Dissertations / Theses: 'Boundary integral method'

1

Yoshida, Kenichi. "Applications of Fast Multipole Method to Boundary Integral Equation Method." Kyoto University, 2001. http://hdl.handle.net/2433/150672.

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2

Shmoylova, Elena. "Boundary Integral Equation Method in Elasticity with Microstructure." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2847.

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Problems involving mechanical behavior of materials with microstructure are receiving an increasing amount of attention in the literature. First of all, it can be attributed to the fact that a number of recent experiments shows a significant discrepancy between results of the classical theory of elasticity and the actual behavior of materials for which microstructure is known to be significant (e. g. synthetic polymers, human bones). Second, materials, for which microstructure contributes significantly in the overall deformation of a whole body, are becoming more and more important for applications in different areas of modern day mechanics, physics and engineering.

Since the classical theory is not adequate for modeling the elastic behavior of such materials, a new theory, which allows us to incorporate microstructure into a classical model, should be used.

The foundations of a theory allowing to account for the effect of material microstructure were developed in the beginning of the twentieth century and is known as the theory of Cosserat (micropolar, asymmetric) elasticity. For the last forty years significant results have been accomplished leading to a better understanding of processes occurring in Cosserat continuum. In particular, significant progress has been achieved in the investigation of three-dimensional problems of micropolar elasticity, plane and anti-plane problems, bending of micropolar plates. These problems can be effectively solved in a very elegant manner using the boundary integral equation method.

However, the boundary integral equation method imposes significant restrictions on properties of boundaries of domains under consideration. In particular, it requires that the boundary be represented by a twice differentiable curve which makes it impossible to apply the method for domains with reduced boundary smoothness or domains containing cuts or cracks. Therefore, the rigorous treatment of boundary value problems of Cosserat elasticity for domains with irregular boundaries has remained untouched until today.

A mathematically sophisticated, but very effective approach which allows to overcome the difficulty relating to the boundary requirement consists of the formulation of the corresponding boundary value problems in terms of the distributional setting in Sobolev spaces. In this case the appropriate weak solution may be found in terms of the corresponding integral potentials which perfectly works for domains with reduced boundary smoothness.

The objective of this work is to develop such a method that allows us to describe and solve the boundary value problems of plane Cosserat elasticity for domains with non-smooth boundaries and for domains weakened by cracks. We illustrate the method by establishing the analytical solutions for boundary value problems of plane Cosserat elasticity, which plays an important role as a pilot problem for the investigation of more challenging problems of three-dimensional theory of micropolar elasticity. We show that the analytical solutions derived in this work may be successfully approximated numerically using the boundary element method and that these solutions can be extremely important for applications in engineering science.

One of the important applied problems considered herein is the problem of stress distribution around a crack in a human bone. The bone is modeled under assumptions of plane Cosserat elasticity and the solution derived on the basis of the method developed in this dissertation shows that material microstructure does indeed have a significant effect on stress distribution around a crack.

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3

Moghaddasi-Tafreshi, Azamolsadat. "Design optimization using the boundary integral equation method." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/46451.

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4

Quesnel, Pierre Carleton University Dissertation Engineering Mechanical. "Boundary integral equation fracture mechanics analysis using the subdomain method." Ottawa, 1988.

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5

Kachanovska, Maryna. "Fast, Parallel Techniques for Time-Domain Boundary Integral Equations." Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-132183.

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This work addresses the question of the efficient numerical solution of time-domain boundary integral equations with retarded potentials arising in the problems of acoustic and electromagnetic scattering. The convolutional form of the time-domain boundary operators allows to discretize them with the help of Runge-Kutta convolution quadrature. This method combines Laplace-transform and time-stepping approaches and requires the explicit form of the fundamental solution only in the Laplace domain to be known. Recent numerical and analytical studies revealed excellent properties of Runge-Kutta convolution quadrature, e.g. high convergence order, stability, low dissipation and dispersion. As a model problem, we consider the wave scattering in three dimensions. The convolution quadrature discretization of the indirect formulation for the three-dimensional wave equation leads to the lower triangular Toeplitz system of equations. Each entry of this system is a boundary integral operator with a kernel defined by convolution quadrature. In this work we develop an efficient method of almost linear complexity for the solution of this system based on the existing recursive algorithm. The latter requires the construction of many discretizations of the Helmholtz boundary single layer operator for a wide range of complex wavenumbers. This leads to two main problems: the need to construct many dense matrices and to evaluate many singular and near-singular integrals. The first problem is overcome by the use of data-sparse techniques, namely, the high-frequency fast multipole method (HF FMM) and H-matrices. The applicability of both techniques for the discretization of the Helmholtz boundary single-layer operators with complex wavenumbers is analyzed. It is shown that the presence of decay can favorably affect the length of the fast multipole expansions and thus reduce the matrix-vector multiplication times. The performance of H-matrices and the HF FMM is compared for a range of complex wavenumbers, and the strategy to choose between two techniques is suggested. The second problem, namely, the assembly of many singular and nearly-singular integrals, is solved by the use of the Huygens principle. In this work we prove that kernels of the boundary integral operators $w_n^h(d)$ ($h$ is the time step and $t_n=nh$ is the time) exhibit exponential decay outside of the neighborhood of $d=nh$ (this is the consequence of the Huygens principle). The size of the support of these kernels for fixed $h$ increases with $n$ as $n^a,a<1$, where $a$ depends on the order of the Runge-Kutta method and is (typically) smaller for Runge-Kutta methods of higher order. Numerical experiments demonstrate that theoretically predicted values of $a$ are quite close to optimal. In the work it is shown how this property can be used in the recursive algorithm to construct only a few matrices with the near-field, while for the rest of the matrices the far-field only is assembled. The resulting method allows to solve the three-dimensional wave scattering problem with asymptotically almost linear complexity. The efficiency of the approach is confirmed by extensive numerical experiments.

