165 research outputs found
θεωρία και εφαρμογές
No full textThe finite element method is a numerical method for calculating approximate solutions of partial differential equations (PDEs). This method is a powerful tool in the study of various problems and finds a large number of applications. We will concentrate here on applying the method to Fluid Mechanics problems. Fluid Mechanics is a particular branch of classical mechanics which has as main object of research and study the static and dynamic behavior of fluids. Fluid is characterized as any substance presenting a flow, i.e. refers to liquids and gases whose cohesion forces are weak, so that they each take the shape of the space they occupy or the medium through which they move.
In this thesis, we will attempt to solve the differential equations describing fluid movement. However, since the solution of these equations is not always possible, as in the case of the Navier-Stokes equations, it is necessary to extend to new ways of solving them, such as the Finite Element method. First, we will present the method along with the basic theorems of existence and uniqueness of the solutions that arise.
We will also analyze the a priori and a posterior errors for linear problems only, as there is a lack of these concepts in more complex systems. We will also refer to baseline functions that help us to distinguish the problem and the types of data that arise.
We will begin the numerical solution with the Advection-Diffusion scalar equation, which presents difficulties in solving it. To overcome this obstacle, we will also present finite element method variants such as the Stabilized Upwind Petrov-Galerkin (SUPG), Galerkin Least Squares (GLS) and Unusual Stabilized FEM (USFEM).
In the fourth chapter, we will deal with the Navier-Stokes equations. We will present the formulation of the equation in the classical method of Finite Element and the advancements of SUPG and Variational Multiscale Scheme. In addition, we will discuss about the Discontinuous Galerkin (DG).
We will continue by presenting a range of test problems for these equations, such as the driven cavity and the backward step. Our goal is to show that these methods provide reliable numerical results in all cases and extended ranges of dimensionless numbers, such as the Reynolds number.
Finally, we will concentrate on the application of the method in a problem of the biomedical field. We will deal with a three-dimensional patient-based carotid structure and present the results obtained from the numerical solution of the problem using the SUPG method.
The obtained results and images resulted from the use of the programs Matlab, FEniCS, SimVascular, Wolfram Mathematica, GeoGebra and LaTeX.Η μέθοδος πεπερασμένων στοιχείων είναι μια αριθμητική μέθοδος για τον υπολογισμό προσεγγιστικών λύσεων μερικών διαφορικών εξισώσεων. Η μέθοδος αυτή αποτελεί ισχυρό εργαλείο στη μελέτη διάφορων προβλημάτων και βρίσκει μεγάλο αριθμό εφαρμογών. Εμείς εδώ θα επικεντρωθούμε στην εφαρμογή της μεθόδου σε προβλήματα Ρευστομηχανικής. Η Ρευστομηχανική αποτελεί ιδιαίτερο κλάδο της κλασικής μηχανικής με κύριο αντικείμενο έρευνας και μελέτης τη στατική και δυναμική συμπεριφορά των ρευστών. Ως ρευστό χαρακτηρίζεται οποιαδήποτε ουσία παρουσιάζει ροή δηλαδή αναφέρεται σε υγρά και αέρια των οποίων οι δυνάμεις συνοχής είναι ασθενείς, έτσι ώστε να λαμβάνουν κάθε φορά το σχήμα του χώρου που καταλαμβάνουν ή του μέσου δια του οποίου κινούνται.
Στην παρούσα εργασία θα επιχειρήσουμε να επιλύσουμε τις μερικές διαφορικές εξισώσεις που περιγράφουν την κίνηση των ρευστών. Επειδή όμως η λύση των εξισώσεων αυτών δεν είναι πάντα εφικτή, όπως στην περίτωση των εξισώσεων Navier-Stokes, είναι αναγκαίο να επεκταθούμε σε νεόυς τρόπους επίλυσης αυτών, όπως την μέθοδο των Πεπερασμένων Στοιχείων. Αρχικά θα παρουσιάσουμε την μέθοδο μαζί με τα βασικά θεωρήματα ύπαρξης και μοναδικότητας των λύσεων που προκύπτουν.
Ακόμη θα αναλύσουμε τα a priori και a posteriori σφάλματα για γραμμικά προβλήματα, καθώς υπάρχει έλλειψη των εννοιών αυτών σε πιο περίπλοκα και μη-γραμμικά συστήματα. Θα αναφερθούμε επιπλέον στις συναρτήσεις βάσεις που μας βοηθούν να διακριτοποιήσουμε το πρόβλημα μας και στα είδη στοιχείων που προκύπτουν.
Θα ξεκινήσουμε την αριθμητική επίλυση με τη βαθμωτή εξίσωση Advection-Diffusion, που παρουσιάζει δυσκολίες στην επίλυσή της. Για να προσπεράσουμε το εμπόδιο αυτό θα παρουσιάσουμε κάποιες παραλλαγές της μεθόδου των Πεπερασμένων Στοιχείων όπως τη Stabilized Upwind Petrov-Galerkin (SUPG), την Galerkin Least Squares (GLS) και την Unusual Stabilized FEM(USFEM).
Στο τέταρτο κεφάλαιο θα ασχοληθούμε με τις εξίσωσεις Navier-Stokes. Θα παρουσιάσουμε τον φορμαλισμό της εξίσωσης με την κλασική μέθοδο των Πεπερασμένων Στοιχείων και τις επεκτάσεις SUPG και Variational Multiscale Scheme (VMS). Επιπλέον θα αναφερθούμε στην Discontinuous Galerkin (DG).
