Efficient finite element methods for solving high-frequency time-harmonic acoustic wave problems in heterogeneous media

This thesis focuses on the efficient numerical solution of frequency-domain wave propagation problems using finite element methods. In the first part of the manuscript, the development of domain decomposition methods is addressed, with the aim of overcoming the limitations of state-of-the art direct and iterative solvers. To this end, a non-overlapping substructured domain decomposition method with high-order absorbing conditions used as transmission conditions (HABC DDM) is first extended to deal with cross-points, where more than two subdomains meet. The handling of cross-points is a well-known issue for non-overlapping HABC DDMs. Our methodology proposes an efficient solution for lattice-type domain partitions, where the domains meet at right angles. The method is based on the introduction of suitable relations and additional transmission variables at the cross-points, and its effectiveness is demonstrated on several test cases. A similar non-overlapping substructured DDM is then proposed with Perfectly Matched Layers instead of HABCs used as transmission conditions (PML DDM). The proposed approach naturally considers cross-points for two-dimensional checkerboard domain partitions through Lagrange multipliers used for the weak coupling between subproblems defined on rectangular subdomains and the surrounding PMLs. Two discretizations for the Lagrange multipliers and several stabilization strategies are proposed and compared. The performance of the HABC and PML DDM is then compared on test cases of increasing complexity, from two-dimensional wave scattering in homogeneous media to three-dimensional wave propagation in highly heterogeneous media. While the theoretical developments are carried out for the scalar Helmholtz equation for acoustic wave propagation, the extension to elastic wave problems is also considered, highlighting the potential for further generalizations to other physical contexts. The second part of the manuscript is devoted to the presentation of the computational tools developed during the thesis and which were used to produce all the numerical results: GmshFEM, a new C++ finite element library based on the application programming interface of the open-source finite element mesh generator Gmsh; and GmshDDM, a distributed domain decomposition library based on GmshFEM.Cette thèse porte sur la résolution numérique efficace de problèmes de propagation d'ondes dans le domaine fréquentiel avec la méthode des éléments finis. Dans la première partie du manuscrit, le développement de méthodes de décomposition de domaine est abordé, dans le but de surmonter les limitations des solveurs directs et itératifs de l'état de l'art. À cette fin, une méthode de décomposition de domaine sous-structurée sans recouvrement avec des conditions absorbante d'ordre élevé utilisées comme conditions de transmission (HABC DDM) est d'abord étendue pour traiter les points de jonction, où plus de deux sous-domaines se rencontrent. Le traitement des points de jonction est un problème bien connu pour les HABC DDM sans recouvrement. La méthodologie proposée mène à une solution efficace pour les partitions en damier, où les domaines se rencontrent à angle droit. La méthode est basée sur l'introduction de variables de transmission supplémentaires aux points de jonction, et son efficacité est démontrée sur plusieurs cas-tests. Une DDM sans recouvrement similaire est ensuite proposée avec des couches parfaitement adaptées au lieu des HABC (DDM PML). L'approche proposée prend naturellement en compte les points de jonction des partitions de domaine en damier par le biais de multiplicateurs de Lagrange couplant les sous-domaines et les couches PML adjacentes. Deux discrétisations pour les multiplicateurs de Lagrange et plusieurs stratégies de stabilisation sont proposées et comparées. Les performances des DDM HABC et PML sont ensuite comparées sur des cas-tests de complexité croissante, allant de la diffraction d'ondes dans des milieux homogènes bidimensionnelles à la propagation d'ondes tridimensionnelles dans des milieux hautement hétérogènes. Alors que les développements théoriques sont effectués pour l'équation scalaire de Helmholtz pour la simulation d'ondes acoustiques, l'extension aux problèmes d'ondes élastiques est également considérée, mettant en évidence le potentiel de généralisation des méthodes développées à d'autres contextes physiques. La deuxième partie du manuscrit est consacrée à la présentation des outils de calcul développés au cours de la thèse et qui ont été utilisés pour produire tous les résultats numériques : GmshFEM, une nouvelle bibliothèque d'éléments finis C++ basée sur le générateur de maillage open-source Gmsh ; et GmshDDM, une bibliothèque de décomposition de domaine distribuée basée sur GmshFEM

An efficient domain decomposition method with cross-point treatment for Helmholtz problems

International audienceThe parallel finite-element solution of large-scale time-harmonic scattering problems is addressed with a non-overlapping domain decomposition method (DDM). It is well known that the efficiency of this method strongly depends on the transmission condition enforced on the interfaces between the subdomains. Local conditions based on high-order absorbing boundary conditions (HABCs) are well suited for configurations without cross points (where more than two subdo-mains meet). In this work, we extend this approach to efficiently deal with cross points. Two-dimensional finite-element results are presented

