subject:(Boundary Integral Equation)

Brunel University

1. Fresneda-Portillo, Carlos. Boundary-domain integral equation systems for the Stokes system with variable viscosity and diffusion equation in inhomogeneous media.

Degree: PhD, 2016, Brunel University

URL: http://bura.brunel.ac.uk/handle/2438/14521 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715863

► The importance of the Stokes system stems from the fact that the Stokes system is the stationary linearised form of the Navier Stokes system [Te01,… (more)

▼ The importance of the Stokes system stems from the fact that the Stokes system is the stationary linearised form of the Navier Stokes system [Te01, Chapter1]. This linearisation is allowed when neglecting the inertial terms at a low Reinolds numbers Re << 1. The Stokes system essentially models the behaviour of a non - turbulent viscous fluid. The mixed interior boundary value problem related to the compressible Stokes system is reduced to two different BDIES which are equivalent to the original boundary value problem. These boundary-domain integral equation systems (BDIES) can be expressed in terms of surface and volume parametrix-based potential type operators whose properties are also analysed in appropriate Sobolev spaces. The invertibility and Fredholm properties related to the matrix operators that de ne the BDIES are also presented. Furthermore, we also consider the mixed compressible Stokes system with variable viscosity in unbounded domains. An analysis of the similarities and differences with regards to the bounded domain case is presented. Furthermore, we outline the mapping properties of the surface and volume parametrix-based potentials in weighted Sobolev spaces. Equivalence and invertibility results still hold under certain decay conditions on the variable coeffi cient The last part of the thesis refers to the mixed boundary value problem for the stationary heat transfer partial di erential equation with variable coe cient. This BVP is reduced to a system of direct segregated parametrix-based Boundary-Domain Integral Equations (BDIEs). We use a parametrix different from the one employed by Chkadua, Mikhailov and Natroshvili in the paper [CMN09]. Mapping properties of the potential type integral operators appearing in these equations are presented in appropriate Sobolev spaces. We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed in both bounded and unbounded domains.

Subjects/Keywords: 515; Boundry domain integral equation; Variable coefficient; Boundary integral equation

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APA (6^th Edition):

Fresneda-Portillo, C. (2016). Boundary-domain integral equation systems for the Stokes system with variable viscosity and diffusion equation in inhomogeneous media. (Doctoral Dissertation). Brunel University. Retrieved from http://bura.brunel.ac.uk/handle/2438/14521 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715863

Chicago Manual of Style (16^th Edition):

Fresneda-Portillo, Carlos. “Boundary-domain integral equation systems for the Stokes system with variable viscosity and diffusion equation in inhomogeneous media.” 2016. Doctoral Dissertation, Brunel University. Accessed April 11, 2021. http://bura.brunel.ac.uk/handle/2438/14521 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715863.

MLA Handbook (7^th Edition):

Fresneda-Portillo, Carlos. “Boundary-domain integral equation systems for the Stokes system with variable viscosity and diffusion equation in inhomogeneous media.” 2016. Web. 11 Apr 2021.

Vancouver:

Fresneda-Portillo C. Boundary-domain integral equation systems for the Stokes system with variable viscosity and diffusion equation in inhomogeneous media. [Internet] [Doctoral dissertation]. Brunel University; 2016. [cited 2021 Apr 11]. Available from: http://bura.brunel.ac.uk/handle/2438/14521 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715863.

Council of Science Editors:

Fresneda-Portillo C. Boundary-domain integral equation systems for the Stokes system with variable viscosity and diffusion equation in inhomogeneous media. [Doctoral Dissertation]. Brunel University; 2016. Available from: http://bura.brunel.ac.uk/handle/2438/14521 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715863

New Jersey Institute of Technology

2. Qi, Haiyang. Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters.

Degree: PhD, Mathematical Sciences, 2017, New Jersey Institute of Technology

URL: https://digitalcommons.njit.edu/dissertations/38

► In this dissertation, an in-depth comparison between boundary integral equation solvers and Domain Decomposition Methods (DDM) for frequency domain Helmholtz transmission problems in composite… (more)

▼ In this dissertation, an in-depth comparison between boundary integral equation solvers and Domain Decomposition Methods (DDM) for frequency domain Helmholtz transmission problems in composite two-dimensional media is presented. Composite media are characterized by piece-wise constant material properties (i.e., index of refraction) and thus, they exhibit interfaces of material discontinuity and multiple junctions. Whenever possible to use, boundary integral methods for solution of Helmholtz boundary value problems are computationally advantageous. Indeed, in addition to the dimensional reduction and straightforward enforcement of the radiation conditions that these methods enjoy, they do not suffer from the pollution effect present in volumetric discretization. The reformulation of Helmholtz transmission problems in composite media in terms of boundary integral equations via multi-traces constitutes one of the recent success stories in the boundary integral equation community. Multi-trace formulations (MTF) incorporate local Dirichlet and Neumann traces on subdomains within Green’s identities and use restriction and extension by zero operators to enforce the intradomain continuity of the fields and fluxes. Through usage of subdomain Calderon projectors, the transmission problem is cast into a linear system form whose unknowns are local Dirichlet and Neumann traces (two such traces per interface of material discontinuity) and whose operator matrix consists of diagonal block boundary integral operators associated with the subdomains and extension/projections off diagonal blocks. This particular form of the matrix operator associated with MTF is amenable to operator preconditioning via Calderon projectors. DDM rely on subdomain solutions that are matched via transmission conditions on the subdomain interfaces that are equivalent to the physical continuity of fields and traces. By choosing the appropriate transmission conditions, the convergence of DDM for frequency domain scattering problems can be accelerated. Traditionally, the intradomain transmission conditions were chosen to be the classical outgoing Robin/impedance boundary conditions. When the ensuing DDM linear system is solved via Krylov subspace methods, the convergence of DDM with classical Robin transmission conditions is slow and adversely affected by the number of subdomains. Heuristically, this behavior is explained by the fact that Robin boundary conditions are first order approximations of transparent boundary conditions, and thus there is significant information that is reflected back into a given subdomain from adjacent subdomains. Clearly, using more sophisticated transparent boundary conditions facilitates the information exchange between subdomains. For instance, Dirichlet-to-Neumann (DtN) operators of adjacent domains or suitable approximations of these can be used in the form of generalized Robin boundary conditions to increase the rate of the convergence of iterative solvers of DDM linear systems.… Advisors/Committee Members: Catalin C. Turc, Michael Siegel, Eliza Zoi-Heleni Michalopoulou.

Subjects/Keywords: Helmholtz transmission problem; Boundary integral equation; Domain decomposition method; Mathematics

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APA (6^th Edition):

Qi, H. (2017). Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters. (Doctoral Dissertation). New Jersey Institute of Technology. Retrieved from https://digitalcommons.njit.edu/dissertations/38

Chicago Manual of Style (16^th Edition):

Qi, Haiyang. “Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters.” 2017. Doctoral Dissertation, New Jersey Institute of Technology. Accessed April 11, 2021. https://digitalcommons.njit.edu/dissertations/38.

MLA Handbook (7^th Edition):

Qi, Haiyang. “Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters.” 2017. Web. 11 Apr 2021.

Vancouver:

Qi H. Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters. [Internet] [Doctoral dissertation]. New Jersey Institute of Technology; 2017. [cited 2021 Apr 11]. Available from: https://digitalcommons.njit.edu/dissertations/38.

Council of Science Editors:

Qi H. Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters. [Doctoral Dissertation]. New Jersey Institute of Technology; 2017. Available from: https://digitalcommons.njit.edu/dissertations/38

University of Alberta

3. Sigaeva, Taisiya. An examination of the design of mathematical models incorporating both microstructural and surface effects in anti-plane deformations.

Degree: PhD, Department of Mechanical Engineering, 2015, University of Alberta

URL: https://era.library.ualberta.ca/files/4q77ft926

► Micropolar theory and surface mechanics are rapidly becoming key tools in the development of more advanced models which can precisely describe the behavior of deformable… (more)

▼ Micropolar theory and surface mechanics are rapidly becoming key tools in the development of more advanced models which can precisely describe the behavior of deformable elastic solids. Renewed interest in these areas has arisen due to the desire of researchers to generalize continuum-based models for applications in a wider class of materials, such as the micro-featured materials, and at smaller scales, such as the nano-scale. The analysis of such classes of materials, in which the effects of both the surface and microstructure are known to be significant, can be greatly benefited from micropolar theory and surface mechanics. However, the multidisciplinary study aimed to develop mathematically and physically adequate models based on both of these theories remains largely absent from the literature due to a number of difficulties. To fill this void in the literature, in this work we employ the theory of linear micropolar elasticity in conjunction with a new representation of micropolar surface mechanics to develop a comprehensive model for the deformations of a linearly micropolar elastic solid subjected to anti-plane shear loading. The proposed model represents the surface effect as a thin micropolar film of separate elasticity, perfectly bonded to the bulk. Hence, this model captures not only the micro-mechanical behavior of the bulk, which is known to be considerable in many real materials, but also the contribution of the surface effect which has been experimentally well-observed for bodies with significant size-dependency and large surface area to volume ratios. Our emphasis in this research is the rigorous mathematical treatment of this model, particularly its well-posedness analysis in the Hadamard's sense. Although challenging, the well-posedness analysis is vital in the development of brand-new models, since it can give a sufficient confidence to find numerically a uniquely existing solution to the problem. To perform this analysis, we apply boundary integral equation methods generalizing and utilizing them as necessary to account for strict requirements of the proposed model. The coupling of surface mechanics to bulk models gives rise to a highly non-standard boundary condition which has not been accommodated by classical studies in this area. Therefore, a portion of this work is devoted to the study of the surface effect in the classical linear elastic analogue of the proposed model. This supplementary model is thoroughly analyzed for well-posedness and an example demonstrating its efficiency is given. These investigations provided valuable insight on how to tackle the mathematical complexity of the general model, for which bulky micropolar governing equations are used in addition to the similar highly non-standard surface effect boundary condition. Accordingly, we supply a rigorous mathematical treatment of the mixed boundary-value problems in finite and infinite domains for the proposed model which combines both microstructural and surface effects. Boundary integral equation methods are employed to…

Subjects/Keywords: Anti-plane deformations; Microstructural effect; Surface effect; Boundary integral equation method

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APA (6^th Edition):

Sigaeva, T. (2015). An examination of the design of mathematical models incorporating both microstructural and surface effects in anti-plane deformations. (Doctoral Dissertation). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/4q77ft926

Chicago Manual of Style (16^th Edition):

Sigaeva, Taisiya. “An examination of the design of mathematical models incorporating both microstructural and surface effects in anti-plane deformations.” 2015. Doctoral Dissertation, University of Alberta. Accessed April 11, 2021. https://era.library.ualberta.ca/files/4q77ft926.

MLA Handbook (7^th Edition):

Sigaeva, Taisiya. “An examination of the design of mathematical models incorporating both microstructural and surface effects in anti-plane deformations.” 2015. Web. 11 Apr 2021.

Vancouver:

Sigaeva T. An examination of the design of mathematical models incorporating both microstructural and surface effects in anti-plane deformations. [Internet] [Doctoral dissertation]. University of Alberta; 2015. [cited 2021 Apr 11]. Available from: https://era.library.ualberta.ca/files/4q77ft926.

Council of Science Editors:

Sigaeva T. An examination of the design of mathematical models incorporating both microstructural and surface effects in anti-plane deformations. [Doctoral Dissertation]. University of Alberta; 2015. Available from: https://era.library.ualberta.ca/files/4q77ft926

University of Wisconsin – Milwaukee

4. Szatkowski, Andrew Joseph. An Adapative Treecode-accelerated Boundary Integral Solver for Computing the Electrostatics of a Biomolecule.