Θα συνεχίσουμε παρουσιάζοντας ένα φάσμα προβλημάτων δοκιμής για τις εξισώσεις αυτές, όπως εκείνα της κίνησης σε δοχείο με κινούμενο άνω άκρο (driven cavity) και του backward step. Στόχος μας είναι να δείξουμε ότι η μέθοδος αυτή μας παρέχει αξιόπιστα αποτελέσματα σε όλες τις περιπτώσεις.
Τέλος θα επικεντρωθούμε στις εφαρμογές της μεθόδου σε προβλήματα Εμβιομηχανικής. Θα ασχοληθούμε με μία τρισδιάστατη δομή καρωτίδας που έχει προκύψει από αναδόμηση της πραγματικής δομής. Θα παρουσιάσουμε τα αποτελέσματα που προέκυψαν από την αριθμητική λύση του προβλήματος χρησιμοποιώντας την SUPG.
Τα αποτελέσματα και οι εικόνες προέκυψαν με την χρήση των προγραμμάτων Matlab, FEniCS, SimVascular, Wolfram Mathematica, GeoGebra και LaTeX.85 σ
Software Metrics and Measurements
No full textIn the past few years, a large number of e-government and e-commerce systems have been developed, thus resulting to a constantly increasing number of software developers involved in software development for such systems. To ensure the production of high quality e-government and ecommerce systems, it is important for developers to collect and analyze measurable data that guide estimation, decision making, and assessment. It is common sense that one can control and manage better what he is able to measure.</jats:p
The Future of Virtual Classroom: Using Existing Features to Move Beyond Traditional Classroom Limitations
No full textSoftware Metrics and Measurements
No full textIn the past few years, a large number of e-government and e-commerce systems have been developed, thus resulting to a constantly increasing number of software developers involved in software development for such systems. To ensure the production of high quality e-government and e-commerce systems, it is important for developers to collect and analyze measurable data that guide estimation, decision making, and assessment. It is common sense that one can control and manage better what he is able to measure. Although there are major differences between e-commerce and e-government (e.g., access, structure and accountability; Jorgenson & Cable, 2002) there are no significant differences in terms of software metrics that can be applied to both. Metrics are used in e-government and e-commerce software development to measure various factors related to software quality and can be classified as product metrics, process metrics and recourse metrics. Product metrics are also called software metrics. These are metrics that are directly related to the product itself, such as code statements, delivered executables, manuals, and strive to measure product quality, or attributes of the product that can be related to product quality. Process metrics focus on the process of software development and measure process characteristics, aiming to detect problems or to push forward successful practices. Resource metrics are related to the resources required for software development and their performance. This article focuses on product metrics and on how such metrics can aid in design, prediction and assessment of the final product quality, provide data used for decision making, cost and effort estimation, fault prevention, testing time reduction, and, consequently, aid in producing better software for e-government and e-commerce sys </jats:p
Technical Issues Related to IT Governance Tactics
No full textThis chapter deals with some technical aspects of the strategies for IT Governance described in most of the other chapters of this book. The practical application of IT Governance techniques and tactics requires the collection and analysis of measurable data that guide estimation, decision-making and assessment, since it is common sense that one can control and manage better what one is able to measure. This chapter aims at introducing the reader to product metrics and measurements, proposing methods relating to the implementation of a measurements program and analyzing how product metrics can be used to control IT development. Focus is placed on product metrics, measurements and process control techniques. Such instruments can aid significantly in monitoring the development process and making IT-related tasks more transparent to IT managers. They also aid in design, prediction and assessment of the IT product quality. They provide data used for decision-making, cost and effort estimation, fault prevention, and testing time reduction. Moreover, the use of product metrics and process control techniques can direct the standardization of IT products and IT development process, as well as the assessment of the process maturity of outsourcing partners. The most commonly used metrics are presented and the reader is introduced to measurement techniques and automation tools. This chapter also discusses the application of metrics along with statistical process control tools. Finally, it provides suggestions on how product metrics can aid towards IT Governance not only in large IT companies, but also in the smaller ones.</jats:p
Remodeling effects of carotid artery stenting versus endarterectomy with patch angioplasty in terms of morphology and hemodynamics
No full textBackground: Carotid endarterectomy (CEA) remains the first-line treatment option of symptomatic and asymptomatic carotid stenosis, while stenting (CAS) is reserved for selected patients at high surgical risk. Here, we compare the vascular remodeling process in CEA-and CAS-treated patients with respect to morphological and hemodynamic features, because of their possible engagement in carotid atherosclerosis. Methods: Twelve (12) patients were included, half with patched CEA and half with CAS. Pre-and post-operative 3D image-based models of the carotid bifurcation were anatomically characterized in terms of flare, tortuosity, and curvature. Individual computational fluid dynamics simulations allowed to quantify the postoperative hemodynamic milieu in terms of (1) wall shear stress and (2) helical flow. Results: Carotid flare increased in all cases, but a more marked increase emerged after CEA compared to CAS. Tortuosity and curvature increased after CEA but decreased after CAS. CEA patients presented with significantly higher postoperative tortuosity than CAS patients. CEA was associated with a worse (non-statistically significant) score in all flow disturbance indicators vs. CAS. Conclusion: The increased flare and tortuosity of the carotid bifurcation after CEA vs. CAS is a marked difference in the vascular remodeling process between the two modalities. CAS seems to induce a less pro-restenosis hemodynamic environment compared to CEA. The emerged differences stimulate further analysis on a larger cohort with long-term outcomes, to shed light on the clinical impact of the observations
Morphological and hemodynamic characterization of post endovascular AAA repair: comparison between two different commercial devices
No full textPatient-specific modelling for the assessment of the hemodynamics risk of failure in endovascular aneurysm repair
No full text- …