An efficient domain decomposition method with cross-point treatment for Helmholtz problems

International audienceThe parallel finite-element solution of large-scale time-harmonic scattering problems is addressed with a non-overlapping domain decomposition method (DDM). It is well known that the efficiency of this method strongly depends on the transmission condition enforced on the interfaces between the subdomains. Local conditions based on high-order absorbing boundary conditions (HABCs) are well suited for configurations without cross points (where more than two subdo-mains meet). In this work, we extend this approach to efficiently deal with cross points. Two-dimensional finite-element results are presented

A non-overlapping domain decomposition method with high-order transmission conditions and cross-point treatment for Helmholtz problems

International audienceA non-overlapping domain decomposition method (DDM) is proposed for the parallel finite-element solution of large-scale time-harmonic wave problems. It is well-known that the convergence rate of this kind of method strongly depends on the transmission condition enforced on the interfaces between the subdomains. Local conditions based on high-order absorbing boundary conditions (HABCs) have proved to be well-suited, as a good compromise between basic impedance conditions, which lead to suboptimal convergence, and conditions based on the exact Dirichlet-to-Neumann (DtN) map related to the complementary of the subdomain — which are too expensive to compute. However, a direct application of this approach for configurations with interior cross-points (where more than two subdomains meet) and boundary cross-points (points that belong to both the exterior boundary and at least two subdomains) is suboptimal and, in some cases, can lead to incorrect results.In this work, we extend a non-overlapping DDM with HABC-based transmission conditions approach to efficiently deal with cross-points for lattice-type partitioning. We address the question of the cross-point treatment when the HABC operator is used in the transmission condition, or when it is used in the exterior boundary condition, or both. The proposed cross-point treatment relies on corner conditions developed for Padé-type HABCs. Two-dimensional numerical results with a nodal finite-element discretization are proposed to validate the approach, including convergence studies with respect to the frequency, the mesh size and the number of subdomains. These results demonstrate the efficiency of the cross-point treatment for settings with regular partitions and homogeneous media. Numerical experiments with distorted partitions and smoothly varying heterogeneous media show the robustness of this treatment

Real-time Tracking of Deformable Target in 3D Ultrasound Images

International audience— In this paper, we present a novel approach for tracking a deformable anatomical target within 3D ultrasound volumes. Our method is able to estimate deformations caused by the physiological motions of the patient. The displacements of moving structures are estimated from an intensity-based approach combined with a physically-based model and has therefore the advantage to be less sensitive to the image noise. Furthermore, our method does not use any fiducial marker and has real-time capabilities. The accuracy of our method is evaluated on real data acquired from an organic phantom. The validation is performed on different types of motions comprising rigid and non-rigid motions. Thus, our approach opens novel possibilities for computer-assisted interventions where deformable organs are involved

Interactive Tracking of Soft Tissues in 2D Ultrasound Images

SURGETICA 2014, Chambery, FranceIn several medical applications such as liver or kidney biopsies, an anatomical region needs to be continuously tracked during the intervention. When using ultrasound (US) image modality, tracking soft tissues remains challenging due to the deformations caused by physiological motions or medical instruments, combined with the generally weak quality of the images. In order to overcome the previous limitation, different techniques based on physical model have been proposed in the literature. [SMSM06] proposed a registration method based on the mass-spring system in order to constrain the deformation, and Zhang et al [ZW13] introduced an other registration technique based on finite element model where the extraction of the scale invariant features is needed. However, their model are built from features which are difficult to extract in US images due to the speckle noise. Finally, Marami et al [MSFC14] presented very recently an elastic registration method applicable to multi-modality image registration where the deformation is computed from modality independent neighborhood descriptor. In this paper, we propose an approach for tracking deformable target within 2D US images based on a physical model driven by smooth displacement field obtained from dense information. This allows to take into account highly localized deformation in the US images. Section 2 presents our method based on a combination of an intensity-based approach and a physically-based model. Section 3 describes the performances of our approach and comparisons on real data. Section 4 concludes the paper

Predicción de la frescura de Sciaena deliciosa “lorna” utilizando imágenes hiperespectrales

El objetivo de esta investigación fue encontrar un modelo basado en imágenes hiperespectrales para predecir la frescura de Sciaena deliciosa. En la investigación se utilizaron muestras de Sciaena deliciosa “lorna” que luego de capturadas, fueron colocadas en un cooler con hielo y transportadas al laboratorio para su respectivo análisis. Para el análisis sensorial se utilizó el esquema sensorial propuesto por Imarpe (Perú) para especies grasas. Respecto a las imágenes hiperespectrales, cada espécimen fue colocado en el equipo para analizar el humor vítreo del ojo y obtener la huella espectral correspondiente. Para el índice de refracción se extrajo el humor vítreo de ojo y colocado en el refractómetro para cuantificar el grado de alteración. Todos estos resultados fueron correlacionados para predecir la frescura, buscando el modelo más adecuado. El modelo de predicción obtenido para la frescura de pescado tuvo un R2 = 0,6359, valor adecuado para considerarlo como un modelo de posible uso práctico.

