Numerical Analysis

Analysis of the discontinuous Galerkin method for elliptic problems on surfaces

by Pravin Madhavan

Co-authored with A. Dedner and B. Stinner.

We extend the discontinuous Galerkin (DG) framework to a linear second-order elliptic problem on a compact smooth... more We extend the discontinuous Galerkin (DG) framework to a linear second-order elliptic problem on a compact smooth connected and oriented surface. An interior penalty (IP) method is introduced on a discrete surface and we derive a-priori error estimates by relating the latter to the original surface via the lift introduced in Dziuk (1988). The estimates suggest that the geometric error terms arising from the surface discretisation do not affect the overall convergence rate of the IP method when using linear ansatz functions. This is then verified numerically for a number of test problems. An intricate issue is the approximation of the surface conormal required in the IP formulation, choices of which are investigated numerically. Furthermore, we present a generic implementation of test problems on surfaces.

Numerical Analysis of Buried Pipelines with Right Angle Elbow under Wave Propagation

by Hamid Arabzadeh

Dynamic Response of Pressurized Submarine Pipelines Subjected To Transverse Impact Loads

by Hamid Arabzadeh

A Low-Dispersion and Low-Dissipation Implicit Runge-Kutta Scheme

by Alireza Najafiyazdi

Random imperfection fields to model the size effect in laboratory wood specimens

by Sara Casciati

Casciati S. and Domaneschi M. (2007). “Random imperfection fields to model the size effect in laboratory wood specimens”. Structural Safety, 29(4), 308-321. ISSN: 0167-4730.

DATA E LUOGO DI PUBBLICAZIONE: October 2007; Elsevier Science Bv, 1000 AE Amsterdam, Netherlands.

ABSTRACT. The composite nature of a wood continuum prevents one from extrapolating the results of laboratory tests on... more ABSTRACT. The composite nature of a wood continuum prevents one from extrapolating the results of laboratory tests on standard wood specimens to structural elements of significant size. Therefore, these elements are usually tested under standardized loading conditions in order to detect a sort of average material behaviour.
In this paper, the initial step consists, instead, of testing the material specimens. The extension of the results to structural elements is then pursued by introducing a random field, or, in a discretized model, a random array of imperfections.
The calibration of the suitable spatial distribution of the imperfections is then investigated by a mixed experimental–numerical approach, for a reference beam. The analyses on the relative finite elements model are iterated to match the response of the full scale laboratory tests.

KEYWORDS: Biaxial tests; Finite element model; Imperfections; Laboratory tests; Random field; Wood specimens

Cohesive Crack Propagation in a Random Elastic Medium

by Sara Casciati

Bruggi M., Casciati S., and Faravelli L. (2008). “Cohesive crack propagation in a random elastic medium”. Probabilistic Engineering Mechanics, 23(1), 23-35. ISSN: 0266-8920.

DATA E LUOGO DI PUBBLICAZIONE: January 2008; Elsevier Sci Ltd, Kidlington, Oxford OX5 1GB, Oxon, England.

ABSTRACT. The issue of generating non-Gaussian, multivariate and correlated random fields, while preserving the... more ABSTRACT. The issue of generating non-Gaussian, multivariate and correlated random fields, while preserving the internal auto-correlation structure of each single-parameter field, is discussed with reference to the problem of cohesive crack propagation. Three different fields are introduced to model the spatial variability of the Young modulus, the tensile strength of the material, and the fracture energy, respectively. Within a finite-element context, the crack-propagation phenomenon is analyzed by coupling a Monte Carlo simulation scheme with an iterative solution algorithm based on a truly-mixed variational formulation which is derived from the Hellinger–Reissner principle. The selected approach presents the advantage of exploiting the finite-element technology without the need to introduce additional modes to model the displacement discontinuity along the crack boundaries. Furthermore, the accuracy of the stress estimate pursued by the truly-mixed approach is highly desirable, the direction of crack propagation being determined on the basis of the principal stress criterion. The numerical example of a plain concrete beam with initial crack under a three-point bending test is considered. The statistics of the response is analyzed in terms of peak load and load–mid deflection curves, in order to investigate the effects of the uncertainties on both the carrying capacity and the post-peak behaviour. A sensitivity analysis is preliminarily performed and its results emphasize the negative effects of not accounting for the auto-correlation structure of each random field. A probabilistic method is then applied to enforce the auto-correlation without significantly altering the target marginal distributions. The novelty of the proposed approach with respect to other methods found in the literature consists of not requiring the a priori knowledge of the global correlation structure of the multivariate random field.

