Dissertations / Theses: 'Boundary element methods'

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Of, Günther, Gregory J. Rodin, Olaf Steinbach, and Matthias Taus. "Coupling Methods for Interior Penalty Discontinuous Galerkin Finite Element Methods and Boundary Element Methods." Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-96885.

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This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element methods are used. Error and stability analysis is presented for some of the methods. Numerical examples suggest that all three methods exhibit very similar convergence properties, consistent with available theoretical results.

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Ostrowski, Jörg. "Boundary element methods for inductive hardening." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=973933941.

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Onyango, Thomas Tonny Mboya. "Boundary element methods for solving inverse boundary conditions identification problems." Thesis, University of Leeds, 2008. http://etheses.whiterose.ac.uk/11283/.

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This thesis explores various features of the boundary element method (BEM) used in solving heat transfer boundary conditions identification problems. In particular, we present boundary integral equation (BIE) formulations and procedures of the numerical computation for the approximation of the boundary temperatures, heat fluxes and space, time or temperature dependent heat transfer coefficients. There are many practical heat transfer situations where such problems occur, for example in high temperature regions or hostile environments, such as in combustion chambers, steel cooling processes, etc., in which the actual method of heat transfer on the surface is unknown. In such situations the boundary condition relating the heat flux to the difference between the boundary temperature and that of the surrounding fluid is represented by an unknown function which may depend on space, time, or temperature. In these inverse heat conduction problems (IHCP), the BEM is formulated as a minimization of some functional that measures the discrepancy between the measured data, say the average temperature on a portion of the boundary or at an instant over the whole domain. The minimization provides solutions that are consistent with the data. This indicates that the BEM algorithms for the IRCP are robust, stable and predict reliable results. When the input data is noisy, we have used the truncated singular value decomposition and the Tikhonov regularisation methods to stabilise the solution of the IRCI' boundary conditions identification. Numerical approximations have been obtained and, where possible, the results obtained are compared to the analytical solutions.

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Shah, Nawazish A. "Boundary element methods for road vehicle aerodynamics." Thesis, Loughborough University, 1985. https://dspace.lboro.ac.uk/2134/26942.

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The technique of the boundary element method consists of subdividing the boundary of the field of a function into a series of discrete elements, over which the function can vary. This technique offers important advantages over domain type solutions such as finite elements and finite differences. One of the most important features of the method is the much smaller system of equations and the considerable reduction in data required to run a program. Furthermore, the method is well-suited to problems with an infinite domain. Boundary element methods can be formulated using two different approaches called the ‘direct' and the ‘indirect' methods.

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Leon, Ernesto Pineda. "Dual boundary element methods for creep fracture." Thesis, Queen Mary, University of London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435177.

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OLIVEIRA, MARIA FERNANDA FIGUEIREDO DE. "CONVENTIONAL, HYBRID AND SIMPLIFIED BOUNDARY ELEMENT METHODS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2004. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=5562@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Apresentam-se as formulações, consolidando a nomenclatura e os principais conceitos dos métodos de elementos de contorno: convencional (MCCEC), híbrido de tensões (MHTEC), híbrido de deslocamentos (MHDEC) e híbrido simplificado de tensões (MHSTEC). proposto o método híbrido simplificado de deslocamentos (MHSDEC), em contrapartida ao MHSTEC, baseando-se nas mesmas hipóteses de aproximação de tensões e deslocamentos do MHDEC e supondo que a solução fundamental em termos de tensões seja válida no contorno. Como decorrência do MHSTEC e do MHSDEC, é apresentado também o método híbrido de malha reduzida dos elementos de contorno (MHMREC), com aplicação computacionalmente vantajosa a problemas no domínio da freqüência ou envolvendo materiais não-homogêneos. A partir da investigação das equações matriciais desses métodos, são identificadas quatro novas relações matriciais, das quais uma verifica-se como válida para a obtenção dos elementos das matrizes de flexibilidade e de deslocamento que não podem ser determinados por integração ou avaliação direta. Também é proposta a correta consideração, ainda não muito bem explicada na literatura, de que forças de superfície devem ser interpoladas em função de atributos de superfície e não de atributos nodais. São apresentadas aplicações numéricas para problemas de potencial para cada método mencionado, em que é verificada a validade das novas relações matriciais.
A consolidated, unified formulation of the conventional (CCBEM), hybrid stress (HSBEM), hybrid displacement (HDBEM) and simplified hybrid stress (SHSBEM) boundary element methods is presented. As a counterpart of SHSBEM, the simplified hybrid displacement boundary element method (SHDBEM) is proposed on the basis of the same stress and displacement approximation hypotheses of the HDBEM and on the assumption that stress fundamental solutions are also valid on the boundary. A combination of the SHSBEM and the SHDBEM gives rise to a provisorily called mesh-reduced hybrid boundary element method (MRHBEM), which seems computationally advantageous when applied to frequency domain problems or non-homogeneous materials. Four new matrix relations are identified, one of which may be used to obtain the flexibility and displacement matrix coefficients that cannot be determined by integration or direct evaluation. It is also proposed the correct consideration, still not well explained in the technical literature, that traction forces should be interpolated as functions of surface and not of nodal attributes. Numerical examples of potential problems are presented for each method, in which the validity of the new matrix relations is verified.

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Zarco, Mark Albert. "Solution fo soil-structure interaction problems by coupled boundary element-finite element method /." This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06062008-164808/.

