Search results for "finite element methods"

showing 6 items of 6 documents

Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three

2020

International audience; We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case.

010103 numerical & computational mathematicsResidual01 natural sciencesPiecewise linear function: Multidisciplinaire généralités & autres [C99] [Ingénierie informatique & technologie]Dimension (vector space)Bank-Weiser estimatorApplied mathematicsfinite element methodssaturation assumption0101 mathematicsReliability (statistics)Mathematicsresidual estimatorBank-WeiserestimatorApplied Mathematics: Multidisciplinary general & others [C99] [Engineering computing & technology]NoveltyEstimatorExtension (predicate logic)16. Peace & justiceFinite element methoda posteriori error estimation010101 applied mathematics: Mathematics [G03] [Physical chemical mathematical & earth Sciences]: Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre][MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
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A finite element-based machine learning approach for modeling the mechanical behavior of the breast tissues under compression in real-time

2017

[EN] This work presents a data-driven method to simulate, in real-time, the biomechanical behavior of the breast tissues in some image-guided interventions such as biopsies or radiotherapy dose delivery as well as to speed up multimodal registration algorithms. Ten real breasts were used for this work. Their deformation due to the displacement of two compression plates was simulated off-line using the finite element (FE) method. Three machine learning models were trained with the data from those simulations. Then, they were used to predict in real-time the deformation of the breast tissues during the compression. The models were a decision tree and two tree-based ensemble methods (extremely…

AdultFinite element methodsMean squared errorComputer scienceQuantitative Biology::Tissues and OrgansINGENIERIA MECANICAFinite Element AnalysisPhysics::Medical PhysicsDecision treeBreast compressionHealth Informatics02 engineering and technologyMachine learningcomputer.software_genreModels Biological030218 nuclear medicine & medical imagingSet (abstract data type)03 medical and health sciencesImaging Three-Dimensional0302 clinical medicineMachine learning0202 electrical engineering electronic engineering information engineeringHumansBreastbusiness.industryModelingEnsemble learningFinite element methodComputer Science ApplicationsRandom forestEuclidean distanceTree (data structure)Female020201 artificial intelligence & image processingArtificial intelligenceBreast biomechanicsbusinesscomputerLENGUAJES Y SISTEMAS INFORMATICOS
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Original strain energy density functions for modeling of anisotropic soft biological tissue

2017

This thesis has focused on the construction of strain energy densities for describing the non-linear behavior of anisotropic materials such as biological soft tissues (ligaments, tendons, arterial walls, etc.) or fiber-reinforced rubbers. The densities we have proposed have been developed with the mathematical theory of invariant polynomials, particularly the Noether theorem and the Reynolds operator. Our work involved two types of anisotropic materials, the first with a single fiber family and the second with a four-fiber family. The concept of polyconvexity has also been studied because it is well known that it plays an important role for ensuring the existence of solutions. In the case o…

Finite element methodsHypérelasticité anisotropeModélisation[SPI.MECA.BIOM] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph]Méthodes éléments finisBiomécaniqueModelingSoft biological tissue[SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph]BiomechanicalAnisotropic hyperelasticityTissus biologiques
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On the use of EMI for the assessment of dental implant stability

2014

The achievement and the maintenance of dental implant stability are prerequisites for the long-term success of the osseointegration process. Since implant stability occurs at different stages, it is clinically required to monitor an implant over time, i.e. between the surgery and the placement of the artificial tooth. In this framework, non-invasive tests able to assess the degree of osseointegration are necessary. In this paper, the electromechanical impedance (EMI) method is proposed to monitor the stability of dental implants. A 3D finite element model of a piezoceramic transducer (PZT) bonded to a dental implant placed into the bone was created, considering the presence of a bone- impla…

Materials sciencemedicine.medical_treatmentStiffnessOsseointegrationTransducerEMIElectromechanical impedance method dental implants finite element methodsmedicinePulp canalImplantmedicine.symptomDental implantAbutment (dentistry)Biomedical engineering
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Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems

2015

This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed

Mathematical optimizationControl and OptimizationMathematicsofComputing_NUMERICALANALYSISFinite element approximations010103 numerical & computational mathematicsType (model theory)01 natural sciencesparabolic time-periodic optimal control problemsError analysisFOS: MathematicsApplied mathematicsMathematics - Numerical AnalysisNumerical testsfunctional a posteriori error estimates0101 mathematicsMathematics - Optimization and Control49N20 35Q61 65M60 65F08Mathematicsta113Time periodicta111Numerical Analysis (math.NA)State (functional analysis)Optimal controlComputer Science Applications010101 applied mathematicsOptimization and Control (math.OC)multiharmonic finite element methodsSignal ProcessingA priori and a posterioriAnalysisNumerical Functional Analysis and Optimization
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On FE-grid relocation in solving unilateral boundary value problems by FEM

1992

We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions, Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction. peerReviewed

finite element methods [keyword]msc:65N50numerical examples [keyword]FE-grid relocation [keyword]msc:65N30nonlinear optimization [keyword]msc:35J05sequential quadratic programming code [keyword]unilateral boundary value problem [keyword]Poisson equation [keyword]grid relocation [keyword]
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