A three-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities

Gomez-Revuelto, I.; Garcı́a-Castillo, L.E.; Llorente‐Romano, Sergio; Pardo, David

doi:10.1016/j.cma.2012.05.013

Cited by 13 publications

(11 citation statements)

References 31 publications

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“…Step strategy [15] that performs first an h-adaptive step followed by a p-adaptive one that leads to non-optimal results; (c) the work of Demkowicz et al presented in [3,4,16] and applied in several contexts, e.g. [17][18][19][20][21][22][23][24][25][26][27][28], that produces almost optimal meshes but needs from solving the problem over a globally refined ( h 2 , p + 1)-grid, which is often prohibitively expensive, and also requires a sophisticated implementation; (d) the work of Houston et al [29], which estimates the regularity of the solution with the Legendre coefficients [30] and, (e) the contribution of Zander et al [31] and applications [32][33][34][35], which combine their multi-level data structure [9, 10] with a classic residual-based estimator [36]. We refer to [30] for a recent (Oct. 2014) review and comparison of some of the existing methods in terms of computational time versus the number of degrees of freedom (dofs).…”

Section: Dirichlet Nodementioning

confidence: 99%

A painless automatic hp-adaptive strategy for elliptic problems

Darrigrand

Pardo

Chaumont-Frelet

et al. 2020

Finite Elements in Analysis and Design

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In this work, we introduce a novel hp-adaptive strategy. The main goal is to minimize the complexity and implementational efforts hence increasing the robustness of the algorithm while keeping close to optimal numerical results. We employ a multi-level hierarchical data structure imposing Dirichlet nodes to manage the so-called hanging nodes. The hp-adaptive strategy is based on performing quasi-optimal unrefinements. Taking advantage of the hierarchical structure of the basis functions both in terms of the element size h and the polynomial order of approximation p, we mark those with the lowest contributions to the energy of the solution and remove them. This straightforward unrefinement strategy does not need from a fine grid or complex data structures, making the algorithm flexible to many practical situations and existing implementations. On the other side, we also identify some limitations of the proposed strategy, namely: (a) data structures only support isotropic h-refinements (although p-anisotropic refinements are enabled), (b) we assume certain quasi-orthogonality properties of the basis functions in the energy norm, and (c) in this work, we restrict to symmetric and positive definite problems. We illustrate these and other advantages and limitations of the proposed hp-adaptive strategy with several one-, two-and three-dimensional Poisson examples.

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Section: Dirichlet Nodementioning

confidence: 99%

A painless automatic hp-adaptive strategy for elliptic problems

Darrigrand

Pardo

Chaumont-Frelet

et al. 2020

Finite Elements in Analysis and Design

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“…The 3D implementation of the hp-adaptivity proposed by the authors (see [9] and the references therein) is based on a selfadaptive strategy devised in [19] and further improved in [15,6]. The hp-adaptive strategy supports anisotropic refinements on irregular meshes with hanging nodes, and isoparametric elements as well as exact-geometry elements.…”

Section: Hp-fem and Automatic Hp-adaptivity In 3dmentioning

confidence: 99%

“…Simultaneous h and p refinements, i.e., local variations of the element size h and the polynomial order of approximation p throughout the mesh are supported (the so called hp-adaptivity [5,6]). Preliminary results of the 3D implementation of the hp-adaptivity proposed by the authors [9] applied to the Petri dish problem were presented in [10], where the cell cultures were modeled as a circular dielectric, i.e., the meniscus shape was not included in the geometry. In this paper, the meniscus shape is included in the computational model.…”

Section: Introductionmentioning

confidence: 99%

High-accuracy adaptive modeling of the energy distribution of a meniscus-shaped cell culture in a Petri dish

Gomez-Revuelto

Garcı́a-Castillo

Pardo

2015

Journal of Computational Science

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Cylindrical Petri dishes embedded in a rectangular waveguide and exposed to a polarized electromagnetic wave are often used to grow cell cultures. To guarantee the success of these cultures, it is necessary to enforce that the specific absorption rate distribution is sufficiently high and uniform over the Petri dish. Accurate numerical simulations are needed to design such systems. These simulations constitute a challenge due to the strong discontinuity of electromagnetic material properties involved, the relative low field value within the dish cultures compared with the rest of the domain, and the presence of the meniscus shape developed at the liquid boundary. The latter greatly increases the level of complexity of the model in terms of geometry and intensity of the gradients/singularities of the field solution. In here, we employ a three-dimensional (3D) hp-adaptive finite element method using isoparametric elements to obtain highly accurate simulations. We analyze the impact of the geometrical modeling of the meniscus shape cell culture in the hp-adaptivity. Numerical results showing the error convergence history indicate the numerical difficulties arisen due to the presence of a meniscus-shaped object. At the same time, the resulting energy distribution shows that to consider such meniscus shape is essential to guarantee the success of the cell culture from the biological point of view.

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“…The exceptions are the works performed by Schwarzbach et al (2011) and Grayver & Kolev (2015), which demonstrate the advantages of high-order basis functions regarding the needs of degrees of freedom (dof) to satisfy the prior chosen quality criteria in the EM responses. HEFEM have also been shown to be beneficial in other areas of EM wave modeling, such as cavity analysis (Jian-Ming Jin et al 2003;Gomez-Revuelto et al 2012), brain microwave studies (Bonazzoli et al 2018), among others with smooth solutions (Bergot & Duruflé 2013;Olm et al 2019;Eisenträger et al 2020).…”

mentioning

confidence: 99%