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6

Kachanovska, Maryna. "Fast, Parallel Techniques for Time-Domain Boundary Integral Equations." Doctoral thesis, Max-Planck-Institut für Mathematik in den Naturwissenschaften, 2013. https://ul.qucosa.de/id/qucosa%3A12278.

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This work addresses the question of the efficient numerical solution of time-domain boundary integral equations with retarded potentials arising in the problems of acoustic and electromagnetic scattering. The convolutional form of the time-domain boundary operators allows to discretize them with the help of Runge-Kutta convolution quadrature. This method combines Laplace-transform and time-stepping approaches and requires the explicit form of the fundamental solution only in the Laplace domain to be known. Recent numerical and analytical studies revealed excellent properties of Runge-Kutta convolution quadrature, e.g. high convergence order, stability, low dissipation and dispersion. As a model problem, we consider the wave scattering in three dimensions. The convolution quadrature discretization of the indirect formulation for the three-dimensional wave equation leads to the lower triangular Toeplitz system of equations. Each entry of this system is a boundary integral operator with a kernel defined by convolution quadrature. In this work we develop an efficient method of almost linear complexity for the solution of this system based on the existing recursive algorithm. The latter requires the construction of many discretizations of the Helmholtz boundary single layer operator for a wide range of complex wavenumbers. This leads to two main problems: the need to construct many dense matrices and to evaluate many singular and near-singular integrals. The first problem is overcome by the use of data-sparse techniques, namely, the high-frequency fast multipole method (HF FMM) and H-matrices. The applicability of both techniques for the discretization of the Helmholtz boundary single-layer operators with complex wavenumbers is analyzed. It is shown that the presence of decay can favorably affect the length of the fast multipole expansions and thus reduce the matrix-vector multiplication times. The performance of H-matrices and the HF FMM is compared for a range of complex wavenumbers, and the strategy to choose between two techniques is suggested. The second problem, namely, the assembly of many singular and nearly-singular integrals, is solved by the use of the Huygens principle. In this work we prove that kernels of the boundary integral operators $w_n^h(d)$ ($h$ is the time step and $t_n=nh$ is the time) exhibit exponential decay outside of the neighborhood of $d=nh$ (this is the consequence of the Huygens principle). The size of the support of these kernels for fixed $h$ increases with $n$ as $n^a,a<1$, where $a$ depends on the order of the Runge-Kutta method and is (typically) smaller for Runge-Kutta methods of higher order. Numerical experiments demonstrate that theoretically predicted values of $a$ are quite close to optimal. In the work it is shown how this property can be used in the recursive algorithm to construct only a few matrices with the near-field, while for the rest of the matrices the far-field only is assembled. The resulting method allows to solve the three-dimensional wave scattering problem with asymptotically almost linear complexity. The efficiency of the approach is confirmed by extensive numerical experiments.

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7

Kang, Tai. "Shape and topology design optimization using the boundary integral equation method." Thesis, Imperial College London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320895.

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8

Tai, Kang. "Shape and topology design optimisation using the boundary integral equation method." Thesis, Imperial College London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294748.

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9

Chatzis, Ilias. "Boundary integral equation method in transient elastodynamics : techniques to reduce computational costs." Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249633.

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10

Harbrecht, Helmut, and Reinhold Schneider. "Wavelets for the fast solution of boundary integral equations." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600540.

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This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators. This yields quasi-sparse system matrices which can be compressed to O(N_J) relevant matrix entries without compromising the accuracy of the underlying Galerkin scheme. Herein, O(N_J) denotes the number of unknowns. The assembly of the compressed system matrix can be performed in O(N_J) operations. Therefore, we arrive at an algorithm which solves boundary integral equations within optimal complexity. By numerical experiments we provide results which corroborate the theory.

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11

Mohamed, Nurul Akmal. "Numerical solution and spectrum of boundary-domain integral equations." Thesis, Brunel University, 2013. http://bura.brunel.ac.uk/handle/2438/7592.