Degree: MS, Mathematics, 2016, University of Wisconsin – Milwaukee

URL: https://dc.uwm.edu/etd/1422

► The Poisson-Boltzmann equation (PBE) is a widely-used model in the calculation of electrostatic potential for solvated biomolecules. PBE is an interface problem defined in… (more)

Subjects/Keywords: Biomolecular Electostatics; Boundary Integral Equation; Finite Element Method; Poisson Boltzmann Equation; Treecode; Mathematics

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APA (6^th Edition):

Szatkowski, A. J. (2016). An Adapative Treecode-accelerated Boundary Integral Solver for Computing the Electrostatics of a Biomolecule. (Thesis). University of Wisconsin – Milwaukee. Retrieved from https://dc.uwm.edu/etd/1422

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Szatkowski, Andrew Joseph. “An Adapative Treecode-accelerated Boundary Integral Solver for Computing the Electrostatics of a Biomolecule.” 2016. Thesis, University of Wisconsin – Milwaukee. Accessed April 11, 2021. https://dc.uwm.edu/etd/1422.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Szatkowski, Andrew Joseph. “An Adapative Treecode-accelerated Boundary Integral Solver for Computing the Electrostatics of a Biomolecule.” 2016. Web. 11 Apr 2021.

Vancouver:

Szatkowski AJ. An Adapative Treecode-accelerated Boundary Integral Solver for Computing the Electrostatics of a Biomolecule. [Internet] [Thesis]. University of Wisconsin – Milwaukee; 2016. [cited 2021 Apr 11]. Available from: https://dc.uwm.edu/etd/1422.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Szatkowski AJ. An Adapative Treecode-accelerated Boundary Integral Solver for Computing the Electrostatics of a Biomolecule. [Thesis]. University of Wisconsin – Milwaukee; 2016. Available from: https://dc.uwm.edu/etd/1422

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

5. Alzaix, Benjamin. Mathematical and numerical analysis of the Herberthson integral equation dedicated to electromagnetic plane wave scattering : Analyse mathématique et numérique de l’équation intégrale de Herberthson dédié à la diffraction d’ondes planes.

Degree: Docteur es, Mathematiques appliquees et calcul scientifique, 2017, Bordeaux

URL: http://www.theses.fr/2017BORD0578

►

Cette thèse porte sur la diffraction d’une onde plane électromagnétique par une surface lisse parfaitement conductrice (PEC). Elle présente l’analyse des propriétés d’une nouvelle formulation… (more)

▼

Cette thèse porte sur la diffraction d’une onde plane électromagnétique par une surface lisse parfaitement conductrice (PEC). Elle présente l’analyse des propriétés d’une nouvelle formulation des trois principales équations intégrales de frontières de la théorie de la diffraction électromagnétique (EFIE, MFIE et CFIE). L’idée est d’adapter les équations intégrales conventionnelles à la diffraction d’une onde plane en supposant que la fonction de phase de l’onde plane incidente détermine la fonction de phase de la distribution de courant induit sur la surface.L’idée d’utiliser la phase dans la diffraction d’ondes planes a déjà été étudiée pour les hautes fréquences, notamment dans les thèses de Zhou (1995) et Darrigrand (2002) qui adaptèrent les espaces d’approximation des éléments finis. Dans cette thèse, cependant, nous suivons une formulation plus récente, donnée par Herberthson (2008), où la fonction de phase est incorporée dans la distribution du noyau des opérateurs intégraux.En présentant les versions modifiées de l’EFIE et de la MFIE (dénommées HEFIE et HMFIE)dans des espaces fonctionnels appropriés, nous prouvons ici l’existence d’une solution unique à cette formulation spécifique et présentons une mise en oeuvre pratique originale qui tire parti de l’expérience acquise sur l’EFIE/MFIE. Par la suite, nous explorons une propriété importante offerte par ces nouvelles formulations: la possibilité de réduire le nombre de degrés de liberté requis pour obtenir une solution précise du problème.

This thesis is about the scattering of an electromagnetic plane wave incidenton a perfectly conducting smooth surface. It presents the analysis of the properties of a newformulation of the three principal boundary integral equations of electromagnetic scattering theory(EFIE, MFIE and CFIE). The basic idea is to adapt the conventional integral equations toplane-wave scattering by supposing that the phase function of an incident plane wave determinesthe phase function of the induced boundary current distribution.This idea of using the phase in plane wave scattering has previously been studied in highfrequencyscattering, in particular in the theses by Zhou (1995) and Darrigrand (2002) whoadapt the finite element approximation spaces. In this thesis, though, we follow a more recentformulation, given by Herberthson (2008), where the phase function is incorporated in the kerneldistribution of the integral operators.Presenting the modified version of the EFIE and the MFIE (denoted HEFIE and HMFIE) inappropriate function spaces, we prove the existence of a unique solution to this specific formulationand developp an original practical implementation which takes advantage of the gainedexperience on the EFIE/MFIE. Then, we explore another important property provided by thenew formulations: the possibility to reduce the number of degrees of freedom required to get anaccurate solution of the problem.

Advisors/Committee Members: Giraud, Luc (thesis director), Poirier, Jean-René (thesis director).

Subjects/Keywords: Diffraction électromagnétique; Equation intégrale de frontières; Onde planes; Electromagnetic scattering; Boundary integral equation; Plane wave

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APA (6^th Edition):

Alzaix, B. (2017). Mathematical and numerical analysis of the Herberthson integral equation dedicated to electromagnetic plane wave scattering : Analyse mathématique et numérique de l’équation intégrale de Herberthson dédié à la diffraction d’ondes planes. (Doctoral Dissertation). Bordeaux. Retrieved from http://www.theses.fr/2017BORD0578

Chicago Manual of Style (16^th Edition):

Alzaix, Benjamin. “Mathematical and numerical analysis of the Herberthson integral equation dedicated to electromagnetic plane wave scattering : Analyse mathématique et numérique de l’équation intégrale de Herberthson dédié à la diffraction d’ondes planes.” 2017. Doctoral Dissertation, Bordeaux. Accessed April 11, 2021. http://www.theses.fr/2017BORD0578.

MLA Handbook (7^th Edition):

Alzaix, Benjamin. “Mathematical and numerical analysis of the Herberthson integral equation dedicated to electromagnetic plane wave scattering : Analyse mathématique et numérique de l’équation intégrale de Herberthson dédié à la diffraction d’ondes planes.” 2017. Web. 11 Apr 2021.

Vancouver:

Alzaix B. Mathematical and numerical analysis of the Herberthson integral equation dedicated to electromagnetic plane wave scattering : Analyse mathématique et numérique de l’équation intégrale de Herberthson dédié à la diffraction d’ondes planes. [Internet] [Doctoral dissertation]. Bordeaux; 2017. [cited 2021 Apr 11]. Available from: http://www.theses.fr/2017BORD0578.

Council of Science Editors:

Alzaix B. Mathematical and numerical analysis of the Herberthson integral equation dedicated to electromagnetic plane wave scattering : Analyse mathématique et numérique de l’équation intégrale de Herberthson dédié à la diffraction d’ondes planes. [Doctoral Dissertation]. Bordeaux; 2017. Available from: http://www.theses.fr/2017BORD0578

Brunel University

6. Al-Jawary, Majeed Ahmed Weli. The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients.

Degree: PhD, 2012, Brunel University

URL: http://bura.brunel.ac.uk/handle/2438/6449 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.555673

► The boundary element method (BEM) has become a powerful method for the numerical solution of boundary-value problems (BVPs), due to its ability (at least for… (more)

Subjects/Keywords: 515.35; Boundary element method; Boundary-domain integral equation; Heat conduction with variable coefficient; ion; Diffusion equation

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APA (6^th Edition):

Al-Jawary, M. A. W. (2012). The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients. (Doctoral Dissertation). Brunel University. Retrieved from http://bura.brunel.ac.uk/handle/2438/6449 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.555673

Chicago Manual of Style (16^th Edition):

Al-Jawary, Majeed Ahmed Weli. “The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients.” 2012. Doctoral Dissertation, Brunel University. Accessed April 11, 2021. http://bura.brunel.ac.uk/handle/2438/6449 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.555673.

MLA Handbook (7^th Edition):

Al-Jawary, Majeed Ahmed Weli. “The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients.” 2012. Web. 11 Apr 2021.

Vancouver:

Al-Jawary MAW. The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients. [Internet] [Doctoral dissertation]. Brunel University; 2012. [cited 2021 Apr 11]. Available from: http://bura.brunel.ac.uk/handle/2438/6449 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.555673.

Council of Science Editors:

Al-Jawary MAW. The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients. [Doctoral Dissertation]. Brunel University; 2012. Available from: http://bura.brunel.ac.uk/handle/2438/6449 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.555673

7. -1218-7450. Implicit boundary integral methods.

Degree: PhD, Mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/32830

► Boundary integral methods (BIMs) solve constant coefficient, linear partial differential equations (PDEs) which have been formulated as integral equations. Implicit BIMs (IBIMs) transform these boundary… (more)

▼ Boundary integral methods (BIMs) solve constant coefficient, linear partial differential equations (PDEs) which have been formulated as integral equations. Implicit BIMs (IBIMs) transform these boundary integrals in a level set framework, where the boundaries are described implicitly as the zero level set of a Lipschitz function. The advantage of IBIMs is that they can work on a fixed Cartesian grid without having to parametrize the boundaries. This dissertation extends the IBIM model and develops algorithms for problems in two application areas. The first part of this dissertation considers nonlinear interface dynamics driven by bulk diffusion, which involves solving Dirichlet Laplace Problems for multiply connected regions and propagating the interface according to the solutions of the PDE at each time instant. We develop an algorithm that inherits the advantages of both level set methods (LSMs) and BIMs to simulate the nonlocal front propagation problem with possible topological changes. Simulation results in both 2D and 3D are provided to demonstrate the effectiveness of the algorithm. The second part considers wave scattering problems in unbounded domains. To obtain solutions at eigenfrequencies, boundary integral formulations use a combination of double and single layer potentials to cover the null space of the single layer integral operator. However, the double layer potential leads to a hypersingular integral in Neumann problems. Traditional schemes involve an interpretation of the integral as its Hadamard's Finite Part or a complicated process of element kernel regularization. In this thesis, we introduce an extrapolatory implicit boundary integral method (EIBIM) that evaluates the natural definition of the BIM. It is able to solve the Helmholtz problems at eigenfrequencies and requires no extra complication in different dimensions. We illustrate numerical results in both 2D and 3D for various boundary shapes, which are implicitly described by level set functions. Advisors/Committee Members: Tsai, Yen-Hsi R. (advisor), Arbogast, Todd (committee member), Biros, George (committee member), Engquist, Bjorn (committee member), Ren, Kui (committee member).

