Examinando por Autor "Vipiana, Francesca"

Mostrando 1 - 7 de 7

A Domain Decomposition Scheme with an Efficient Multitrace Multiresolution Preconditioner for the Simulation of Complex Composite Problems
(International Union of Radio Science, 2023) Martin, Victor F.; Taboada, Jose M.; Vipiana, Francesca
In this work we present a multitrace method including an automatic and multilevel quasi-Helmholtz decomposition integrated with the domain decomposition method for the solution of arbitrary complex geometries composed of piecewise homogeneous composite objects. A numerical experiment demonstrates the flexibility of the proposed approach for the solution of large multi-scale objects composed of multiple materials.
A Multi-Resolution Preconditioner for Nonconformal Meshes in the MoM Solution of Large Multiscale Structures
(Institute of Electrical and Electronics Engineers, 2023-04-26) Martin, Victor F.; Taboada, Jose M.; Vipiana, Francesca
The paper presents a multi-resolution preconditioner able to improve the solution convergence, via the method of moments and the multilevel fast multipole algorithm, in the case of non-conformal meshes applying the multi-branch Rao-Wilton-Glisson basis functions. The proposed preconditioner enables, for the first time, an automatic multi-level quasi-Helmholtz decomposition on non-conforming meshes, including also the generation of the topological (global) loop functions. Moreover, the generation of the proposed preconditioning schemeis fully parallelized in a multicore shared-memory enviroment. Numerical results show the great flexibility of this approach for the solution of electrically-large multi-scale objects including hrefinement discretizations.
A novel MultiResolution Preconditioner Including Piecewise Homogeneous Dielectric Objects
(Institute of Electrical and Electronics Engineers, 2023) Martin, Victor F.; Solis, Diego M.; Taboada, Jose M.; Vipiana, Francesca
An extensive literature demonstrates the capabilities of the hierarchical quasi-Helmholtz decomposition multiresolution preconditioner both to address the breakdowns for the surface integral equations and to improve the convergence in multiscale problems, until now only applied to perfect electrical conductors. In this work we present a novel methodology based on this efficient preconditioner able to solve arbitrary complex geometries composed of piecewise homogeneous composite objects, that automatically satisfies the boundary conditions. To the authors’ knowledge, this is the first work where a multilevel quasi-Helmholtz decomposition is applied to objects with dielectric junctions without the need of a weak enforcement of the continuity or a number-of-unknown-reduction scheme. Numerical examples demonstrate the efficiency of the proposed approach for the solution of complex problems involving multiple materials (dielectric and conductors).
Automatic MoM Source Integral Quadrature Selection via a Machine Learning Approach
(European Conference on Antennas and Propagation, EuCAP, 2024) Martin, Victor F.; Ricci, Marco; Wilton, Donald R.; Johnson, William A.; Vipiana, Francesca
In this paper, a new technique, based on machine learning (ML) and dimensionality reduction, is proposed for drastically improving the performance in the evaluation of the singular and near singular potential integrals in the method of moments (MoM). The MoM source surface integral is first reduced to a line integral via a dimensionality reduction method, and, then, an ML algorithm is trained on a set of line integrals evaluated with Gauss-Legendre (GL) quadrature schemes of different orders. Finally, the trained ML algorithm is used to determine the minimum number of GL sample points and weights required for each potential line integral to get the requested accuracy.
Multiresolution Preconditioners for Solving Realistic Multi-Scale Complex Problems
(Institute of Electrical and Electronics Engineers, 2022-02-21) Solis, Diego M.; Martin, Victor F.; Taboada, Jose M.; Vipiana, Francesca
In this work, the hierarchic multiresolution (MR) preconditioner is combined with the multilevel fast multipole algorithm-fast Fourier transform (MLFMA-FFT) and eficiently parallelized in multicore computers for computing electromagnetic scattering and radiation from complex problems exhibiting deep multi-scale features. The problem is formulated using the thin-dielectric-sheet (TDS) approximation for thin dielectric materials and the electric and combined field integral equations (EFIE/CFIE) for conducting objects. The parallel MLFMA-FFT is tailored to accommodate the MR hierarchical functions, which provide vast improvement of the matrix system conditioning by accurately handling multi-scale mesh features in different levels of detail. The higher (coarser) level hierarchical functions are treated by an algebraic incomplete LU decomposition preconditioner, which has been ef ciently embedded into the parallel framework to further accelerate the solution. Numerical examples are presented to demonstrate the precision and eficiency of the proposed approach for the solution of realistic multi-scale scattering and radiation problems.
On the Use of a Localized Huygens’ Surface Scheme for the Adaptive H-Refinement of Multiscale Problems
(Institute of Electrical and Electronics Engineers, 2023-09-27) Tobon V., Jorge A.; Martin, Victor F.; Serna, Alberto; Peng, Zhen; Vipiana, Francesca
This work proposes a domain decomposition method (DDM) based on Huygens’ equivalence principle to efficiently perform an adaptive h-refinement technique for the electromagnetic analysis of multiscale structures via surface integral equations (SIEs). The procedure starts with the discretization of the structure under analysis via an initial coarse mesh, divided into domains. Then, each domain is treated independently, and the coupling to the rest of the object is obtained through the electric and magnetic current densities on the equivalent Huygens’ surfaces (EHSs), surrounding each domain. From the initial solution, the error is estimated on the whole structure, and an adaptive h-refinement is applied accordingly. Both the error estimation and the adaptive h-refined solution are obtained through the defined EHSs, keeping the problem local. The adaptive h-refinement is obtained by a nonconformal submeshing, where multibranch Rao–Wilton–Glisson (MB-RWG) basis functions are defined. Numerical experiments of multiscale perfect-electricconductor (PEC) structures in air, analyzed via the combined field integral equation, show the performance of the proposed approach.
The Multi-resolution preconditioner
(Scitech Publishing, 2024) Vipiana, Francesca; Martin, Victor F.; Taboada, Jose M.
The purpose of this chapter is to provide the main guidelines for an efficient implementation of the multi-resolution (MR) preconditioner for the electromagnetic (EM) analysis of perfect electric conductor (PEC) structures of arbitrary 3-D shape via the method of moments (MoM) applied to the electric field integral equation (EFIE) and to the combined field integral equation (CFIE). The chapter is structured in four main parts. First, the generation of the MR basis functions as a linear combination of the standard basis functions is described. Second, the generation of a multi-level set of meshes, starting from the usual mesh, is reported: the MR functions are defined on each level of the generated set of meshes. These two parts are essential to implement the proposed preconditioner. Then, the third part is dedicated to the insertion of the MR preconditioner into the solution algorithm, together with the description of some implementation tricks. Finally, numerical results, where the MR preconditioner is applied to complex realistic 3-D structures, are reported and commented. The expected property of the MR preconditioner is an improvement of the convergence rates of iterative solvers, with a limited computational cost for its generation and application. The proposed preconditioner can be applied to realistic structures with arbitrary topological complexity.