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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 to the Neumann and Dirichlet boundary value problem for a scalar elliptic PDE with variable coefficient is discussed in this thesis. The BDIE and LBDIE related to Neumann problem are reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretisation of the BDIE/BDIDEs and LBDIE/LBDIDEs with quadrilateral domain elements leads to systems of linear algebraic equations (discretised BDIE/BDIDEs/LBDIE/BDIDEs). Then the systems obtained from BDIE/BDIDE (discretised BDIE/BDIDE) are solved by the LU decomposition method and Neumann iterations. Convergence of the iterative method is analyzed in relation with the eigen-values of the corresponding discrete BDIE/BDIDE operators obtained numerically. The systems obtained from LBDIE/LBDIDE (discretised LBDIE/LBDIDE) are solved by the LU decomposition method as the Neumann iteration method diverges.

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12

Preston, Mark Daniel. "A boundary integral equation method for solving second kind integral equations arising in unsteady water waves problems." Thesis, University of Reading, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.493803.

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In this thesis we consider two dimensional, half-plane, unsteady water wave problems and their solution by boundary integral methods. Well-posed boundary integral solutions and convergent numerical schemes exist within the literature under the restrictive assumption of periodicity in both the boundary and the boundary data (overturning, or breaking, waves are included). The boundary integral formulation presented within gives a well-posed solution and leads to a convergent numerical scheme without the restriction of periodicity in the boundary and boundary data (while still allowing overturning waves).

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13

Martinot-Lagarde, Vincent. "An integral turbulent boundary-layer method and the residuary resistance of ships." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/13042.

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14

Poole, Mark W. "Numerical solution of an electropaint problem." Thesis, Cranfield University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309789.

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15

Azis, Mohammad Ivan. "On the boundary integral equation method for the solution of some problems for inhomogeneous media." Title page, contents and summary only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09pha995.pdf.

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Errata pasted onto front end-paper. Bibliography: leaves 101-104. This thesis employs integral equation methods, or boundary element methods (BEMs), for the solution of three kinds of engineering problems associated with inhomogeneous materials or media: a class of elliptical boundary value problems (BVPs), the boundary value problem of static linear elasticity, and the calculation of the solution of the initial-boundary value problem of non-linear heat conduction for anisotropic media.

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16

Zakikhani, Mansour. "Study of flow and mass transport in multilayered aquifers using boundary integral method." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/20163.

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17

Zhang, Huaijian. "Boundary Integral Techniques in Three Dimensions for Deep Water Waves." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306712208.

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18

Pai, Ravindra. "Calculation of wave resistance and elevation of arbitrarily shaped bodies using the boundary integral element method." Thesis, This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-10222009-125057/.

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19

Ioannidis, Anastasios S. "An integral method for quasi three-dimensional boundary layer analysis with rotational effects." Thesis, Massachusetts Institute of Technology, 1990. http://hdl.handle.net/1721.1/14149.

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20

Mughal, Bilal Hafeez. "A calculation method for the three-dimensional boundary-layer equations in integral form." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/12938.

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21

Haroldsen, David John Meiron Daniel I. Meiron Daniel I. "The numerical calculation of three-dimensional water waves using a boundary integral method /." Diss., Pasadena, Calif. : California Institute of Technology, 1997. http://resolver.caltech.edu/CaltechETD:etd-01102008-153911.

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22

McGregor, Peter Stanley. "Modelling the Effect of Suspended Bodies on Cavitation Bubbles near a Ridgid Boundary using a Boundary Integral Approach." Queensland University of Technology, 2003. http://eprints.qut.edu.au/15822/.

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Cavitation is the spontaneous vaporisation of a liquid to its gaseous state due to the local absolute pressure falling to the liquid's vapour pressure (Douglas, Gasiorek et al. 1995). Cavitation is present in a wide range of mechanical systems ranging from ship screws to journal bearing. Generally, cavitation is unavoidable and may cause considerable damage and efficiency losses to these systems. This thesis considers hydraulic systems specifically, and uses a modified Greens equation to develop a boundary integral method to simulate the effect that suspended solid bodies have on a single cavitation bubble. Because of the limitations of accurately modelling cavitation bubbles beyond touchdown, results are only presented for cases up to touchdown. The aim of the model is to draw insight into the reasons there is a measurable change in cavitation erosion rate with increasing oil-in-water emulsion percentage. This principle was extended to include the effect that ingested particulates may have on cavitation in hydraulic machinery. Two particular situations are modelled; the first consists of stationary rigid particles in varying proximity to a cavitation bubble near a rigid boundary. The second case is similar; however the suspended particle is allowed to move under the influence of the pressure differential caused by the expanding/contracting cavitation bubble. Numerous characteristics of the domain are considered, including domain pressures and fluid field motion, and individual boundary surface characteristics. The conclusion of the thesis is that solid bodies, either stationary or moving, have little effect on the cavity from an energy perspective. Regardless of size or density, all energy transferred from the cavity to the solid body is returned indicating that there is no net change. As this energy is ultimately responsible for the peak pressure experienced by the domain (and hence responsible for eroding the rigid boundary) as the cavity rebounds, it then serves that a cavity with a solid body will rebound at the same pressure as a cavity without a suspended body present. If this is coupled with the observation that the cavity centroid at touchdown is largely unaffected by the presence of a suspension, then it would appear that the bubble near a solid would rebound at a very similar position as a cavity without a solid. Consequently, the damage potential of a cavity is unaffected by a suspension. However, there is one point of contention as the profile of the re-entrant jet of the cavity is altered by the presence of a suspension. As energy is radiated away from the cavity during penetration, it is possible that the shape of the jet may alter the rate that energy is radiated away during penetration. However, this requires further research to be definitive.