Subjects/Keywords: Boundary integral methods; Level set methods; Mullins-Sekerka; Helmholtz equation; Laplace equation; Multiply connected domain; Exterior problem; Differential equation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

-1218-7450. (2015). Implicit boundary integral methods. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/32830

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-1218-7450. “Implicit boundary integral methods.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed April 11, 2021. http://hdl.handle.net/2152/32830.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-1218-7450. “Implicit boundary integral methods.” 2015. Web. 11 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-1218-7450. Implicit boundary integral methods. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/2152/32830.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-1218-7450. Implicit boundary integral methods. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/32830

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

NSYSU

8. Feng, Chih-ting. Dynamic analysis of a floating barge with a liquid container.

Degree: Master, Marine Environment and Engineering, 2010, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0527110-005702

► This study is to develop a 2D fully nonlinear numerical wave tank used to investigate the wave-induced dynamic properties of a dual pontoon floating structure… (more)

▼ This study is to develop a 2D fully nonlinear numerical wave tank used to investigate the wave-induced dynamic properties of a dual pontoon floating structure (DPFS) with a liquid container on the top. The nonlinear numerical wave tank, developed based on the velocity potential function and the boundary element method (BEM), is to simulate dynamic properties including sway, heave, roll, and tension response. In addition, a physical model of the dual floating pontoon is tested in a hydrodynamic wave tank to validate the numerical model for simulation of wave and structure interaction. In the numerical model, a boundary integral equation method (BIEM) with linear element scheme is applied to establish a 2D fully nonlinear numerical wave tank (NWT). The nonlinear free surface condition is treated by combining the Mixed Eulerian and Lagrangian method (MEL), the fourth-order Runge-Kutta method (RK4) and a cubic spline scheme. The second-order Stokes wave theory is used to generate the velocity flux on the input boundary. Numerical damping zones are deployed at both ends of the NWT to dissipate or absorb the transmitted and reflected waves. Acceleration potential method and modal decomposition method are adopted to solve the unsteady potential functions Î¦1,t and Î¦2,t, while the system of motion equation is established according to Newton's 2nd law. Finally, the RK4 is applied to predict the motion of the platform, and the variation of free surface. As for the hydrodynamic laboratory model test, an image process scheme is applied to trace the floating structure motion and the variation of water surface inside the sloshing tank, while the mooring tension is measured by a load cell and stored in a data logger. The comparisons of numerical simulations and experimental data indicate that the numerical predictions are larger than measurements especially near the resonance frequency. This discrepancy is probably due to the fluid viscous effect. To overcome this problem and maintain the calculation efficiency, an uncoupled damping coefficient obtained through a damping ratio (Î¶=C/Ccr=0.02) is incorporated into the vibration system. Results reveal that responses of body motion near the resonant frequencies of each mode have significantly reduced and close to the measurements. Therefore, the suitable value of the damping ratio for the floating platform is Î¶=0.02. Then the numerical model with a damping ratio is applied to investigate the dynamic properties of the floating platform for different arrangements, including different mooring angle, spring constant, spacing, and the liquid container. Results demonstrate that the resonant frequency of each mode, responses of body motion and mooring tensions change along with the settings. As a whole, the platform with smaller mooring angle, longer spacing between the pontoons, higher water depth and wider width of the liquid container has relatively stable body motions and less mooring tension. Finally, the comparisons of the effects of random and regular waves on the floating structure… Advisors/Committee Members: Bang-Fuh Chen (chair), Chai-Cheng Huang (committee member), Gung-Rong Chen (chair), Der-Liang Young (chair).

Subjects/Keywords: fully nonlinear numerical wave tank; Boundary integral equation method; dual pontoon floating structure

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APA (6^th Edition):

Feng, C. (2010). Dynamic analysis of a floating barge with a liquid container. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0527110-005702

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Feng, Chih-ting. “Dynamic analysis of a floating barge with a liquid container.” 2010. Thesis, NSYSU. Accessed April 11, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0527110-005702.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Feng, Chih-ting. “Dynamic analysis of a floating barge with a liquid container.” 2010. Web. 11 Apr 2021.

Vancouver:

Feng C. Dynamic analysis of a floating barge with a liquid container. [Internet] [Thesis]. NSYSU; 2010. [cited 2021 Apr 11]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0527110-005702.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Feng C. Dynamic analysis of a floating barge with a liquid container. [Thesis]. NSYSU; 2010. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0527110-005702

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

NSYSU

9. Tang, Hung-jie. Study on the Floating Platform for Cage Aquaculture.

Degree: PhD, Marine Environment and Engineering, 2008, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-1223108-193753

► This paper is to investigate the wave-induced dynamic properties of the floating platform for cage aquaculture. Considering the calculation efficiency and its applicability, this problem… (more)

▼ This paper is to investigate the wave-induced dynamic properties of the floating platform for cage aquaculture. Considering the calculation efficiency and its applicability, this problem is simplified by: (1) assuming the flow field is inviscid, incompressible and irrotational; (2) the form drag and inertia drag on the fish net is calculated by the modified Morison equation (or Morison type equation of relative motion), including the material and geometric properties; (3) the moorings is treated as a symmetric linear spring system and the influence of hydrodynamic forces on the mooring lines is neglected; and (4) the net-volume is assumed as un-deformable to avoid the inversely prolonging computing time because the mass of fish net with is too light comparing with the mass of floating platform and cause the marching time step tremendously small to reach the steady-state condition which may lead to larger numerical errors (e.g. truncation errors) in computation. The BIEM with linear element scheme is applied to establish a 2D fully nonlinear numerical wave tank (NWT). The nonlinear free surface condition is treated by combining the Mixed Eulerian and Lagrangian method (MEL), the fourth-order Runge-Kutta method (RK4) and the cubic spline scheme. The second-order Stokes wave theory is adopted to give the velocity on the input boundary. Numerical damping zones are deployed at both ends of the NWT to dissipate or absorb the transmitted and reflected wave energy. The velocity and acceleration fields should be solved simultaneously in order to obtain the wave-induced dynamic property of the floating platform. Thus, both the acceleration potential method and modal decomposition method are adopted to solve the wave forces on the floating body, while the wave forces on the fish net are calculated by the modified Morison equation. According to Newtonâs second law, the total forces on the gravity center of the floating platform form the equation of motion. Finally, the RK4 is applied to predict the displacement and velocity of the platform. Firstly, the NWT is validated by comparing the wave elevation, internal velocity and acceleration with those from the second-order Stokes wave theory. Moreover, the numerical damping zone is suitable for long time simulation with a wide range of wave depth. The simulated results on wave-body interactions of fixed or freely floating body also indicate good agreement with those of other published results. Secondly, in the case of the interaction of waves and the floating platform, the simulated results show well agreement with experimental data, except at the vicinity of resonant frequency of roll and heave motions. This discrepancy is due to the fluid viscous effect. To overcome this problem and maintain the calculation efficiency, an uncoupled damping coefficient obtained by a damping ratio (Î¾=0.1 ) is incorporated into the vibration system. Results reveal that responses of body motion near the resonant frequencies of each mode have significant reduction and close to the experimental data.… Advisors/Committee Members: Tai-Wen Hsu (chair), Min-Chih Huang (chair), Chai-Cheng Huang (committee member), Chung-Pan Lee (chair), Hwung-Hweng Hwung (chair), Yang-Yih Chen (chair).

Subjects/Keywords: resonance; floating platform; Boundary integral equation method; fully nonlinear numerical wave tank; cage aquaculture

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Tang, H. (2008). Study on the Floating Platform for Cage Aquaculture. (Doctoral Dissertation). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-1223108-193753

Chicago Manual of Style (16^th Edition):

Tang, Hung-jie. “Study on the Floating Platform for Cage Aquaculture.” 2008. Doctoral Dissertation, NSYSU. Accessed April 11, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-1223108-193753.

MLA Handbook (7^th Edition):

Tang, Hung-jie. “Study on the Floating Platform for Cage Aquaculture.” 2008. Web. 11 Apr 2021.

Vancouver:

Tang H. Study on the Floating Platform for Cage Aquaculture. [Internet] [Doctoral dissertation]. NSYSU; 2008. [cited 2021 Apr 11]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-1223108-193753.

Council of Science Editors:

Tang H. Study on the Floating Platform for Cage Aquaculture. [Doctoral Dissertation]. NSYSU; 2008. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-1223108-193753

University of Oulu

10. Kemppainen, J. (Jukka). Behaviour of the boundary potentials and boundary integral solution of the time fractional diffusion equation.

Degree: 2010, University of Oulu

URL: http://urn.fi/urn:isbn:9789514261329

► Abstract The dissertation considers the time fractional diffusion equation (TFDE) with the Dirichlet boundary condition in the sub-diffusion case, i.e. the order of the time… (more)

Subjects/Keywords: boundary integral equation; double layer potential; single layer potential; spline collocation; time fractional diffusion

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APA (6^th Edition):

Kemppainen, J. (. (2010). Behaviour of the boundary potentials and boundary integral solution of the time fractional diffusion equation. (Doctoral Dissertation). University of Oulu. Retrieved from http://urn.fi/urn:isbn:9789514261329

Chicago Manual of Style (16^th Edition):

Kemppainen, J (Jukka). “Behaviour of the boundary potentials and boundary integral solution of the time fractional diffusion equation.” 2010. Doctoral Dissertation, University of Oulu. Accessed April 11, 2021. http://urn.fi/urn:isbn:9789514261329.

MLA Handbook (7^th Edition):

Kemppainen, J (Jukka). “Behaviour of the boundary potentials and boundary integral solution of the time fractional diffusion equation.” 2010. Web. 11 Apr 2021.

Vancouver:

Kemppainen J(. Behaviour of the boundary potentials and boundary integral solution of the time fractional diffusion equation. [Internet] [Doctoral dissertation]. University of Oulu; 2010. [cited 2021 Apr 11]. Available from: http://urn.fi/urn:isbn:9789514261329.

Council of Science Editors:

Kemppainen J(. Behaviour of the boundary potentials and boundary integral solution of the time fractional diffusion equation. [Doctoral Dissertation]. University of Oulu; 2010. Available from: http://urn.fi/urn:isbn:9789514261329

University of Michigan

11. Wu, Bowei. Spectrally-Accurate Close Evaluation Schemes for Stokes Boundary Integral Operators.

Degree: PhD, Applied and Interdisciplinary Mathematics, 2019, University of Michigan

URL: http://hdl.handle.net/2027.42/153404

► Dense particulate flow simulations using integral equation methods demand accurate evaluation of Stokes layer potentials on arbitrarily close interfaces. In this thesis, two spectrally-accurate integration… (more)

Subjects/Keywords: particulate flow, Stokes equations, boundary integral equation, numerical integration, spectrally accurate, electrohydrodynamics; Mathematics; Science

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APA (6^th Edition):

Wu, B. (2019). Spectrally-Accurate Close Evaluation Schemes for Stokes Boundary Integral Operators. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/153404

Chicago Manual of Style (16^th Edition):

Wu, Bowei. “Spectrally-Accurate Close Evaluation Schemes for Stokes Boundary Integral Operators.” 2019. Doctoral Dissertation, University of Michigan. Accessed April 11, 2021. http://hdl.handle.net/2027.42/153404.

MLA Handbook (7^th Edition):

Wu, Bowei. “Spectrally-Accurate Close Evaluation Schemes for Stokes Boundary Integral Operators.” 2019. Web. 11 Apr 2021.

Vancouver:

Wu B. Spectrally-Accurate Close Evaluation Schemes for Stokes Boundary Integral Operators. [Internet] [Doctoral dissertation]. University of Michigan; 2019. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/2027.42/153404.

Council of Science Editors:

Wu B. Spectrally-Accurate Close Evaluation Schemes for Stokes Boundary Integral Operators. [Doctoral Dissertation]. University of Michigan; 2019. Available from: http://hdl.handle.net/2027.42/153404

Stellenbosch University

12. Strydom, Willem Jacobus. Recovery based error estimation for the Method of Moments.

Degree: MEng, Electrical and Electronic Engineering, 2015, Stellenbosch University

URL: http://hdl.handle.net/10019.1/96881

►

ENGLISH ABSTRACT: The Method of Moments (MoM) is routinely used for the numerical solution of electromagnetic surface integral equations. Solution errors are inherent to any… (more)

▼

ENGLISH ABSTRACT: The Method of Moments (MoM) is routinely used for the numerical solution of electromagnetic surface integral equations. Solution errors are inherent to any numerical computational method, and error estimators can be effectively employed to reduce and control these errors. In this thesis, gradient recovery techniques of the Finite Element Method (FEM) are formulated within the MoM context, in order to recover a higher-order charge of a Rao-Wilton-Glisson (RWG) MoM solution. Furthermore, a new recovery procedure, based specifically on the properties of the RWG basis functions, is introduced by the author. These recovered charge distributions are used for a posteriori error estimation of the charge. It was found that the newly proposed charge recovery method has the highest accuracy of the considered recovery methods, and is the most suited for applications within recovery based error estimation. In addition to charge recovery, the possibility of recovery procedures for the MoM solution current are also investigated. A technique is explored whereby a recovered charge is used to find a higher-order divergent current representation. Two newly developed methods for the subsequent recovery of the solenoidal current component, as contained in the RWG solution current, are also introduced by the author. A posteriori error estimation of the MoM current is accomplished through the use of the recovered current distributions. A mixed second-order recovered current, based on a vector recovery procedure, was found to produce the most accurate results. The error estimation techniques developed in this thesis could be incorporated into an adaptive solver scheme to optimise the solution accuracy relative to the computational cost.

