materials and arbitrarily shaped connections between them can be combined by using the so-called multiregion vector basis functions. The SIE-DD approach has been widely reported in the literature, mainly applied to scattering problems or small radiation problems. Complementarily, in this article, the focus is placed on realistic radiation problems, involving tens of antennas and sensors and including multiscale ingredients and multiple materials. Such kind of problems are very demanding in terms of both convergence and computational resources. Throughout two realistic case studies, the proposed SIE-DD approach is shown to be a powerful electromagnetic modeling tool to provide the accurate and fast solution which is indispensable to rigorously accomplish real-life EMC/EMI studies.Agencia Estatal de Investigación | Ref. TEC2017-85376-C2-1-RAgencia Estatal de Investigación | Ref. TEC2017-85376-C2-2-

Effective transmission conditions for domain decomposition methods applied to the time-harmonic curl-curl Maxwell's equations

The time-harmonic Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental for the simulation of many modern devices we have become used to in everyday life. The numerical solution of these equations is hampered by two fundamental problems: first, in the high frequency regime, very fine meshes need to be used in order to avoid the pollution effect well known for the Helmholtz equation, and second the large scale systems obtained from the vector valued equations in three spatial dimensions need to be solved by iterative methods, since direct factorizations are not feasible any more at that scale. As for the Helmholtz equation, classical iterative methods applied to discretized Maxwell equations have severe convergence problems.We explain in this paper a family of domain decomposition methods based on well chosen transmission conditions. We show that all transmission conditions proposed so far in the literature, both for the first and second order formulation of Maxwell's equations, can be written and optimized in the common framework of optimized Schwarz methods, independently of the first or second order formulation one uses, and the performance of the corresponding algorithms is identical. We use a decomposition into transverse electric and transverse magnetic fields to describe these algorithms, which greatly simplifies the convergence analysis of the methods. We illustrate the performance of our algorithms with large scale numerical simulations

Electromagnetic Environment In Payload Fairing Cavities

An accurate determination of a spacecraft’s radio frequency electromagnetic field environment during launch and flight is critical for mission success. Typical fairing structures consist of a parabolic nose and a cylindrical core with diameters of 1 to 5 meters resulting in electrically large dimensions for typical operational sources at S, C and X band where the free space wavelength varies from 0.15 m to 0.03 m. These electrically large size and complex structures at present have internal fairing electromagnetic field evaluation that is limited to general approximation methods and some test data. Though many of today’s computational electromagnetic tools can model increasingly complex and large structures, they still have many limitations when used for field determination in electrically large cavities. In this dissertation, a series of test anchored, full wave computational electromagnetic models along with a novel application of the equivalent material property technique are presented to address the electrical, geometrical, and boundary constraints for electromagnetic field determination in composite fairing cavity structures and fairings with acoustic blanketing layers. Both external and internal excitations for these fairing configurations are examined for continuous wave and transient sources. A novel modification of the Nicholson Ross Weir technique is successfully applied to both blanketed aluminum and composite fairing structures and a significant improvement in computational efficiency over the multilayered model approach is obtained. The advantages and disadvantages of using commercially available tools by incorporating Multilevel Fast Multipole Method (MLFMM) and higher order method of moments (HO MoM) to extend their application of MoM to electrically large objects is examined for each continuous wave transmission case. The results obtained with these models are ii compared with those obtained using approximation techniques based on the Q factor, commonly utilized in the industry, and a significant improvement is seen in a prediction of the fields in these large cavity structures. A statistical distribution of data points within the fairing cavity is examined to study the nature of the fairing cavity field distribution and the effect of the presence of a spacecraft load on these fields is also discussed. In addition, a model with external application of Green’s function is examined to address the shielding effectiveness of honeycomb panels in a fairing cavity. Accurate data for lightning induced effects within a fairing structure is not available and hence in this dissertation, a transmission line matrix method model is used to examine induced lightning effects inside a graphite composite fairing structure. The simulated results are compared with test data and show good agreement