1,721,301 research outputs found
Spectral Filtering and Regularization of the Integral-Equation for Planar and Quasi-planar Structure
No full textIntegral Equations for Real-Life Multiscale Electromagnetic Problems
Full text linkIntegral Equations for Real-Life Multiscale Electromagnetic Problems brings together and explains the main available approaches for the numerical solution of surface integral equations that can be used to analyse real-world multi-scale electromagnetic problems. In computational electromagnetics, formulations based on surface integral equations are currently the most commonly-used option for the analysis of electrically large and complex structures, but it is essential to have available state-of-the-art techniques to solve them in an efficient and accurate way.
The book is organised into seven scientific chapters, which thoroughly and systematically explore these advanced techniques. Topics covered include: surface integral equation formulations; kernel-based fast factorization techniques; kernel-independent fast factorization methods for multiscale electromagnetic problems; domain decomposition method (DDM); multi-resolution preconditioner; Calderón preconditioners for electromagnetic integral equations; and decoupled potential integral equation. Finally, the editors share their conclusions and perspectives, and provide context on the important role of software simulation of electromagnetic phenomena in various engineering endeavours.
Compiled and curated by two expert editors with more than 20 years' experience in computational electromagnetics, and with substantial experience in developing algorithms to numerically solve integral equations in the case of discretized real-life structures, this book is a valuable resource for any and all researchers working in the field of computational electromagnetics or on associated software and tools
Numerical evaluation of near strongly singular integrals via singularity cancellation techniques
No full textOn the numerical evaluation of near-hypersingular integrals involving the gradient of Helmholtz-type potentials
No full textNumerical evaluation via singularity cancellation schemes of near-singular integrals involving the gradient of Helmholtz-type potentials
No full textIn this work we present a purely numerical procedure to evaluate strongly near-singular integrals involving the gradient of Helmholtz-type potentials for observation points at finite, arbitrarily small distances from the source domain. In the proposed approach the source domain is subdivided into a disc plus truncated subtriangles, and proper variable transformations are applied in each integration domain to exactly cancel the kernel singularity. A novel feature of the proposed angular transform is that required discrete values of the inverse transform, which is transcendental, are determined via a rootfinding procedure; the same idea can also be applied to other transforms that arise in singularity cancellation methods. The resulting integral may then evaluated via a low order Gauss- Legendre quadrature schem
A multiresolution system of Rao-Wilton-Glisson functions
No full textA multiresolution (MR) basis is described for the method of moments (MoM) analysis of a generic 3-D conductor discretized with triangular cells. The MR basis functions are constructed as linear combination of Rao-Wilton-Glisson (RWG) basis functions, thus allowing direct applicability on existing MoM codes. With respect to previous work by the authors, the generation of the MR functions is significantly simplified, yet keeping similar applicability and performance, in terms of conditioning of the MoM matrix, convergence of the iterative solvers, and possibility of sparsifying the MoM matrix by clipping. Moreover, with the proposed basis the basis-change matrix from RWG to MR is highly sparse at all levels; this allows a more efficient generation of the MR-MoM matrix
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