AFRIKAANSE OPSOMMING: Die Moment Metode (MoM) vind algemene toepassing in die numeriese oplossing van elektromagnetiese oppervlak integraalvergelykings. Numeriese foute is inherent tot die prosedure: foutberamingstegnieke is dus nodig om die betrokke foute te analiseer en te reduseer. Gradiënt verhalingstegnieke van die Eindige Element Metode word in hierdie tesis in die MoM konteks geformuleer. Hierdie tegnieke word ingespan om die oppervlaklading van 'n Rao-Wilton-Glisson (RWG) MoM oplossing na 'n verbeterde hoër-orde voorstelling te neem. Verder is 'n nuwe lading verhalingstegniek deur die outeur voorgestel wat spesifiek op die eienskappe van die RWG basis funksies gebaseer is. Die verhaalde ladingsverspreidings is geïmplementeer in a posteriori fout beraming van die lading. Die nuut voorgestelde tegniek het die akkuraatste resultate gelewer, uit die groep verhalingstegnieke wat ondersoek is. Addisioneel tot ladingsverhaling, is die moontlikheid van MoM-stroom verhalingstegnieke ook ondersoek. 'n Metode vir die verhaling van 'n hoër-orde divergente stroom komponent, gebaseer op die verhaalde lading, is geïmplementeer. Verder is twee nuwe metodes vir die verhaling van die solenodiale komponent van die RWG stroom deur die outeur voorgestel. A…

Advisors/Committee Members: Botha, Matthys M., Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering..

Subjects/Keywords: Computational electromagnetics; Error estimator; Gradient recovery; Electromagnetic surface integral equation; Boundary element method; UCTD

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Strydom, W. J. (2015). Recovery based error estimation for the Method of Moments. (Thesis). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/96881

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Strydom, Willem Jacobus. “Recovery based error estimation for the Method of Moments.” 2015. Thesis, Stellenbosch University. Accessed April 11, 2021. http://hdl.handle.net/10019.1/96881.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Strydom, Willem Jacobus. “Recovery based error estimation for the Method of Moments.” 2015. Web. 11 Apr 2021.

Vancouver:

Strydom WJ. Recovery based error estimation for the Method of Moments. [Internet] [Thesis]. Stellenbosch University; 2015. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/10019.1/96881.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Strydom WJ. Recovery based error estimation for the Method of Moments. [Thesis]. Stellenbosch University; 2015. Available from: http://hdl.handle.net/10019.1/96881

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Brunel University

13. Mohamed, Nurul Akmal. Numerical solution and spectrum of boundary-domain integral equations.

Degree: PhD, 2013, Brunel University

URL: http://bura.brunel.ac.uk/handle/2438/7592 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.575680

► A numerical implementation of the direct Boundary-Domain Integral Equation (BDIE)/ Boundary-Domain Integro-Differential Equations (BDIDEs) and Localized Boundary-Domain Integral Equation (LBDIE)/Localized Boundary-Domain Integro-Differential Equations (LBDIDEs) related… (more)

Subjects/Keywords: 515; Localised boundary-domain integral equation; Spectrum; Neumann series; Bilinear interpolation; Semi-analytic method

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mohamed, N. A. (2013). Numerical solution and spectrum of boundary-domain integral equations. (Doctoral Dissertation). Brunel University. Retrieved from http://bura.brunel.ac.uk/handle/2438/7592 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.575680

Chicago Manual of Style (16^th Edition):

Mohamed, Nurul Akmal. “Numerical solution and spectrum of boundary-domain integral equations.” 2013. Doctoral Dissertation, Brunel University. Accessed April 11, 2021. http://bura.brunel.ac.uk/handle/2438/7592 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.575680.

MLA Handbook (7^th Edition):

Mohamed, Nurul Akmal. “Numerical solution and spectrum of boundary-domain integral equations.” 2013. Web. 11 Apr 2021.

Vancouver:

Mohamed NA. Numerical solution and spectrum of boundary-domain integral equations. [Internet] [Doctoral dissertation]. Brunel University; 2013. [cited 2021 Apr 11]. Available from: http://bura.brunel.ac.uk/handle/2438/7592 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.575680.

Council of Science Editors:

Mohamed NA. Numerical solution and spectrum of boundary-domain integral equations. [Doctoral Dissertation]. Brunel University; 2013. Available from: http://bura.brunel.ac.uk/handle/2438/7592 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.575680

14. Mohamed, Nurul Akmal. Numerical solution and spectrum of boundary-domain integral equations.

Degree: 2013, Brunel University London

URL: http://bura.brunel.ac.uk/handle/2438/7592

► A numerical implementation of the direct Boundary-Domain Integral Equation (BDIE)/ Boundary-Domain Integro-Differential Equations (BDIDEs) and Localized Boundary-Domain Integral Equation (LBDIE)/Localized Boundary-Domain Integro-Differential Equations (LBDIDEs) related… (more)

Subjects/Keywords: Localised boundary-domain integral equation; Spectrum; Neumann series; Bilinear interpolation; Semi-analytic method

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mohamed, N. A. (2013). Numerical solution and spectrum of boundary-domain integral equations. (Thesis). Brunel University London. Retrieved from http://bura.brunel.ac.uk/handle/2438/7592

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Mohamed, Nurul Akmal. “Numerical solution and spectrum of boundary-domain integral equations.” 2013. Thesis, Brunel University London. Accessed April 11, 2021. http://bura.brunel.ac.uk/handle/2438/7592.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Mohamed, Nurul Akmal. “Numerical solution and spectrum of boundary-domain integral equations.” 2013. Web. 11 Apr 2021.

Vancouver:

Mohamed NA. Numerical solution and spectrum of boundary-domain integral equations. [Internet] [Thesis]. Brunel University London; 2013. [cited 2021 Apr 11]. Available from: http://bura.brunel.ac.uk/handle/2438/7592.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mohamed NA. Numerical solution and spectrum of boundary-domain integral equations. [Thesis]. Brunel University London; 2013. Available from: http://bura.brunel.ac.uk/handle/2438/7592

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

15. Bez, Luiz Fernando. An integral equation formulation for 2D steady-state advection-diffusion-reaction problems with variable coefficients.

Degree: 2020, Brazil

URL: http://hdl.handle.net/10183/218654

►

Este trabalho apresenta uma formulação de equação integral de contorno e domínio para problemas de advecção-difusão-reação com coeficientes variáveis e termo fonte. A formulação usa… (more)

▼

Este trabalho apresenta uma formulação de equação integral de contorno e domínio para problemas de advecção-difusão-reação com coeficientes variáveis e termo fonte. A formulação usa uma versão da solução fundamental que evita overflow numérico dos termos exponenciais e underflow dos termos em função de Bessel, para qualquer número de Péclet e qualquer tamanho de domínio. Os coeficientes usados na solução fundamental são os coeficientes locais da equação diferencial, afim de minimizar a contribuição do domínio no problema. A formulação é aplicada sem modificações para problemas puramente difusivos ou de difusão-reação. A equação integral é discretizada usando o método dos elementos de contorno, com elementos de contorno contínuos e células de domínio descontínuas. O método é validado com cinco problemas de benchmark que possuem soluções analíticas, apresentando um erro NRMSD abaixo de 1% para malhas com 1348 graus de liberdade, em todos os casos. A metodologia é usada para o estudo de dois problemas práticos. O primeiro é o problema de Graetz-Nusselt adimensional para Pe = f0; 1; 5; 10g. O segundo é um problema de pluma de dispersão de poluentes para uma fonte pontual em escoamentos de camada limite atmosférica neutramente estratificada.

This work presents a boundary-domain integral equation formulation for advection-diffusionreaction problems with variable coefficients and source term. The formulation uses a version of the fundamental solution that avoids numerical overflow of the exponential term and underflow of the Bessel term, for any Péclet number and domain size. Furthermore, the coefficients used in the fundamental solution are the local coefficients of the differential equation, in order to minimize the domain contribution for the problem. The formulation is applied as-is for purely diffusive or diffusion-reaction problems. The integral equation is discretized using the boundary element method with continuous boundary elements and discontinuous domain cells. The scheme is validated against five benchmark problems with analytical solutions, presenting a NRMSD error under 1% for meshes with 1348 degrees of freedom, in all cases. The methodology is used to study two practical problems. The first is the dimensionless Graetz-Nusselt problem for Pe = f0; 1; 5; 10g. The second is the pollutant dispersion plume for a point source in neutrally stratified atmospheric boundary layer flows.

Advisors/Committee Members: Vilhena, Marco Tullio Menna Barreto de, Marczak, Rogerio Jose.

Subjects/Keywords: Elementos de contorno; Equações integrais; Integral equation; Boundary element method; Scalar transport; Point source

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bez, L. F. (2020). An integral equation formulation for 2D steady-state advection-diffusion-reaction problems with variable coefficients. (Masters Thesis). Brazil. Retrieved from http://hdl.handle.net/10183/218654

Chicago Manual of Style (16^th Edition):

Bez, Luiz Fernando. “An integral equation formulation for 2D steady-state advection-diffusion-reaction problems with variable coefficients.” 2020. Masters Thesis, Brazil. Accessed April 11, 2021. http://hdl.handle.net/10183/218654.

MLA Handbook (7^th Edition):

Bez, Luiz Fernando. “An integral equation formulation for 2D steady-state advection-diffusion-reaction problems with variable coefficients.” 2020. Web. 11 Apr 2021.

Vancouver:

Bez LF. An integral equation formulation for 2D steady-state advection-diffusion-reaction problems with variable coefficients. [Internet] [Masters thesis]. Brazil; 2020. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/10183/218654.

Council of Science Editors:

Bez LF. An integral equation formulation for 2D steady-state advection-diffusion-reaction problems with variable coefficients. [Masters Thesis]. Brazil; 2020. Available from: http://hdl.handle.net/10183/218654

16. Santos, Claudia Gomes de Oliveira. Formulação hipersingular do método dos elementos de contorno para a solução de problemas bidimensionais de elastostática.

Degree: 2013, Universidade Federal de Goiás; Programa de Pós-graduação em Geotecnia, Estruturas e Construção Civil (EEC); UFG; Brasil; Escola de Engenharia Civil – EEC (RG)

URL: http://repositorio.bc.ufg.br/tede/handle/tede/3159

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES

The Boundary Element Method (BEM) has been successfully employed in the analysis of various engineering problems. The BEM consists in a mathematical modeling, for a numerical solution of a system of integral equations, and in their cores may appear singularities. This paper presents the Classical and Hypersingular formulation of the Boundary Element Method for dimensional elastostatic problems with smooth boundary geometry. The improper integrals arising from the singularities of the core in the hypersingular formulation are treated by Hadamard finite parts. In the discretization process two types of interpolation are used, one traditional and the other special. Traditional interpolation is used in all bondary elements that have no point , special interpolation ensures the continuity of the tangential derivative of displacements on the element that contains the point . To accomplish this, a theoretical mathematics study of related topics was performed. The hypersingular formulation developed in this work was implemented through the Intel Visual Fortran compiler. Some problems were analyzed and the obtained results were compared with those of analytical solution or through the Finite Element Method. The results achieved were satisfactory validating the proposed formulation

O Método dos Elementos de Contorno (MEC) vem sendo empregado com sucesso na análise de diversos problemas de engenharia. O MEC consisti em uma modelagem matemática, para resolução numérica de um sistema de equações integrais, e que em seus núcleos podem aparecer singularidades. Nesse trabalho apresenta a formulação Clássica e Hipersingular do Método dos Elementos de Contorno para problemas de elastostática bidimensional com geometria de contornos não suaves. As integrais impróprias que surgem da singularidade do núcleo na formulação hipersingular são tratados por partes finitas de Hadamard. No processo de discretização utiliza-se de dois tipos de interpolação, uma tradicional e outra especial. A interpolação tradicional é utilizada em todos os elementos de…

Advisors/Committee Members: Prado, Ademir Aparecido, Prado, Ademir Aparecido, Almeida, Sylvia Regina Mesquita de, Ferreira, Walnório Graça.