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23

McGregor, Peter Stanley. "Modelling the effect of suspended bodies on cavitation bubbles near a rigid boundary using a boundary integral approach." Thesis, Queensland University of Technology, 2003. https://eprints.qut.edu.au/15822/1/Peter_McGregor_Thesis.pdf.

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Cavitation is the spontaneous vaporisation of a liquid to its gaseous state due to the local absolute pressure falling to the liquid's vapour pressure (Douglas, Gasiorek et al. 1995). Cavitation is present in a wide range of mechanical systems ranging from ship screws to journal bearing. Generally, cavitation is unavoidable and may cause considerable damage and efficiency losses to these systems. This thesis considers hydraulic systems specifically, and uses a modified Greens equation to develop a boundary integral method to simulate the effect that suspended solid bodies have on a single cavitation bubble. Because of the limitations of accurately modelling cavitation bubbles beyond touchdown, results are only presented for cases up to touchdown. The aim of the model is to draw insight into the reasons there is a measurable change in cavitation erosion rate with increasing oil-in-water emulsion percentage. This principle was extended to include the effect that ingested particulates may have on cavitation in hydraulic machinery. Two particular situations are modelled; the first consists of stationary rigid particles in varying proximity to a cavitation bubble near a rigid boundary. The second case is similar; however the suspended particle is allowed to move under the influence of the pressure differential caused by the expanding/contracting cavitation bubble. Numerous characteristics of the domain are considered, including domain pressures and fluid field motion, and individual boundary surface characteristics. The conclusion of the thesis is that solid bodies, either stationary or moving, have little effect on the cavity from an energy perspective. Regardless of size or density, all energy transferred from the cavity to the solid body is returned indicating that there is no net change. As this energy is ultimately responsible for the peak pressure experienced by the domain (and hence responsible for eroding the rigid boundary) as the cavity rebounds, it then serves that a cavity with a solid body will rebound at the same pressure as a cavity without a suspended body present. If this is coupled with the observation that the cavity centroid at touchdown is largely unaffected by the presence of a suspension, then it would appear that the bubble near a solid would rebound at a very similar position as a cavity without a solid. Consequently, the damage potential of a cavity is unaffected by a suspension. However, there is one point of contention as the profile of the re-entrant jet of the cavity is altered by the presence of a suspension. As energy is radiated away from the cavity during penetration, it is possible that the shape of the jet may alter the rate that energy is radiated away during penetration. However, this requires further research to be definitive.

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24

Arens, Tilo. "The scattering of elastic waves by rough surfaces." Thesis, Brunel University, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.311560.

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25

Benson, A. "A new approach to the boundary integral method for the three dimensional Neumann problem." Thesis, University of Salford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356179.

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26

Kurniasih, Neny. "APPLICATIONS OF TIME DOMAIN BOUNDARY INTEGRAL EQUATION METHOD TO FORWARD AND INVERSE ELASTODYNAMIC PROBLEMS." Kyoto University, 2001. http://hdl.handle.net/2433/150670.

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27

Hibbs, T. T. "C'('1') continuous representations and advanced singular kernal integrations in the three dimensional boundary integral method." Thesis, Teesside University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384606.

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28

Misawa, Ryota. "Boundary integral equation methods for the calculation of complex eigenvalues for open spaces." 京都大学 (Kyoto University), 2017. http://hdl.handle.net/2433/225738.

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29

Ballani, Jonas. "Fast Evaluation of Near-Field Boundary Integrals using Tensor Approximations." Doctoral thesis, Universitätsbibliothek Leipzig, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-97317.

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In this dissertation, we introduce and analyse a scheme for the fast evaluation of integrals stemming from boundary element methods including discretisations of the classical single and double layer potential operators. Our method is based on the parametrisation of boundary elements in terms of a d-dimensional parameter tuple. We interpret the integral as a real-valued function f depending on d parameters and show that f is smooth in a d-dimensional box. A standard interpolation of f by polynomials leads to a d-dimensional tensor which is given by the values of f at the interpolation points. This tensor may be approximated in a low rank tensor format like the canonical format or the hierarchical format. The tensor approximation has to be done only once and allows us to evaluate interpolants in O(dr(m+1)) operations in the canonical format, or O(dk³ + dk(m + 1)) operations in the hierarchical format, where m denotes the interpolation order and the ranks r, k are small integers. In particular, we apply an efficient black box scheme in the hierarchical tensor format in order to adaptively approximate tensors even in high dimensions d with a prescribed (but heuristic) target accuracy. By means of detailed numerical experiments, we demonstrate that highly accurate integral values can be obtained at very moderate costs.