Molecular evolution of the human SRPX2 gene that causes brain disorders of the Rolandic and Sylvian speech areas

<p>Abstract</p> <p>Background</p> <p>The X-linked <it>SRPX2 </it>gene encodes a Sushi Repeat-containing Protein of unknown function and is mutated in two disorders of the Rolandic/Sylvian speech areas. Since it is linked to defects in the functioning and the development of brain areas for speech production, <it>SRPX2 </it>may thus have participated in the adaptive organization of such brain regions. To address this issue, we have examined the recent molecular evolution of the <it>SRPX2 </it>gene.</p> <p>Results</p> <p>The complete coding region was sequenced in 24 human X chromosomes from worldwide populations and in six representative nonhuman primate species. One single, fixed amino acid change (R75K) has been specifically incorporated in human SRPX2 since the human-chimpanzee split. The R75K substitution occurred in the first sushi domain of SRPX2, only three amino acid residues away from a previously reported disease-causing mutation (Y72S). Three-dimensional structural modeling of the first sushi domain revealed that Y72 and K75 are both situated in the hypervariable loop that is usually implicated in protein-protein interactions. The side-chain of residue 75 is exposed, and is located within an unusual and SRPX-specific protruding extension to the hypervariable loop. The analysis of non-synonymous/synonymous substitution rate (Ka/Ks) ratio in primates was performed in order to test for positive selection during recent evolution. Using the branch models, the Ka/Ks ratio for the human branch was significantly different (p = 0.027) from that of the other branches. In contrast, the branch-site tests did not reach significance. Genetic analysis was also performed by sequencing 9,908 kilobases (kb) of intronic <it>SRPX2 </it>sequences. Despite low nucleotide diversity, neither the HKA (Hudson-Kreitman-Aguadé) test nor the Tajima's D test reached significance.</p> <p>Conclusion</p> <p>The R75K human-specific variation occurred in an important functional loop of the first sushi domain of SRPX2, indicating that this evolutionary mutation may have functional importance; however, positive selection for R75K could not be demonstrated. Nevertheless, our data contribute to the first understanding of molecular evolution of the human <it>SPRX2 </it>gene. Further experiments are now required in order to evaluate the possible consequences of R75K on SRPX2 interactions and functioning.</p

Hypomethylation and aberrant expression of the glioma pathogenesis-related 1 gene in Wilms tumors

Wilms tumors (WTs) have a complex etiology, displaying genetic and epigenetic changes, including loss of imprinting (LOI) and tumor suppressor gene silencing. To identify new regions of epigenetic perturbation in WTs, we screened kidney and tumor DNA using CpG island (CGI) tags associated with cancer-specific DNA methylation changes. One such tag corresponded to a paralog of the glioma pathogenesis-related 1/related to testis-specific, vespid, and pathogenesis proteins 1 (GLIPR1/RTVP-1) gene, previously reported to be a tumor-suppressor gene silenced by hypermethylation in prostate cancer. Here we report methylation analysis of the GLIPR1/RTVP-1 gene in WTs and normal fetal and pediatric kidneys. Hypomethylation of the GLIPR1/RTVP-1 5′-region in WTs relative to normal tissue is observed in 21/24 (87.5%) of WTs analyzed. Quantitative analysis of GLIPR1/RTVP-1 expression in 24 WTs showed elevated transcript levels in 16/24 WTs (67%), with 12 WTs displaying in excess of 20-fold overexpression relative to fetal kidney (FK) control samples. Immunohistochemical analysis of FK and WT corroborates the RNA expression data and reveals high GLIPR1/RTVP-1 in WT blastemal cells together with variable levels in stromal and epithelial components. Hypomethylation is also evident in the WT precursor lesions and nephrogenic rests (NRs), supporting a role for GLIPR1/RTVP-1 deregulation early in Wilms tumorigenesis. Our data show that, in addition to gene dosage changes arising from LOI and hypermethylation-induced gene silencing, gene activation resulting from hypomethylation is also prevalent in WTs. Copyright © 2007 Neoplasia Press, Inc. All rights reserved

Skunk River Fall 1998

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