Subjects/Keywords: Métodos dos Elementos de Contorno; Elastostática; Formulação Hipersingular; Equação Integral; Boundary Element Methods; Elastostatic; Hypersingular Formulation; Integral Equation; ENGENHARIA CIVIL::ESTRUTURAS

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APA (6^th Edition):

Santos, C. G. d. O. (2013). Formulação hipersingular do método dos elementos de contorno para a solução de problemas bidimensionais de elastostática. (Masters Thesis). Universidade Federal de Goiás; Programa de Pós-graduação em Geotecnia, Estruturas e Construção Civil (EEC); UFG; Brasil; Escola de Engenharia Civil – EEC (RG). Retrieved from http://repositorio.bc.ufg.br/tede/handle/tede/3159

Chicago Manual of Style (16^th Edition):

Santos, Claudia Gomes de Oliveira. “Formulação hipersingular do método dos elementos de contorno para a solução de problemas bidimensionais de elastostática.” 2013. Masters Thesis, Universidade Federal de Goiás; Programa de Pós-graduação em Geotecnia, Estruturas e Construção Civil (EEC); UFG; Brasil; Escola de Engenharia Civil – EEC (RG). Accessed April 11, 2021. http://repositorio.bc.ufg.br/tede/handle/tede/3159.

MLA Handbook (7^th Edition):

Santos, Claudia Gomes de Oliveira. “Formulação hipersingular do método dos elementos de contorno para a solução de problemas bidimensionais de elastostática.” 2013. Web. 11 Apr 2021.

Vancouver:

Santos CGdO. Formulação hipersingular do método dos elementos de contorno para a solução de problemas bidimensionais de elastostática. [Internet] [Masters thesis]. Universidade Federal de Goiás; Programa de Pós-graduação em Geotecnia, Estruturas e Construção Civil (EEC); UFG; Brasil; Escola de Engenharia Civil – EEC (RG); 2013. [cited 2021 Apr 11]. Available from: http://repositorio.bc.ufg.br/tede/handle/tede/3159.

Council of Science Editors:

Santos CGdO. Formulação hipersingular do método dos elementos de contorno para a solução de problemas bidimensionais de elastostática. [Masters Thesis]. Universidade Federal de Goiás; Programa de Pós-graduação em Geotecnia, Estruturas e Construção Civil (EEC); UFG; Brasil; Escola de Engenharia Civil – EEC (RG); 2013. Available from: http://repositorio.bc.ufg.br/tede/handle/tede/3159

Iowa State University

17. Gurrala, Praveen. Full-wave modeling of ultrasonic scattering for non-destructive evaluation.

Degree: 2020, Iowa State University

URL: https://lib.dr.iastate.edu/etd/18133

► The physical modeling and simulation of nondestructive evaluation (NDE) measurements has a major role in the advancement of NDE and structural health monitoring (SHM). In… (more)

▼ The physical modeling and simulation of nondestructive evaluation (NDE) measurements has a major role in the advancement of NDE and structural health monitoring (SHM). In ultrasonic NDE (UNDE) simulations, evaluating the scattering of ultrasound by defects is a computationally-intensive process. Many UNDE system models treat the scattering process using exact analytical methods or high-frequency approximations such as the Kirchhoff approximation (KA) to make the simulation effort tractable. These methods naturally have a limited scope. This thesis aims to supplement the existing scattering models with fast and memory-efficient full-wave models that are based on the boundary element method (BEM). For computational efficiency, such full-wave models should be applied only to those problems wherein the existing approximation methods are not suitable. Therefore, the adequacy of different scattering models for representing various test scenarios has to be studied. Although analyzing scattering models by themselves is helpful, their true adequacy is revealed only when they are combined with models of other elements of the NDE system, and the resulting predictions are evaluated against measurements. Very few comprehensive studies of this nature exist, particularly for full-wave scattering models. To fill this gap, two different scattering models – the KA and a boundary-element method – are integrated into a UNDE system model in this work, and their predictions for standard measurement outputs are compared with experimental data for various benchmark problems. This quantitative comparison serves as a guideline for selecting between the KA and full-wave scattering models for performing UNDE simulations. In accordance with theoretical expectations, the KA is shown to be inappropriate for modeling penetrable (inclusion-type) defects and non-specular scattering, such as diffraction from thin cracks above certain angles of incidence. A key challenge to the use of full-wave scattering methods in UNDE system models is the high computational cost incurred during simulations. Whereas the development of fast finite element methods (FEM) has inspired various applications of the FEM for ultrasound modeling in 3D heterogeneous and anisotropic media, very few applications of the BEM exist despite the progress in accelerated BEMs for elastodynamics. The BEM is highly efficient for modeling scattering from arbitrary shaped 3D defects in homogeneous isotropic media due to a reduction in the dimensionality of the scattering problem, and this potential has not been exploited for UNDE. Therefore, building on recent developments, this work proposes a fast and memory-efficient implementation of the BEM for elastic-wave scattering in UNDE applications. This method features three crucial elements that provide robustness and fast convergence. They include the use of (1) high-order discretization methods for fast convergence, (2) the combined-field integral equation (CFIE) formulation for overcoming the fictitious eigenfrequency problem, and (3) the…

Subjects/Keywords: Boundary Element Method; Elastodynamic Scattering; Fast Multipole Method; High-order BEM; Hypersingular Boundary Integral Equation; Ultrasonic Nondestructive Evaluation

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APA (6^th Edition):

Gurrala, P. (2020). Full-wave modeling of ultrasonic scattering for non-destructive evaluation. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/18133

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Gurrala, Praveen. “Full-wave modeling of ultrasonic scattering for non-destructive evaluation.” 2020. Thesis, Iowa State University. Accessed April 11, 2021. https://lib.dr.iastate.edu/etd/18133.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Gurrala, Praveen. “Full-wave modeling of ultrasonic scattering for non-destructive evaluation.” 2020. Web. 11 Apr 2021.

Vancouver:

Gurrala P. Full-wave modeling of ultrasonic scattering for non-destructive evaluation. [Internet] [Thesis]. Iowa State University; 2020. [cited 2021 Apr 11]. Available from: https://lib.dr.iastate.edu/etd/18133.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gurrala P. Full-wave modeling of ultrasonic scattering for non-destructive evaluation. [Thesis]. Iowa State University; 2020. Available from: https://lib.dr.iastate.edu/etd/18133

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Colorado

18. Davis, Christopher-Ian Raphael. Numerical Tests of the Fokas Method for Helmholtz-type Partial Differential Equations: Dirichlet to Neumann Maps.

Degree: MS, Applied Mathematics, 2011, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/17

► A method for solving boundary value problems for linear partial differential equations in convex polygons developed by A.S. Fokas in the late 1990s is… (more)

Subjects/Keywords: Boundary integral method; Dirichlet-Neumann map; Fokas transform method; Helmholtz equation; modified Helmholtz equation; polygonal domain; Applied Mathematics

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APA (6^th Edition):

Davis, C. R. (2011). Numerical Tests of the Fokas Method for Helmholtz-type Partial Differential Equations: Dirichlet to Neumann Maps. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/17

Chicago Manual of Style (16^th Edition):

Davis, Christopher-Ian Raphael. “Numerical Tests of the Fokas Method for Helmholtz-type Partial Differential Equations: Dirichlet to Neumann Maps.” 2011. Masters Thesis, University of Colorado. Accessed April 11, 2021. https://scholar.colorado.edu/appm_gradetds/17.

MLA Handbook (7^th Edition):

Davis, Christopher-Ian Raphael. “Numerical Tests of the Fokas Method for Helmholtz-type Partial Differential Equations: Dirichlet to Neumann Maps.” 2011. Web. 11 Apr 2021.

Vancouver:

Davis CR. Numerical Tests of the Fokas Method for Helmholtz-type Partial Differential Equations: Dirichlet to Neumann Maps. [Internet] [Masters thesis]. University of Colorado; 2011. [cited 2021 Apr 11]. Available from: https://scholar.colorado.edu/appm_gradetds/17.

Council of Science Editors:

Davis CR. Numerical Tests of the Fokas Method for Helmholtz-type Partial Differential Equations: Dirichlet to Neumann Maps. [Masters Thesis]. University of Colorado; 2011. Available from: https://scholar.colorado.edu/appm_gradetds/17

19. Steif, Bassam. Formulation courants et charges pour la résolution par équations intégrales des équations de l'électromagnétisme : Currents and charges formulation for the numerical solution by integrals equations of equation of electromagnetism.

Degree: Docteur es, Mathématiques Appliquées, 2012, Toulouse, INSA

URL: http://www.theses.fr/2012ISAT0028

►

Cette thèse a consisté à élaborer une méthode qui permet de résoudre l’équation intégrale comportant comme inconnues les courants et les charges introduite récemment par… (more)

▼

Cette thèse a consisté à élaborer une méthode qui permet de résoudre l’équation intégrale comportant comme inconnues les courants et les charges introduite récemment par Taskinen et Ylä-Oijala par une méthode d’éléments frontière sans aucune contrainte de continuité au niveau des interfaces des éléments aussi bien pour les courants que pour les charges. Nous avons d’abord montré comment on pouvait construire cette équation de façon simple et similaire à celle des formulations intégrales usuelles en imposant au problème intérieur relatif au système de Picard, qui est en fait une extension du système de Maxwell, des conditions aux limites adéquates. Pour des géométries régulières de l’objet diffractant, nous avons établi de façon théorique la stabilité et la convergence des schémas numériques ci-dessus en montrant que cette équation peut être décomposée sous la forme d’un système elliptique coercif et d’un opérateur compact dans le cadre des fonctions de carré intégrable.Toute cette étude a été confirmée par des tests numériques tridimensionnels. Comme pour les équations intégrales usuelles de seconde espèce, le cadre théorique valable pour des surfaces régulières ne l’est plus pour des surfaces avec des singularités. L’utilisation formelle de cette équation,pour des surfaces singulières, a donné des résultats entachés d’erreur. Nous avons mis en évidence l’origine des instabilités numériques à l’origine de ces erreurs lorsque les géométries sont singulières en développant une version bidimensionnelle de cette équation. Cette version nous a permis en particulier de montrer que les instabilités étaient dues à des oscillations parasites concentrées autour des singularités de la géométrie. Dans ce cadre nous avons pu mettre en oeuvre plus aisément des approches pour supprimer ou atténuer ces oscillations parasites ou leur effet sur les calculs en champ lointain. Nous avons montré qu’un procédé d’augmentation des degrés de liberté pour la charge par rapport au courant pouvait sensiblement réduire ces instabilités. A la suite de l’amélioration observée sur les résultats dans le cas 2D, nous avons transposé cette procédure au cas tridimensionnel. A travers divers tests, nous avons constaté l’amélioration de la qualité de l’approximation amenée par la procédure de stabilisation

The objective of this thesis was to develop a method that solves the integral equation whose unknowns are the currents and the charges, recently introduced by Taskinen and Ylä-Oijala, by a boundary element method without any continuity constraint at the interfaces of the elements,for both the unknowns. We first show how to construct this equation in a simple way, similar tothe usual integral formulations, through imposing to the internal problem related to the Picard system,which is an extension of the Maxwell system, appropriate boundary conditions. For regular geometries, we have established a theoretical background ensuring the stability and the convergence of numerical scheme, by proving that this equation can be decomposed in a coercive…

Advisors/Committee Members: Bendali, Abderrahmane (thesis director).