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30

Desiderio, Luca. "H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLY002/document.

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Cette thèse porte sur l'étude théorique et numérique des méthodes rapides pour résoudre les équations de l'élastodynamique 3D en domaine fréquentiel, et se place dans le cadre d'une collaboration avec la société Shell en vue d'optimiser la convergence des problèmes d'inversion sismique. La méthode repose sur l'utilisation des éléments finis de frontière (BEM) pour la discrétisation et sur les techniques de matrices hiérarchiques (H-matrices) pour l'accélération de la résolution du système linéaire. Dans le cadre de cette thèse on a développé un solveur direct pour les BEMs en utilisant une factorisation LU et un stockage hiérarchique. Si le concept des H-matrices est simple à comprendre, sa mise en oeuvre requiert des développements algorithmiques importants tels que la gestion de la multiplication de matrices représentées par des structures différentes (compressées ou non) qui ne comprend pas mois de 27 sous-cas. Un autre point délicat est l'utilisation des méthodes d'approximations par matrices compressées (de rang faible) dans le cadre des problèmes vectoriels. Une étude algorithmique a donc été faite pour mettre en oeuvre la méthode des H-matrices. Nous avons par ailleurs estimé théoriquement le rang faible attendu pour les noyaux oscillants, ce qui constitue une nouveauté, et montré que la méthode est utilisable en élastodynamique. En outre on a étudié l'influence des divers paramètres de la méthode en acoustique et en élastodynamique 3D, à fin de calibrer leur valeurs numériques optimales. Dans le cadre de la collaboration avec Shell, un cas test spécifique a été étudié. Il s'agit d'un problème de propagation d'une onde sismique dans un demi-espace élastique soumis à une force ponctuelle en surface. Enfin le solveur direct développé a été intégré au code COFFEE développé a POEMS (environ 25000 lignes en Fortran 90)
This thesis focuses on the theoretical and numerical study of fast methods to solve the equations of 3D elastodynamics in frequency-domain. We use the Boundary Element Method (BEM) as discretization technique, in association with the hierarchical matrices (H-matrices) technique for the fast solution of the resulting linear system. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundaries. Thus, this method is well suited to treat seismic wave propagation problems. A major drawback of classical BEM is that it results in dense matrices, which leads to high memory requirement (O (N 2 ), if N is the number of degrees of freedom) and computational costs.Therefore, the simulation of realistic problems is limited by the number of degrees of freedom. Several fast BEMs have been developed to improve the computational eﬃciency. We propose a fast H-matrix based direct BEM solver

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31

Pvillalta, Jose Samuel. "FINITE ELEMENT-BOUNDARY INTEGRAL METHOD AND ITS APPLICATION TO IMPLANTABLE ANTENNA DESIGN FOR WIRELESS DATA TELEMETRY." MSSTATE, 2006. http://sun.library.msstate.edu/ETD-db/theses/available/etd-07072006-114241/.

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A non-stationary Krylov subspace based iterative solver for the three dimensional finite element-boundary integral (FE-BI) method for implantable antennas is presented. The present method numerically solves the frequency domain Maxwell?s equations in the variational form to formulate the finite element solution using hexahedral discretization elements in conjunction with the appropriate boundary integral equations. Four different solvers are used to investigate the convergence behavior of the FE-BI technique on the design of the antennas. The scheme is then applied to two miniaturized planar inverted-F antennas (PIFA): a serpentine and a spiral. The antennas are designed for the Medical Implant Communication Service (MICS) band (402-405 MHz). Validations and comparisons are done using High Frequency Electromagnetic Simulation (HFSS) software. Return loss, gain, near fields, and far fields are presented for the serpentine and spiral antenna.

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32

Thompson, R. M. "The boundary-integral equation method applied to the derivation of stress concentration and stress intensity factors." Thesis, Cranfield University, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.353628.

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33

Yang, Yang. "Two-dimensional dynamic analysis of functionally graded structures by using meshfree boundary-domain integral equation method." Thesis, University of Macau, 2015. http://umaclib3.umac.mo/record=b3335354.

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34

Thomas, Gregory Robert. "A combined high-order spectral and boundary integral equation method for modelling wave interactions with submerged bodies." Thesis, Monterey, California. Naval Postgraduate School, 1996. http://hdl.handle.net/10945/8098.

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35

Liou, Sy Yeuan. "Hybrid boundary integral equation method for the hydrodynamic analysis of marine structures in open and confined water." Thesis, University of Newcastle Upon Tyne, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315619.

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36

Thomas, Gregory Robert. "A combined high-order spectral and boundary integral equation method for modelling wave interactions with submerged bodies." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/17432.