KEYWORDS: Multivariate non-Gaussian random fields; Auto-correlation; Cohesive crack propagation; Truly-mixed finite element method; Monte Carlo simulations

Vertical linear antennas in the presence of a lossy half-space: An improved approximate model

by Milica Rancic

Co-authored with Predrag D. Rancic, published in AEU - International Journal of Electronics and Communications, Volume 60, Issue 5, 2 May 2006, Pages 376-386

The unknown current distribution (UCD) and the input impedance/admittance of the vertical dipole previous... more The unknown current distribution (UCD) and the input impedance/admittance of the vertical dipole previous termantennanext term (VDA) in the previous termpresencenext term of the homogeneous and isotropic previous termlossynext termprevious termhalfnext term-previous termspacenext term are determined in this paper. The moment method (MoM) with an entire domain polynomial current approximation for numerical approach to the system of integral equations of Hallen's type (SIE-H) is applied for solving of this problem. The influence of the finite ground conductivity, expressed by the Sommerfeld's integral kernel (SIK), is modelled in previous termanext term new simple way without limitations for the refraction index. This previous termmodelnext term gives output numerical results of enviable accuracy.

Horizontal linear antennas above a lossy half-space: A new model for the Sommerfeld's integral kernel

by Milica Rancic

Co-authored with Predrag D. Rancic, published in AEU - International Journal of Electronics and Communications, Volume 65, Issue 10, October 2011, Pages 879-887

Unknown current distribution (UCD) and input impedance/admittance of a horizontal dipole antenna (HDA) placed above a... more Unknown current distribution (UCD) and input impedance/admittance of a horizontal dipole antenna (HDA) placed above a homogenous and isotropic lossy half-space (LHS) will be determined in this paper. Integrals of Sommerfeld's type, which occur in potential expressions, will be solved approximately applying a new simple, very accurate and efficient model. Firstly, the accuracy of the proposed model for the Sommerfeld's integral kernel (SIK) is going to be verified, comparing the obtained results with corresponding ones of other authors. In order to illustrate validity of the proposed method, the system of integral equations of Hallen's type (SIE-H) will be numerically solved using the point-matching method (PMM), assuming the polynomial approximation for the current along the antenna conductors. Results obtained for the current distribution and input impedance of the observed HDA will be graphically illustrated and, also, compared with corresponding ones of other authors.

Simple Numerical Approach in Analysis of Horizontal Dipole Antennas Above Lossy Half-Space

by Milica Rancic

Co-authored with Slavoljub Aleksić, published in IJES - International Journal of Emerging Sciences (selected paper from the 10th International Conference on Applied Electromagnetics PES 2011, Niš, Serbia, September 25-29), Vol. 1, No. 4, pp. 586-596, 2011. ISSN 2222-4254

Numerological Interpretations of Book III, Canto 6 of The Faerie Queene

by Stacey Pounsberry

draft only

This paper was a part of the senior seminar where I fell in love with Edmund Spenser, the "sonne of a... more This paper was a part of the senior seminar where I fell in love with Edmund Spenser, the "sonne of a myrchante" and oppressor of the Irish (begrudgingly).

Beobachtungsmethode und numerische Analyse bei Ausführung einer tiefen Baugrube in weichem Seeton

by Patrick Becker

In German. In 26. Christian Veder Kolloquium, Mitteilung Gruppe Geotechnik TU Graz, Heft 40, S. 281-296.

Die Planung und Ausführung von tiefen Baugruben in weichen Böden im innerstädtischen Bereich ist für alle Beteiligten... more Die Planung und Ausführung von tiefen Baugruben in weichen Böden im innerstädtischen Bereich ist für alle Beteiligten eine große Herausforderung. In diesem Beitrag wird die Herstellung einer 8 m tiefen Baugrube mit unmittelbarer Nachbarbebauung in Konstanz vorgestellt. Hierzu werden umfangreiche Messergebnisse gezeigt, die im Rahmen der bei Baugruben in weichen Böden unverzichtbaren Beobachtungsmethode erfasst wurden, und mit den Ergebnissen einer numerischen Analyse unter Berücksichtigung der räumlichen und zeitabhängigen Effekte verglichen. Darüber hinaus werden die erforderlichen Nachweise für den Grenzzustand der Tragfähigkeit unter Berücksichtigung der komplexen Baugrund-Tragwerk-Interaktion präsentiert. Insbesondere wird ein modifizierter Ansatz zur Berechnung der Aufbruchsicherheit einer verankerten Baugrubensohle nach den Vorgaben des Eurocodes EC7-1 in Anlehnung an die Empfehlungen des Arbeitskreises „Baugruben“ der Deutschen Gesellschaft für Geotechnik vorgestellt.
Die Baugrube mit einem annähernd quadratischen Grundriss wurde im Jahr 2008 in weich-breiigem Seeton mit zwei Untergeschossen hergestellt. Als Verbauwand wurde eine eingepresste Spundwand verwendet, die in einer Höhe von –1,80 m durch einen oberen Aussteifungsring aus einer Gurtung mit diagonalen Ecksteifen und mit einer abschnittweise hergestellten Unterbetonsohle in einer Tiefe von –7,80 m ausgesteift wurde. Die räumlichen Einflüsse der Baugrund-Tragwerk-Interaktion, die für dieses Projekt durch den Einbau einer rautenförmigen oberen und unteren Aussteifung und den abschnittweisen Einbau der Betonsohle bestimmt wurden, konnten in einer zweidimensionalen numerischen Analyse mit Mobilisierungsfaktoren und unter Berücksichtigung der spannungspfadabhängigen Steifigkeit des Seetons zutreffend erfasst werden.
Dieses Ausführungsbeispiel einer tiefen Baugrube in weichen Böden verdeutlicht besonders die Wichtigkeit eines umfangreichen begleitenden Messprogramms im Hinblick auf die Anwendungsgrenzen der Finiten Elemente Methode bei Verwendung derzeit kommerziell verfügbarer höherwertigerer Stoffgesetze. In dem Beitrag wird darüber hinaus eine Methode zur Berücksichtigung der spannungspfadabhängigen Steifigkeit von weichen Böden vorgestellt.