Subjects/Keywords: Méthode des éléments de frontière; Equations intégrales de frontière; Equations intégrales courants et charges; Diffraction d’ondes électromagnétiques; Boundary element method; Current and charge equation; Electromagnetic scattering; Boundary integral equation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Steif, B. (2012). Formulation courants et charges pour la résolution par équations intégrales des équations de l'électromagnétisme : Currents and charges formulation for the numerical solution by integrals equations of equation of electromagnetism. (Doctoral Dissertation). Toulouse, INSA. Retrieved from http://www.theses.fr/2012ISAT0028

Chicago Manual of Style (16^th Edition):

Steif, Bassam. “Formulation courants et charges pour la résolution par équations intégrales des équations de l'électromagnétisme : Currents and charges formulation for the numerical solution by integrals equations of equation of electromagnetism.” 2012. Doctoral Dissertation, Toulouse, INSA. Accessed April 11, 2021. http://www.theses.fr/2012ISAT0028.

MLA Handbook (7^th Edition):

Steif, Bassam. “Formulation courants et charges pour la résolution par équations intégrales des équations de l'électromagnétisme : Currents and charges formulation for the numerical solution by integrals equations of equation of electromagnetism.” 2012. Web. 11 Apr 2021.

Vancouver:

Steif B. Formulation courants et charges pour la résolution par équations intégrales des équations de l'électromagnétisme : Currents and charges formulation for the numerical solution by integrals equations of equation of electromagnetism. [Internet] [Doctoral dissertation]. Toulouse, INSA; 2012. [cited 2021 Apr 11]. Available from: http://www.theses.fr/2012ISAT0028.

Council of Science Editors:

Steif B. Formulation courants et charges pour la résolution par équations intégrales des équations de l'électromagnétisme : Currents and charges formulation for the numerical solution by integrals equations of equation of electromagnetism. [Doctoral Dissertation]. Toulouse, INSA; 2012. Available from: http://www.theses.fr/2012ISAT0028

Cornell University

20. CHANG, CHE-WEI. WAVE ATTENUATION BY COASTAL FORESTS.

Degree: PhD, Civil and Environmental Engineering, 2017, Cornell University

URL: http://hdl.handle.net/1813/56881

► Extreme weather events and rising sea level have largely raised attention to shore protection. As a natural means against ocean waves, coastal vegetation on dissipating… (more)

▼ Extreme weather events and rising sea level have largely raised attention to shore protection. As a natural means against ocean waves, coastal vegetation on dissipating incoming wave energy has been extensively studied via mathematical/numerical modeling and laboratory/field observations. The hydrodynamics and sediment transport within vegetated areas have also received an increasing interest. However, the vegetation effects on damping waves have not been fully understood and are awaiting further investigation. In addition, the model forests in most of the existing literature are impractical and still far from real situations. Most importantly, a reliable approach to predict wave attenuation by coastal vegetation is still demanded. In this dissertation, accordingly, the theoretical development in Mei et al. (2011, 2014) is extended to study water waves propagating through a heterogeneous coastal forest of arbitrary shape. Arrays of rigid and surface-piercing cylinders are used to model the trees. Assuming that the incident wavelength is much longer than the characteristic cylinder spacing (and cylinder diameter), the multi-scale perturbation theory of homogenization (Mei and Vernescu 2010) is applied to separate the micro-scale flow problem within a unit cell from the macro-scale wave dynamics throughout the entire vegetated area. Driven by the macro-scale (wavelength-scale) pressure gradients, the flow motion within a unit cell, which can have one or a few cylinders inside, is obtained by solving the micro-scale boundary-value-problem. The cell-averaged equations governing the macro-scale wave dynamics are derived with consideration of the cell effects, which would be parameterized into the complex coefficients. Employing the boundary integral equation method, the macro-scale wave dynamics is solved numerically in which a coastal forest can be composed of multiple patches of arbitrary shape. Each patch can be further divided into several subzones based on different properties, e.g. vegetation sizes, planting arrangements and porosity. Each subzone is then considered as a homogeneous region where a constant bulk value of eddy viscosity can be yielded. The integral formulations for a forest subzone and the open water region are both provided. The matching conditions along the boundaries are also presented. Two types of small-amplitude waves are first considered. To model wind waves, the theoretical model for periodic waves of relatively short wavelength in Mei et al. (2014) is extended from two-dimensional to three-dimensional applications. The constant bulk value of eddy viscosity for each homogenous forest subzone is determined by invoking the balance of time-averaged energy dissipation rate and the averaged rate of work done by wave forces on cylinders within the specific subzone. Morison-type formula (Morison et al. 1950) is used to model the wave forces, in which the drag coefficient formula is constructed based on the experimental data in Hu et al. (2014). A computing program is established based on the present… Advisors/Committee Members: Liu, Philip Li-Fan (chair), Diamessis, Peter J. (committee member), Jenkins, James Thomas (committee member).

Subjects/Keywords: Boundary Integral Equation Method; Coastal Forest; Eddy Viscosity; Harmonics Generation; Homogenization Theory; Wave Attenuation; Civil engineering; Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

CHANG, C. (2017). WAVE ATTENUATION BY COASTAL FORESTS. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/56881

Chicago Manual of Style (16^th Edition):

CHANG, CHE-WEI. “WAVE ATTENUATION BY COASTAL FORESTS.” 2017. Doctoral Dissertation, Cornell University. Accessed April 11, 2021. http://hdl.handle.net/1813/56881.

MLA Handbook (7^th Edition):

CHANG, CHE-WEI. “WAVE ATTENUATION BY COASTAL FORESTS.” 2017. Web. 11 Apr 2021.

Vancouver:

CHANG C. WAVE ATTENUATION BY COASTAL FORESTS. [Internet] [Doctoral dissertation]. Cornell University; 2017. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/1813/56881.

Council of Science Editors:

CHANG C. WAVE ATTENUATION BY COASTAL FORESTS. [Doctoral Dissertation]. Cornell University; 2017. Available from: http://hdl.handle.net/1813/56881

McMaster University

21. Peng, Xiaohui. OPTIMAL GEOMETRY IN A SIMPLE MODEL OF TWO-DIMENSIONAL HEAT TRANSFER.

Degree: MSc, 2011, McMaster University

URL: http://hdl.handle.net/11375/10153

►

This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems used in hybrid/electric vehicles. We consider a… (more)

Subjects/Keywords: Shape Differentiation; Cost Functional; Adjoint System; Spectral Method; Boundary Integral Equation; Shape Gradient; Numerical Analysis and Computation; Numerical Analysis and Computation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Peng, X. (2011). OPTIMAL GEOMETRY IN A SIMPLE MODEL OF TWO-DIMENSIONAL HEAT TRANSFER. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/10153

Chicago Manual of Style (16^th Edition):

Peng, Xiaohui. “OPTIMAL GEOMETRY IN A SIMPLE MODEL OF TWO-DIMENSIONAL HEAT TRANSFER.” 2011. Masters Thesis, McMaster University. Accessed April 11, 2021. http://hdl.handle.net/11375/10153.

MLA Handbook (7^th Edition):

Peng, Xiaohui. “OPTIMAL GEOMETRY IN A SIMPLE MODEL OF TWO-DIMENSIONAL HEAT TRANSFER.” 2011. Web. 11 Apr 2021.

Vancouver:

Peng X. OPTIMAL GEOMETRY IN A SIMPLE MODEL OF TWO-DIMENSIONAL HEAT TRANSFER. [Internet] [Masters thesis]. McMaster University; 2011. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/11375/10153.

Council of Science Editors:

Peng X. OPTIMAL GEOMETRY IN A SIMPLE MODEL OF TWO-DIMENSIONAL HEAT TRANSFER. [Masters Thesis]. McMaster University; 2011. Available from: http://hdl.handle.net/11375/10153

University of Wollongong

22. Le, Tan Nhat. Pricing American-style Parisian options.

Degree: PhD, 2016, University of Wollongong

URL: 010205 Financial Mathematics, 0102 APPLIED MATHEMATICS, 0103 NUMERICAL AND COMPUTATIONAL MATHEMATICS ; https://ro.uow.edu.au/theses/4654

► Barrier options are the most common path-dependent options traded in financial markets. They are particularly attractive to investors, because not only are they cheaper… (more)

Subjects/Keywords: Integral equation approach; Parisian options; Barrier options; Fourier Sine transform; optimal exercise boundary; Black-Scholes model.

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APA (6^th Edition):

Le, T. N. (2016). Pricing American-style Parisian options. (Doctoral Dissertation). University of Wollongong. Retrieved from 010205 Financial Mathematics, 0102 APPLIED MATHEMATICS, 0103 NUMERICAL AND COMPUTATIONAL MATHEMATICS ; https://ro.uow.edu.au/theses/4654

Chicago Manual of Style (16^th Edition):

Le, Tan Nhat. “Pricing American-style Parisian options.” 2016. Doctoral Dissertation, University of Wollongong. Accessed April 11, 2021. 010205 Financial Mathematics, 0102 APPLIED MATHEMATICS, 0103 NUMERICAL AND COMPUTATIONAL MATHEMATICS ; https://ro.uow.edu.au/theses/4654.

MLA Handbook (7^th Edition):

Le, Tan Nhat. “Pricing American-style Parisian options.” 2016. Web. 11 Apr 2021.

Vancouver:

Le TN. Pricing American-style Parisian options. [Internet] [Doctoral dissertation]. University of Wollongong; 2016. [cited 2021 Apr 11]. Available from: 010205 Financial Mathematics, 0102 APPLIED MATHEMATICS, 0103 NUMERICAL AND COMPUTATIONAL MATHEMATICS ; https://ro.uow.edu.au/theses/4654.

Council of Science Editors:

Le TN. Pricing American-style Parisian options. [Doctoral Dissertation]. University of Wollongong; 2016. Available from: 010205 Financial Mathematics, 0102 APPLIED MATHEMATICS, 0103 NUMERICAL AND COMPUTATIONAL MATHEMATICS ; https://ro.uow.edu.au/theses/4654

23. Pesudo, Laure. Une méthode hybride couplant la méthode des équations intégrales et la méthode des rayons en vue d'applications au contrôle non destructif ultrasonore. : A hybrid strategy combining the integral equation method and the ray tracing method for high frequency diffraction involved in ultrasonic non destructive testing.

Degree: Docteur es, Mathématiques appliquées, 2017, Université Paris-Saclay (ComUE)

URL: http://www.theses.fr/2017SACLY009

►

Le Contrôle Non Destructif (CND) permet de sonder l’intérieur d’un milieu dans le but desurveiller son intégrité et son vieillissement. Assisté d’outils de simulation il… (more)

▼

Le Contrôle Non Destructif (CND) permet de sonder l’intérieur d’un milieu dans le but desurveiller son intégrité et son vieillissement. Assisté d’outils de simulation il permet de détecter, caractériseret localiser des défauts de structure du milieu inspecté mais sa fiabilité dépend de la précision des méthodesde simulation. Dans le cadre du CND ultrasonore, les méthodes usuelles (numériques et asymptotiques) sontbien souvent inadéquates pour simuler la diffraction par les défauts. On leur préfère des techniques hybrides.On propose dans cette thèse une nouvelle approche hybride pour la simulation numérique de la diffractionhaute fréquence en milieu étendu (configuration critique pour le CND). Combinant la méthode des équationsintégrales et la méthode des rayons, cette approche exploite le caractère multi-échelle du problème hautefréquence en proposant un modèle d’obstacle à deux échelles. Elle permet le calcul précis de la diffraction etla propagation rayon des champs. D’abord mise au point dans le cadre de la diffraction d’ondes acoustiquespar un obstacle de taille inférieure à la longueur d’onde (méthode barycentrique), l’approche est ensuiteétendue à des configurations de diffraction par des obstacles de l’ordre de la longueur d’onde grâce àl’introduction d’un partitionnement de l’unité de sa surface (méthode multi-centres). Pour accélérerl’approche hybride, on propose une procédure de résolution Online-Offline, basée sur un pré-calcul de lamatrice de diffraction associée à un ensemble réduit de directions d’incidence et d’observation et sur uneinterpolation polynomiale de ses vecteurs singuliers pour son évaluation dans des directions quelconquesd’émetteurs et de récepteurs. On étudie ensuite la stratégie dans le cadre de l’acoustique 3D puis on en faitune extension de principe à l’élastodynamique. On donne enfin un ensemble de pistes pour étendre l’approchehybride dans des cas de diffraction par un ou plusieurs obstacles pouvant être proches des bords du milieu.