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37

Ylä-Oijala, Pasi. "Multipacting analysis and electromagnetic field computation by the boundary integral equation method in RF cavities and waveguides." Helsinki : University of Helsinki, 1999. http://ethesis.helsinki.fi/julkaisut/mat/rolfn/vk/yla-oijala/.

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38

Saeed, Usman. "Adaptive numerical techniques for the solution of electromagnetic integral equations." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41173.

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Various error estimation and adaptive refinement techniques for the solution of electromagnetic integral equations were developed. Residual based error estimators and h-refinement implementations were done for the Method of Moments (MoM) solution of electromagnetic integral equations for a number of different problems. Due to high computational cost associated with the MoM, a cheaper solution technique known as the Locally-Corrected Nyström (LCN) method was explored. Several explicit and implicit techniques for error estimation in the LCN solution of electromagnetic integral equations were proposed and implemented for different geometries to successfully identify high-error regions. A simple p-refinement algorithm was developed and implemented for a number of prototype problems using the proposed estimators. Numerical error was found to significantly reduce in the high-error regions after the refinement. A simple computational cost analysis was also presented for the proposed error estimation schemes. Various cost-accuracy trade-offs and problem-specific limitations of different techniques for error estimation were discussed. Finally, a very important problem of slope-mismatch in the global error rates of the solution and the residual was identified. A few methods to compensate for that mismatch using scale factors based on matrix norms were developed.

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Al-Jawary, Majeed Ahmed Weli. "The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients." Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/6449.

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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 problems with constant coefficients) of reducing a BVP for a linear partial differential equation (PDE) defined in a domain to an integral equation defined on the boundary, leading to a simplified discretisation process with boundary elements only. On the other hand, the coefficients in the mathematical model of a physical problem typically correspond to the material parameters of the problem. In many physical problems, the governing equation is likely to involve variable coefficients. The application of the BEM to these equations is hampered by the difficulty of finding a fundamental solution. The first part of this thesis will focus on the derivation of the boundary integral equation (BIE) for the Laplace equation, and numerical results are presented for some examples using constant elements. Then, the formulations of the boundary-domain integral or integro-differential equation (BDIE or BDIDE) for heat conduction problems with variable coefficients are presented using a parametrix (Levi function), which is usually available. The second part of this thesis deals with the extension of the BDIE and BDIDE formulations to the treatment of the two-dimensional Helmholtz equation with variable coefficients. Four possible cases are investigated, first of all when both material parameters and wave number are constant, in which case the zero-order Bessel function of the second kind is used as fundamental solution. Moreover, when the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or a BDIDE. Finally, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. In the third part, the radial integration method (RIM) is introduced and discussed in detail. Modifications are introduced to the RIM, particularly the fact that the radial integral is calculated by using a pure boundary-only integral which relaxes the “star-shaped” requirement of the RIM. Then, the RIM is used to convert the domain integrals appearing in both BDIE and BDIDE for heat conduction and Helmholtz equations to equivalent boundary integrals. For domain integrals consisting of known functions the transformation is straightforward, while for domain integrals that include unknown variables the transformation is accomplished with the use of augmented radial basis functions (RBFs). The most attractive feature of the method is that the transformations are very simple and have similar forms for both 2D and 3D problems. Finally, the application of the RIM is discussed for the diffusion equation, in which the parabolic PDE is initially reformulated as a BDIE or a BDIDE and the RIM is used to convert the resulting domain integrals to equivalent boundary integrals. Three cases have been investigated, for homogenous, non-homogeneous and variable coefficient diffusion problems.

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Zhang, Yan. "Analysis of Elastic and Electrical Fields in Quantum Structures by Novel Green's Functions and Related Boundary Integral Methods." University of Akron / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=akron1290184113.

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Jagtap, Nimish V. "Application of the Hypersingular Boundary Integral Equation in Evaluating Stress Intensity Factors for 2D Elastostatic Fracture Mechanics Problems." University of Cincinnati / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1163788461.

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Strydom, Willem Jacobus. "Recovery based error estimation for the Method of Moments." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96881.

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Thesis (MEng)--Stellenbosch University, 2015.
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 posteriori foutberaming van die MoM-stroom is met behulp van die verhaalde stroom verspreidings gerealiseer, en daar is gevind dat 'n gemengde tweede-orde verhaalde stroom, gebaseer op 'n vektor metode, die beste resultate lewer. Die foutberamingstegnieke wat in hierdie tesis ondersoek is, kan in 'n aanpasbare skema opgeneem word om die akkuraatheid van 'n numeriese oplossing, relatief tot die berekeningskoste, te optimeer.

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Guckenberger, Achim [Verfasser], and Stephan [Akademischer Betreuer] Gekle. "From models to applications: Simulation of blood flow with an extended boundary integral method / Achim Guckenberger ; Betreuer: Stephan Gekle." Bayreuth : Universität Bayreuth, 2018. http://d-nb.info/1159633142/34.

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Milewski, William Michael. "Three-dimensional viscous flow computations using the integral boundary layer equations simultaneously coupled with a low order panel method." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/10399.