Comparison of different limit state design approaches of retaining structures

by Patrick Becker

In: Geotechnical Engineering in Urban Environments. Proceeding of the XIV European Conf. on Soil Mechanics and Geotechnical Engineering, Madrid, Vol. 2 pp.219-226.

The choice of the different design approaches has a substantial effect on the limit state analysis of geotechnical... more The choice of the different design approaches has a substantial effect on the limit state analysis of geotechnical structures. In particular, the soil-structure interaction behaviour is complicated in supported excavations, since the actions and resistances due to the earth pressure on the excavation walls are dependant on the deformations and has to be taken into consideration with different partial safety factors.
The limit state conditions of excavations had been investigated according to the German approach with consideration of the national annex to the EC 7-1 and the national recommendations for “Excavations” EAB (2006). The determination of the required embedment depth and the corresponding section forces are of special importance in the design of the retaining walls in the ultimate limit state (ULS) according to EC 7-1 and DIN 1054:2005. For a practical application, this has been illustrated in the paper on the basis of a numerical and analytical analysis of an idealized excavation. The results are compared with other alternative design approaches
of the EC 7-1.

Modeling of TNT transport from landmines: Numerical approach

by Maik Irrazabal

Unconstrained Optimization Techniques for the Acceleration of Alternating Projection Methods

by Luis Manuel Hernandez Ramos

Co-authored with R. Escalante and M. Raydan

Alternating projection methods have been extensively used to find the closest point, to a
given point, in the... more Alternating projection methods have been extensively used to find the closest point, to a
given point, in the intersection of several given sets that belong to a Hilbert space. One of
the characteristics of these schemes is the slow convergence that can be observed in practical
applications. To overcome this difficulty, several techniques, based on different ideas, have
been developed to accelerate their convergence. Recently, a successful acceleration scheme was
developed specially for Cimmino’s method when applied to the solution of large-scale saddle point
problems. This specialized acceleration scheme is based on the use of the well-known conjugate
gradient method for minimizing a related convex quadratic map. In this work, we extend and
further analyze this optimization approach for several alternating projection methods on different
scenarios. In particular, we include a specialized analysis and treatment for the acceleration of
von Neumann-Halperin’s method and Cimmino’s method on subspaces, and Kaczmarz method
on linear varieties. For some specific applications we illustrate the advantages of our acceleration
schemes with encouraging numerical experiments.

Analysis of truncation errors and design of physically optimized discretizations

by Stefan Hickel

Quality and Reliability of Large-Eddy Simulations; J. Meyers, B. Geurts, P.Sagaut (Eds.), Springer.

Further development of Large Eddy Simulation (LES) faces as major obstacle the strong coupling between subgrid-scale... more Further development of Large Eddy Simulation (LES) faces as major obstacle the strong coupling between subgrid-scale (SGS) model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. In this paper, we explore how implicit SGS models can be derived systematically and propose a procedure for design, analysis, and optimization of nonlinear discretizations. Implicit LES can be made rigorous by requiring that the numerical dissipation approximates the SGS dissipation obtained from the analysis of nonlinear interactions in turbulence.

Fast estimation of transverse fields in high-finesse optical cavities

by Partha Saha

Numerical Analysis of Space Charge Effects in Electron Bunches at Laser-Driven Plasma Accelerators

by Anthony Ashmore

Laser-driven Plasma Accelerators (LPA) have successfully generated high energy, high charge electron bunches which can... more Laser-driven Plasma Accelerators (LPA) have successfully generated high energy, high charge electron bunches which can reach many kA peak current, over short distances. Space charge issues, even in transport lines as simple as a drift section, have to be carefully taken into account since they can degrade the beam quality, preventing any further application of such electron beams. We analyse the space charge effects within an electron bunch with numerical simulations in order to assess their effect on the beam. We use LPA beam parameters published in previous experimental studies. These studies can give an indication of the working point where space charge can dominate the beam dynamics and has to be taken into account in the application of such beams.

Response Surface Approximation using Sparse Grid Design

by Ranjan Ganguli

Fractal Boundaries of Basin of Attraction of Newton-Raphson Method in Helicopter Trim

by Ranjan Ganguli

Application of homotopy perturbation method to find an analytical solution for magnetohydrodynamic flows of viscoelastic fluids in converging/diverging channels

by Mostafa Safdari Shadloo