Non Destructive Testing (NDT) aims at probing a medium to check its integrity and aging. Withthe help of simulation tools, it allows to detect, caracterize and locate flaws inside a material with a precisiondepending on that of the simulation methods. Usual numerical and asymptotic methods nevertheless often failat precisely computing diffraction for ultrasonic NDT. Hybrid approaches are thus prefered in this framework.In this thesis, we propose a new hybrid strategy combining the boundary integral equation method and raytracing to compute high frequency diffraction of an obstacle in a large medium (critical NDT configuration).This strategy allows to compute precisely the diffraction effects and to convert and propagate the diffractedfield as rays. The proposed strategy relies on a two-scale model of the diffracting obstacle. First developpedto simulate acoustic waves diffraction on an obstacle of size less than the wave length (barycentric method),the hybrid strategy is then extended to compute the diffraction by an obstacle of size some wave…

Advisors/Committee Members: Bonnet, Marc (thesis director).

Subjects/Keywords: Diffraction haute fréquence; Couplage; Équations intégrales; Methode des rayons; High frequency diffraction; Hybridization; Boundary integral equation; Ray tracing; 515.4

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APA (6^th Edition):

Pesudo, L. (2017). Une méthode hybride couplant la méthode des équations intégrales et la méthode des rayons en vue d'applications au contrôle non destructif ultrasonore. : A hybrid strategy combining the integral equation method and the ray tracing method for high frequency diffraction involved in ultrasonic non destructive testing. (Doctoral Dissertation). Université Paris-Saclay (ComUE). Retrieved from http://www.theses.fr/2017SACLY009

Chicago Manual of Style (16^th Edition):

Pesudo, Laure. “Une méthode hybride couplant la méthode des équations intégrales et la méthode des rayons en vue d'applications au contrôle non destructif ultrasonore. : A hybrid strategy combining the integral equation method and the ray tracing method for high frequency diffraction involved in ultrasonic non destructive testing.” 2017. Doctoral Dissertation, Université Paris-Saclay (ComUE). Accessed April 11, 2021. http://www.theses.fr/2017SACLY009.

MLA Handbook (7^th Edition):

Pesudo, Laure. “Une méthode hybride couplant la méthode des équations intégrales et la méthode des rayons en vue d'applications au contrôle non destructif ultrasonore. : A hybrid strategy combining the integral equation method and the ray tracing method for high frequency diffraction involved in ultrasonic non destructive testing.” 2017. Web. 11 Apr 2021.

Vancouver:

Pesudo L. Une méthode hybride couplant la méthode des équations intégrales et la méthode des rayons en vue d'applications au contrôle non destructif ultrasonore. : A hybrid strategy combining the integral equation method and the ray tracing method for high frequency diffraction involved in ultrasonic non destructive testing. [Internet] [Doctoral dissertation]. Université Paris-Saclay (ComUE); 2017. [cited 2021 Apr 11]. Available from: http://www.theses.fr/2017SACLY009.

Council of Science Editors:

Pesudo L. Une méthode hybride couplant la méthode des équations intégrales et la méthode des rayons en vue d'applications au contrôle non destructif ultrasonore. : A hybrid strategy combining the integral equation method and the ray tracing method for high frequency diffraction involved in ultrasonic non destructive testing. [Doctoral Dissertation]. Université Paris-Saclay (ComUE); 2017. Available from: http://www.theses.fr/2017SACLY009

Miami University

24. Petrovic, Milena. Effects of the Object’s Mass and Distance on the Location of Preferred Critical Boundary, Discomfort, and Muscle Activation during a Seated Reaching Task.

Degree: PhD, Psychology, 2012, Miami University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=miami1343567265

► When reaching for objects, actors have to determine the distance at which they will have to change from using one reach mode to another. This… (more)

Subjects/Keywords: Psychology; Seated reaching; affordance; preferred critical boundary; discomfort; electromyography (integral and maximum amplitude); EMG; General Estimating Equation; GEE

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Petrovic, M. (2012). Effects of the Object’s Mass and Distance on the Location of Preferred Critical Boundary, Discomfort, and Muscle Activation during a Seated Reaching Task. (Doctoral Dissertation). Miami University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=miami1343567265

Chicago Manual of Style (16^th Edition):

Petrovic, Milena. “Effects of the Object’s Mass and Distance on the Location of Preferred Critical Boundary, Discomfort, and Muscle Activation during a Seated Reaching Task.” 2012. Doctoral Dissertation, Miami University. Accessed April 11, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=miami1343567265.

MLA Handbook (7^th Edition):

Petrovic, Milena. “Effects of the Object’s Mass and Distance on the Location of Preferred Critical Boundary, Discomfort, and Muscle Activation during a Seated Reaching Task.” 2012. Web. 11 Apr 2021.

Vancouver:

Petrovic M. Effects of the Object’s Mass and Distance on the Location of Preferred Critical Boundary, Discomfort, and Muscle Activation during a Seated Reaching Task. [Internet] [Doctoral dissertation]. Miami University; 2012. [cited 2021 Apr 11]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=miami1343567265.

Council of Science Editors:

Petrovic M. Effects of the Object’s Mass and Distance on the Location of Preferred Critical Boundary, Discomfort, and Muscle Activation during a Seated Reaching Task. [Doctoral Dissertation]. Miami University; 2012. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=miami1343567265

King Abdullah University of Science and Technology

25. Alharthi, Noha. Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2019, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/660105

► Acoustic and electromagnetic scattering from arbitrarily shaped structures can be numerically characterized by solving various surface integral equations (SIEs). One of the most effective techniques… (more)

▼ Acoustic and electromagnetic scattering from arbitrarily shaped structures can be numerically characterized by solving various surface integral equations (SIEs). One of the most effective techniques to solve SIEs is the Nyström method. Compared to other existing methods,the Nyström method is easier to implement especially when the geometrical discretization is non-conforming and higher-order representations of the geometry and unknowns are desired. However,singularities of the Green’s function are more difﬁcult to”manage”since they are not ”smoothened” through the use of a testing function. This dissertation describes purely numerical schemes to account for different orders of singularities that appear in acoustic and electromagnetic SIEs when they are solved by a high-order Nyström method utilizing a mesh of curved discretization elements. These schemes make use of two sets of basis functions to smoothen singular integrals: the grid robust high-order Lagrange and the high-order Silvester-Lagrange interpolation basis functions. Numerical results comparing the convergence of two schemes are presented. Moreover, an extremely scalable implementation of fast multipole method (FMM) is developed to efﬁciently (and iteratively) solve the linear system resulting from the discretization of the acoustic SIEs by the Nyström method. The implementation results in O(N log N) complexity for high-frequency scattering problems. This FMM-accelerated solver can handle N =2 billion on a 200,000-core Cray XC40 with 85% strong scaling efﬁciency. Iterative solvers are often ineffective for ill-conditioned problems. Thus, a fast direct (LU)solver,which makes use of low-rank matrix approximations,is also developed. This solver relies on tile low rank (TLR) data compression format, as implemented in the hierarchical computations on many corearchitectures (HiCMA) library. This requires to taskify the underlying SIE kernels to expose ﬁne-grained computations. The resulting asynchronous execution permit to weaken the artifactual synchronization points,while mitigating the overhead of data motion. We compare the obtained performance results of our TLRLU factorization against the state-of-the-art dense factorizations on shared memory systems. We achieve up to a fourfold performance speedup on a 3D acoustic problem with up to 150 K unknowns in double complex precision arithmetics. Advisors/Committee Members: Keyes, David E. (advisor), Hadwiger, Markus (committee member), Bagci, Hakan (committee member), Kressner, Daniel (committee member).

Subjects/Keywords: Boundary Integral Equation; Acoustic Scattering; LU-Based Solver; Fast Solvers; Fast Multipole Solvers; Tile Low-Rank Approximations

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APA (6^th Edition):

Alharthi, N. (2019). Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/660105

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Alharthi, Noha. “Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems.” 2019. Thesis, King Abdullah University of Science and Technology. Accessed April 11, 2021. http://hdl.handle.net/10754/660105.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Alharthi, Noha. “Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems.” 2019. Web. 11 Apr 2021.

Vancouver:

Alharthi N. Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2019. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/10754/660105.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Alharthi N. Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems. [Thesis]. King Abdullah University of Science and Technology; 2019. Available from: http://hdl.handle.net/10754/660105

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Louisiana State University

26. Ghulam, Ashar. Method of the Riemann-Hilbert Problem for the Solution of the Helmholtz Equation in a Semi-infinite Strip.

Degree: PhD, Applied Mathematics, 2016, Louisiana State University

URL: etd-06142016-133552 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3487

► In this dissertation, a new method is developed to study BVPs of the modified Helmholtz and Helmholtz equations in a semi-infinite strip subject to the… (more)

Subjects/Keywords: theory of integral transforms; theory of complex variables; residue theory of complex variables; higher order boundary conditions; Impedance boundary conditions; Poincare type boundary conditions; triangular case; Burniston-Siewert method; finite integral transform; scalar case; Modified Helmholtz equation; RHP; Riemann Hilbert problems; BVPs; boundary value problems

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APA (6^th Edition):

Ghulam, A. (2016). Method of the Riemann-Hilbert Problem for the Solution of the Helmholtz Equation in a Semi-infinite Strip. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-06142016-133552 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3487

Chicago Manual of Style (16^th Edition):

Ghulam, Ashar. “Method of the Riemann-Hilbert Problem for the Solution of the Helmholtz Equation in a Semi-infinite Strip.” 2016. Doctoral Dissertation, Louisiana State University. Accessed April 11, 2021. etd-06142016-133552 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3487.

MLA Handbook (7^th Edition):

Ghulam, Ashar. “Method of the Riemann-Hilbert Problem for the Solution of the Helmholtz Equation in a Semi-infinite Strip.” 2016. Web. 11 Apr 2021.

Vancouver:

Ghulam A. Method of the Riemann-Hilbert Problem for the Solution of the Helmholtz Equation in a Semi-infinite Strip. [Internet] [Doctoral dissertation]. Louisiana State University; 2016. [cited 2021 Apr 11]. Available from: etd-06142016-133552 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3487.

Council of Science Editors:

Ghulam A. Method of the Riemann-Hilbert Problem for the Solution of the Helmholtz Equation in a Semi-infinite Strip. [Doctoral Dissertation]. Louisiana State University; 2016. Available from: etd-06142016-133552 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3487

27. Passos, José Jarbson Salustiano dos. Análise da estabilidade estatíca e dinâmica de vigas pelo método dos elementos de contorno.