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Ma, Jianfeng. "Meshless method for modeling large deformation with elastoplasticity." Diss., Manhattan, Kan. : Kansas State University, 2007. http://hdl.handle.net/2097/402.

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Akeab, Imad. "Accurate techniques for 2D electromagnetic scattering." Licentiate thesis, Linnéuniversitetet, Institutionen för fysik och elektroteknik (IFE), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-31523.

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This thesis consists of three parts. The first part is an introduction and referencessome recent work on 2D electromagnetic scattering problems at high frequencies. It alsopresents the basic integral equation types for impenetrable objects. A brief discussionof the standard elements of the method of moments is followed by summaries of thepapers.Paper I presents an accurate implementation of the method of moments for a perfectlyconducting cylinder. A scaling for the rapid variation of the solution improves accuracy.At high frequencies, the method of moments leads to a large dense system of equations.Sparsity in this system is obtained by modifying the integration path in the integralequation. The modified path reduces the accuracy in the deep shadow.In paper II, a hybrid method is used to handle the standing waves that are prominentin the shadow for the TE case. The shadow region is treated separately, in a hybridscheme based on a priori knowledge about the solution. An accurate method to combinesolutions in this hybrid scheme is presented.

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Rasadurai, Rajavaheinthan. "Forced water entry and exit of two-dimensional bodies through a free surface." Thesis, Brunel University, 2014. http://bura.brunel.ac.uk/handle/2438/8327.

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The forced water entry and exit of two-dimensional bodies through a free surface is computed for various 2D bodies (symmetric wedges, asymmetric wedges, truncated wedges and boxes). These bodies enter or exit water with constant velocity or constant acceleration. The calculations are based on the fully non-linear timestepping complex-variable method of Vinje and Brevig. The model was formulated as an initial boundary-value problem with boundary conditions specified on the boundaries (dynamic and kinematic free-surface boundary conditions) and initial conditions at time zero (initial velocity and position of the body and free-surface particles). The formulated problem was solved by means of a boundary-element method using collocation points on the boundary of the domain and solutions at each time were calculated using time stepping (Runge-Kutta and Hamming predictor corrector) methods. Numerical results for the deformed free-surface profile, the speed of the point at the intersection of the body and free surface, the pressure along the wetted region of the bodies and force experienced by the bodies, are given for the entry and exit. To verify the results, various tests such as convergence checks, self-similarity for entry (gravity-free solutions) and Froude number effect for constant velocity entry and exit (half-wedge angles 5 up to 55 degrees) are investigated. The numerical results are compared with Mackie's analytical theory for water entry and exit with constant velocities, and the analytical added mass force computed for water entry and exit of symmetric wedges and boxes with constant acceleration and velocity using conformal mapping. Finally, numerical results showing the effect of finite depth are investigated for entry and exit.

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Sztulzaft, Patrick. "Green-expert : un solveur généralisé associé à un générateur de formulations pour la méthode des intégrales de frontières." Grenoble INPG, 1994. https://hal.archives-ouvertes.fr/tel-01331763.

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De nombreux secteurs de l'industrie et de la recherche utilisent la modélisation des phénomènes de la physique des milieux continus. Les équations aux dérivées partielles décrivant ces phénomènes sont résolues à l'aide de diverses méthodes numériques. Les modélisations utilisées sont de plus en plus pointues, tant au niveau physique qu'au niveau numérique. Les réponses logicielles à ces problèmes doivent donc être évolutives. Ce travail s'insère dans une dynamique de recherche dans le domaine de la modélisation des phénomènes complexes qui a débuté avec l'élaboration du programme Flux-Expert®, basé sur la Méthode des Eléments Finis. Afin d'élargir le champ des possibilités offertes par ce programme, nous avons choisi d'y associer la Méthodes des Intégrales de Frontières. Dans cette optique, après une présentation didactique de la Méthode des Intégrales de Frontières, nous proposons une décomposition générale de la résolution numérique d'un problème à l'aide de cette méthode. Nous décrivons ensuite le logiciel issu de cette analyse : Green-Expert. L'originalité de la démarche réside dans l'association d'un programme Générateur de Formulations et d'un programme Solveur généralisé. Ce Solveur est capable de résoudre tout problème décrit à l'aide d'une formulation issue du Générateur et d'une Géométrie discrétisée. La dernière partie de ce mémoire est consacré à la validation. Des exemples de couplage entre la Méthode des Intégrales de Frontières et la Méthode des Éléments Finis sont présentés. Enfin, des exemples de résolution 2D et 3D permettent de valider le Générateur et le Solveur de Green-Expert
Investigations in many sectors of industry and research require the modelling of phenomena observed in the physics of continuous media. The partial differential equations describing these phenomena are solved using a wide range of numerical methods. The models used are increasingly sophisticated, from both a physical and numerical point of view. Software used to solve these problems must therefore be capable of evolving. This work is a continuation of research efforts devoted to the modelling of complex phenomena that began with the development of the Flux-Expert® program, based on the Finite Element Method. In order to extend the possibilities offered by this program, we decided to combine it with the Boundary Element Method. After reviewing the Boundary Element Method, we propose a general decomposition of the numerical solution of a problem using this method. We then describe the Green-Expert software developed on the basis of this analysis. The original aspect of the approach lies in the combination of a formulations generator and a general solver. This solver is capable of solving any problem described using a formulation coming from the Generator and a discrete geometry. The last part of this thesis is devoted to the validation phase. Examples of the combined use of the Boundary Elements and the Finite Element Methods are presented and examples of 2D and 3D resolution are used to validate the Green-Expert Solver and Generator

