Mesh-based multi-frontal solver with reuse of partial LU factorizations for antenna array

Martínez-Fernández, Ignacio; Woźniak, Maciej; Garcı́a-Castillo, L.E.; Paszyński, Maciej

doi:10.1016/j.jocs.2016.10.008

Cited by 4 publications

(2 citation statements)

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“…To leverage this problem in FEM, some techniques have been proposed in the last years: Domain Decomposition Methods (DDM) [2][3][4] have increased the size of the problems that can be solved at the expense of a more difficult formulation and the use of iterative solvers; Model Order Reduction (MOR) techniques [5,6] reduce the number of simulations required for a given bandwidth using polynomial interpolation techniques; multigrid methods [7,8] are used as preconditioners for iterative solvers; and finally, substructuring methods that are purely algebraic approaches based on the Schur complement [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Test-Driven Development of a Substructuring Technique for the Analysis of Electromagnetic Finite Periodic Structures

2021

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In this paper, we follow the Test-Driven Development (TDD) paradigm in the development of an in-house code to allow for the finite element analysis of finite periodic type electromagnetic structures (e.g., antenna arrays, metamaterials, and several relevant electromagnetic problems). We use unit and integration tests, system tests (using the Method of Manufactured Solutions—MMS), and application tests (smoke, performance, and validation tests) to increase the reliability of the code and to shorten its development cycle. We apply substructuring techniques based on the definition of a unit cell to benefit from the repeatability of the problem and speed up the computations. Specifically, we propose an approach to model the problem using only one type of Schur complement which has advantages concerning other substructuring techniques.

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Section: Introductionmentioning

confidence: 99%

“…As seen in (10), we use a discretization of finite elements to solve a problem with FEM. This leads to having a direct correspondence between the local (to each element) unknown and the global (in the final system of equations) unknown that identifies univocally that unknown in the whole problem.…”

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confidence: 99%