Degree: 2014, Universidade Federal da Paraíba; Programa de Pós-Graduação em Engenharia Mecânica; UFPB; BR; Engenharia Mecânica

URL: https://repositorio.ufpb.br/jspui/handle/tede/5387

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Made available in DSpace… (more)

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Made available in DSpace on 2015-05-08T14:59:59Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2498464 bytes, checksum: f14d53abab590dc87f310472963c08ad (MD5) Previous issue date: 2014-09-29

Made available in DSpace on 2018-07-21T00:03:42Z (GMT). No. of bitstreams: 2 arquivototal.pdf: 2498464 bytes, checksum: f14d53abab590dc87f310472963c08ad (MD5) arquivototal.pdf.jpg: 2127 bytes, checksum: 2bc09ba3175a53372c50aff888e9910a (MD5) Previous issue date: 2014-09-29

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES

In this work new solutions based on the direct Boundary Element Method (BEM) for static and dynamic stability beam problems are presented. Both Euler-Bernoulli and Timoshenko models are used to represent the beam responses. All discussions on mathematical steps to write down the BEM representation are presented. Alternative fundamental solutions for static and dynamic Euler-Bernoulli beam stability problems are proposed, resulting in the simpler forms than conventional fundamental solutions commonly used for the problems. In addition, the effects of Pasternak elastic foundations are incorporated into the expressions of proposed fundamental solutions. For the case of the Timoshenko static and dinamic stability, all the direct BEM representation (integral equations, fundamental solutions and algebraic equations) here proposed are inovative. Their fundamental solutions incorporate Pasternak foundation effects as well. A convenient strategy is also presented in order to deal with elastic end supports and discontinuities at beam domain such as abrupt change of cross section geometry (stepped beams), internetiated axial load, rigid or elastic supports at beam domain. Numerical examples incorporating various types of boundary conditions and domain discontinuities in order to validate the proposed BEM solution are presented.

Neste trabalho, novas soluções, baseadas no Método dos Elementos de Contorno (MEC) direto, são apresentadas para os problemas de estabilidade estática e dinâmica de vigas. Ambos modelos de Euler-Bernoulli e Timoshenko são usados para representar as respostas da viga. Todas as discussões sobre os passos matemáticos para escrever a representação do MEC são apresentadas. Soluções fundamentais alternativas são propostas para o problema da estabilidade estática e dinâmica de vigas de Euler-Bernoulli, resultando em formas mais simples que as comumente usadas para esses problemas. Além disso, os efeitos de fundações elásticas de Pasternak são incorporadas nas expressões das soluções fundamentais propostas. Para o caso da estabilidade estática e dinâmica de Timoshenko, toda a representação do MEC (equações integrais, soluções fundamentais e equações algébricas) aqui proposta é inovadora. Suas soluções fundamentais incorporam os efeitos da base elástica de Pasternak também. Uma estratégia conveniente é também apresentada para lidar com apoios elásticos no contorno e com discontinuidades no domínio tais como: mudança abrupta de geometria da seção…

Advisors/Committee Members: Mendonça, Angelo Vieira.

Subjects/Keywords: Método dos Elementos de Contorno (MEC); Flambagem; Solução Fundamental; Equação Integral; Boundary Element Method (BEM); Buckling loads; Fundamental solution; Integral Equation; ENGENHARIAS::ENGENHARIA MECANICA

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Passos, J. J. S. d. (2014). Análise da estabilidade estatíca e dinâmica de vigas pelo método dos elementos de contorno. (Masters Thesis). Universidade Federal da Paraíba; Programa de Pós-Graduação em Engenharia Mecânica; UFPB; BR; Engenharia Mecânica. Retrieved from https://repositorio.ufpb.br/jspui/handle/tede/5387

Chicago Manual of Style (16^th Edition):

Passos, José Jarbson Salustiano dos. “Análise da estabilidade estatíca e dinâmica de vigas pelo método dos elementos de contorno.” 2014. Masters Thesis, Universidade Federal da Paraíba; Programa de Pós-Graduação em Engenharia Mecânica; UFPB; BR; Engenharia Mecânica. Accessed April 11, 2021. https://repositorio.ufpb.br/jspui/handle/tede/5387.

MLA Handbook (7^th Edition):

Passos, José Jarbson Salustiano dos. “Análise da estabilidade estatíca e dinâmica de vigas pelo método dos elementos de contorno.” 2014. Web. 11 Apr 2021.

Vancouver:

Passos JJSd. Análise da estabilidade estatíca e dinâmica de vigas pelo método dos elementos de contorno. [Internet] [Masters thesis]. Universidade Federal da Paraíba; Programa de Pós-Graduação em Engenharia Mecânica; UFPB; BR; Engenharia Mecânica; 2014. [cited 2021 Apr 11]. Available from: https://repositorio.ufpb.br/jspui/handle/tede/5387.

Council of Science Editors:

Passos JJSd. Análise da estabilidade estatíca e dinâmica de vigas pelo método dos elementos de contorno. [Masters Thesis]. Universidade Federal da Paraíba; Programa de Pós-Graduação em Engenharia Mecânica; UFPB; BR; Engenharia Mecânica; 2014. Available from: https://repositorio.ufpb.br/jspui/handle/tede/5387

28. XIE HUA. Hybrid meshless methods for elasticity and poroelasticity.

Degree: 2008, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/13186

Subjects/Keywords: Elasticity; poroelasticity; boundary integral equation; local boundary integral equation; meshless method; radial basis function

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

HUA, X. (2008). Hybrid meshless methods for elasticity and poroelasticity. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/13186

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

HUA, XIE. “Hybrid meshless methods for elasticity and poroelasticity.” 2008. Thesis, National University of Singapore. Accessed April 11, 2021. http://scholarbank.nus.edu.sg/handle/10635/13186.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

HUA, XIE. “Hybrid meshless methods for elasticity and poroelasticity.” 2008. Web. 11 Apr 2021.

Vancouver:

HUA X. Hybrid meshless methods for elasticity and poroelasticity. [Internet] [Thesis]. National University of Singapore; 2008. [cited 2021 Apr 11]. Available from: http://scholarbank.nus.edu.sg/handle/10635/13186.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

HUA X. Hybrid meshless methods for elasticity and poroelasticity. [Thesis]. National University of Singapore; 2008. Available from: http://scholarbank.nus.edu.sg/handle/10635/13186

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Illinois – Urbana-Champaign

29. Guan, Jian. Multi-solver schemes for electromagnetic modeling of large and complex objects.

Degree: PhD, Electrical & Computer Engr, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98097

► The work in this dissertation primarily focuses on the development of numerical algorithms for electromagnetic modeling of large and complex objects. First, a GPU-accelerated multilevel… (more)

▼ The work in this dissertation primarily focuses on the development of numerical algorithms for electromagnetic modeling of large and complex objects. First, a GPU-accelerated multilevel fast multipole algorithm (MLFMA) is presented to improve the efficiency of the traditional MLFMA by taking advantage of GPU hardware advancement. The proposed hierarchical parallelization strategy ensures a high computational throughput for the GPU calculation. The resulting OpenMP-based multi-GPU implementation is capable of solving real-life problems with over one million unknowns with a remarkable speedup. The radar cross sections (RCS) of a few benchmark objects are calculated to demonstrate the accuracy of the solution. The results are compared with those from the CPU-based MLFMA and measurements. The capability and efficiency of the presented method are analyzed through the examples of a sphere, an aircraft, and a missile-like object. Compared with the 8-threaded CPU-based MLFMA, the OpenMP-CUDA-MLFMA method can achieve from 5 to 20 times total speedup. Second, an efficient and accurate finite element – boundary integral (FE-BI) method is proposed for solving electromagnetic scattering and radiation problems. A mixed testing scheme, in which the Rao-Wilton-Glisson and the Buffa-Christiansen functions are both employed as the testing functions, is first presented to improve the accuracy of the FE-BI method. An efficient absorbing boundary condition (ABC)-based preconditioner is then proposed to accelerate the convergence of the iterative solution. To further improve the efficiency of the total computation, a GPU-accelerated MLFMA is applied to the iterative solution. The RCSs of several benchmark objects are calculated to demonstrate the numerical accuracy of the solution and also to show that the proposed method not only is free of interior resonance corruption, but also has a better convergence than the conventional FE-BI methods. The capability and efficiency of the proposed method are analyzed through several numerical examples, including a large dielectric coated sphere, a partial human body, and a coated missile-like object. Compared with the 8-threaded CPU-based algorithm, the GPU-accelerated FE-BI-MLFMA algorithm can achieve a total speedup up to 25.5 times. Third, a multi-solver (MS) scheme based on combined field integral equation (CFIE) is proposed. In this scheme, an object is decomposed into multiple bodies based on its material property and geometry. To model bodies with complicated materials, the FE-BI method is applied. To model bodies with homogeneous or conducting materials, the method of moments is employed. Specifically, three solvers are integrated in this multi-solver scheme: the FE-BI(CFIE) for inhomogeneous objects, the CFIE for dielectric objects, and the CFIE for conducting objects. A mixed testing scheme that utilizes both the Rao-Wilton-Glisson and the Buffa-Christiansen functions is adopted to obtain a good accuracy of the proposed multi-solver algorithm. In the iterative solution of the… Advisors/Committee Members: Jin, Jianming (advisor), Jin, Jianming (Committee Chair), Schutt-Aine, Jose E. (committee member), Hirani, Anil N. (committee member), Kloeckner, Andreas (committee member).

Subjects/Keywords: Boundary integral equation; Buffa-Christiansen function; Combined field integral equation (CFIE); Compute unified device architecture (CUDA); Electromagnetic scattering; Finite element method; Finite element-boundary integral (FE-BI); Hybrid parallel programming model; Multi-graphics processing unit (GPU); Message passing interface (MPI); Multilevel fast multipole algorithm; Multi-solver scheme; Open Multi-Processing (OpenMP); Radar cross section; Robin transmission condition; Method of moments (MoM)

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Guan, J. (2017). Multi-solver schemes for electromagnetic modeling of large and complex objects. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98097

Chicago Manual of Style (16^th Edition):

Guan, Jian. “Multi-solver schemes for electromagnetic modeling of large and complex objects.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed April 11, 2021. http://hdl.handle.net/2142/98097.

MLA Handbook (7^th Edition):

Guan, Jian. “Multi-solver schemes for electromagnetic modeling of large and complex objects.” 2017. Web. 11 Apr 2021.

Vancouver:

Guan J. Multi-solver schemes for electromagnetic modeling of large and complex objects. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/2142/98097.

Council of Science Editors:

Guan J. Multi-solver schemes for electromagnetic modeling of large and complex objects. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98097

Brno University of Technology

30. Géze, Daniel. Modelování šíření elektromagnetického pole v tunelech: Modeling of electromagnetic field propation in tunnels.

Degree: 2014, Brno University of Technology

URL: http://hdl.handle.net/11012/31629

► The submitted master’s thesis aims at the numerical analysis of electromagnetic-wave propagation in tunnels. To this end, an integral-equation formulation has been formulated and numerically… (more)

Subjects/Keywords: Metóda hraničných prvkov; okrajové podmienky; integrálna rovnica; Helmholtzova rovnica; Maxwellove rovnice; líniový prúdový zdroj; profil tunela; analytická metóda; Boundary element method; boundary conditions; integral equation; wave equation (Helmholtz); Maxwell’s equations; line current source; tunnel profile; analytical method

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Géze, D. (2014). Modelování šíření elektromagnetického pole v tunelech: Modeling of electromagnetic field propation in tunnels. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/31629

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Géze, Daniel. “Modelování šíření elektromagnetického pole v tunelech: Modeling of electromagnetic field propation in tunnels.” 2014. Thesis, Brno University of Technology. Accessed April 11, 2021. http://hdl.handle.net/11012/31629.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Géze, Daniel. “Modelování šíření elektromagnetického pole v tunelech: Modeling of electromagnetic field propation in tunnels.” 2014. Web. 11 Apr 2021.

Vancouver:

Géze D. Modelování šíření elektromagnetického pole v tunelech: Modeling of electromagnetic field propation in tunnels. [Internet] [Thesis]. Brno University of Technology; 2014. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/11012/31629.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Géze D. Modelování šíření elektromagnetického pole v tunelech: Modeling of electromagnetic field propation in tunnels. [Thesis]. Brno University of Technology; 2014. Available from: http://hdl.handle.net/11012/31629

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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Open Access Theses and Dissertations