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Pillain, Axelle. "Line, Surface, and Volume Integral Equations for the Electromagnetic Modelling of the Electroencephalography Forward Problem." Thesis, Télécom Bretagne, 2016. http://www.theses.fr/2016TELB0412/document.

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La reconstruction des sources de l'activité cérébrale à partir des mesures de potentiel fournies par un électroencéphalographie (EEG) nécessite de résoudre le problème connu sous le nom de « problème inverse de l'EEG ». La solution de ce problème dépend de la solution du « problème direct de l'EEG », qui fournit à partir de sources de courant connues, le potentiel mesuré au niveau des électrodes. Pour des modèles de tête réels, ce problème ne peut être résolut que de manière numérique. En particulier, les équations intégrales de surfaces requièrent uniquement la discrétisation des interfaces entre les différents compartiments constituant le milieu cérébral. Cependant, les formulations intégrales existant actuellement ne prennent pas en comptent l'anisotropie du milieu. Le travail présenté dans cette thèse introduit deux nouvelles formulations intégrales permettant de palier à cette faiblesse. Une formulation indirecte capable de prendre en compte l'anisotropie du cerveau est proposée. Elle est discrétisée à l'aide de fonctions conformes aux propriétés spectrales des opérateurs impliqués. L'effet de cette discrétisation de type mixe lors de la reconstruction des sources cérébrales est aussi étudié. La seconde formulation se concentre sur l'anisotropie due à la matière blanche. Calculer rapidement la solution du système numérique obtenu est aussi très désirable. Le travail est ainsi complémenté d'une preuve de l'applicabilité des stratégies de préconditionnement de type Calderon pour les milieux multicouches. Le théorème proposé est appliqué dans le contexte de la résolution du problème direct de l'EEG. Un préconditionneur de type Calderon est aussi introduit pour l'équation intégrale du champ électrique (EFIE) dans le cas de structures unidimensionnelles. Finalement, des résultats préliminaires sur l'impact d'un solveur rapide direct lors de la résolution rapide du problème direct de l'EEG sont présentés
Electroencephalography (EEG) is a very useful tool for characterizing epileptic sources. Brain source imaging with EEG necessitates to solve the so-called EEG inverse problem. Its solution depends on the solution of the EEG forward problem that provides from known current sources the potential measured at the electrodes positions. For realistic head shapes, this problem can be solved with different numerical techniques. In particular surface integral equations necessitates to discretize only the interfaces between the brain compartments. However, the existing formulations do not take into account the anisotropy of the media. The work presented in this thesis introduces two new integral formulations to tackle this weakness. An indirect formulation that can handle brain anisotropies is proposed. It is discretized with basis functions conform to the mapping properties of the involved operators. The effect of this mixed discretization on brain source reconstruction is also studied. The second formulation focuses on the white matter fiber anisotropy. Obtaining the solution to the obtained numerical system rapidly is also highly desirable. The work is hence complemented with a proof of the preconditioning effect of Calderon strategies for multilayered media. The proposed theorem is applied in the context of solving the EEG forward problem. A Calderon preconditioner is also introduced for the wire electric field integral equation. Finally, preliminary results on the impact of a fast direct solver in solving the EEG forward problem are presented

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Oudin, Hervé. "Etude du comportement hydroelastique des structures marines par une formulation mixte : equations integrales-elements finis." Nantes, 1986. http://www.theses.fr/1986NANT2062.

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Nous presentons divers modeles, bases sur le couplage da la methode des equations integrales et de la methode des elements finis, permettant de determiner le comportement dynamique des structures marines en presence de houle. L'interface entre le logiciel "aquadyn" traitant le probleme hydrodynamique et des elements poutres 3 d, permet d'obtenir l'equation matricielle du mouvement. Pour resoudre cette equation complexe dont certains coefficients dependent de la frequence, nous proposons un algorithme de recherche des frequences de resonnance et de la frequence a partir de laquelle une formulation asymptotique peut etre utilisee pour obtenir une equation a coefficients constants. Des mesures et des tests numeriques permettent de comparer les divers modeles. Dans le cas de la surface libre equipotentielle, nous avons introduit des elements finis fluides au voisinage de la structure, couples soit avec la methode des equations integrales, soit avec des elements finis, des comparaisons numeriques etant faites pour un pieu vertical

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Dissertations / Theses on the topic 'Boundary integral method'

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