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Vu, Thu Hang. "Enhancing the scaled boundary finite element method." University of Western Australia. School of Civil and Resource Engineering, 2006. http://theses.library.uwa.edu.au/adt-WU2006.0068.

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[Truncated abstract] The scaled boundary finite element method is a novel computational method developed by Wolf and Song which reduces partial differential equations to a set of ordinary linear differential equations. The method, which is semi-analytical, is suitable for solving linear elliptic, parabolic and hyperbolic partial differential equations. The method has proved to be very efficient in solving various types of problems, including problems of potential flow and diffusion. The method out performs the finite element method when solving unbounded domain problems and problems involving stress singularities and discontinuities. The scaled boundary finite element method involves solution of a quadratic eigenproblem, the computational expense of which increases rapidly as the number of degrees of freedom increases. Consequently, to a greater extent than the finite element method, it is desirable to obtain solutions at a specified level of accuracy while using the minimum number of degrees of freedom necessary. In previous work, no systematic study had been performed so far into the use of elements of higher order, and no consideration made of p adaptivity. . . The primal problem is solved normally using the basic scaled boundary finite element method. The dual problem is solved by the new technique using the fundamental solution. A guaranteed upper error bound based on the Cauchy-Schwarz inequality is derived. A iv goal-oriented p-hierarchical adaptive procedure is proposed and implemented efficiently in the scaled boundary finite element method.

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Yan, Shu. "Efficient numerical methods for capacitance extraction based on boundary element method." Texas A&M University, 2005. http://hdl.handle.net/1969.1/3230.

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Fast and accurate solvers for capacitance extraction are needed by the VLSI industry in order to achieve good design quality in feasible time. With the development of technology, this demand is increasing dramatically. Three-dimensional capacitance extraction algorithms are desired due to their high accuracy. However, the present 3D algorithms are slow and thus their application is limited. In this dissertation, we present several novel techniques to significantly speed up capacitance extraction algorithms based on boundary element methods (BEM) and to compute the capacitance extraction in the presence of floating dummy conductors. We propose the PHiCap algorithm, which is based on a hierarchical refinement algorithm and the wavelet transform. Unlike traditional algorithms which result in dense linear systems, PHiCap converts the coefficient matrix in capacitance extraction problems to a sparse linear system. PHiCap solves the sparse linear system iteratively, with much faster convergence, using an efficient preconditioning technique. We also propose a variant of PHiCap in which the capacitances are solved for directly from a very small linear system. This small system is derived from the original large linear system by reordering the wavelet basis functions and computing an approximate LU factorization. We named the algorithm RedCap. To our knowledge, RedCap is the first capacitance extraction algorithm based on BEM that uses a direct method to solve a reduced linear system. In the presence of floating dummy conductors, the equivalent capacitances among regular conductors are required. For floating dummy conductors, the potential is unknown and the total charge is zero. We embed these requirements into the extraction linear system. Thus, the equivalent capacitance matrix is solved directly. The number of system solves needed is equal to the number of regular conductors. Based on a sensitivity analysis, we propose the selective coefficient enhancement method for increasing the accuracy of selected coupling or self-capacitances with only a small increase in the overall computation time. This method is desirable for applications, such as crosstalk and signal integrity analysis, where the coupling capacitances between some conductors needs high accuracy. We also propose the variable order multipole method which enhances the overall accuracy without raising the overall multipole expansion order. Finally, we apply the multigrid method to capacitance extraction to solve the linear system faster. We present experimental results to show that the techniques are significantly more efficient in comparison to existing techniques.

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Hamina, M. (Martti). "Some boundary element methods for heat conduction problems." Doctoral thesis, University of Oulu, 2000. http://urn.fi/urn:isbn:951425614X.

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Abstract This thesis summarizes certain boundary element methods applied to some initial and boundary value problems. Our model problem is the two-dimensional homogeneous heat conduction problem with vanishing initial data. We use the heat potential representation of the solution. The given boundary conditions, as well as the choice of the representation formula, yield various boundary integral equations. For the sake of simplicity, we use the direct boundary integral approach, where the unknown boundary density appearing in the boundary integral equation is a quantity of physical meaning. We consider two different sets of boundary conditions, the Dirichlet problem, where the boundary temperature is given and the Neumann problem, where the heat flux across the boundary is given. Even a nonlinear Neumann condition satisfying certain monotonicity and growth conditions is possible. The approach yields a nonlinear boundary integral equation of the second kind. In the stationary case, the model problem reduces to a potential problem with a nonlinear Neumann condition. We use the spaces of smoothest splines as trial functions. The nonlinearity is approximated by using the L2-orthogonal projection. The resulting collocation scheme retains the optimal L2-convergence. Numerical experiments are in agreement with this result. This approach generalizes to the time dependent case. The trial functions are tensor products of piecewise linear and piecewise constant splines. The proposed projection method uses interpolation with respect to the space variable and the orthogonal projection with respect to the time variable. Compared to the Galerkin method, this approach simplifies the realization of the discrete matrix equations. In addition, the rate of the convergence is of optimal order. On the other hand, the Dirichlet problem, where the boundary temperature is given, leads to a single layer heat operator equation of the first kind. In the first approach, we use tensor products of piecewise linear splines as trial functions with collocation at the nodal points. Stability and suboptimal L2-convergence of the method were proved in the case of a circular domain. Numerical experiments indicate the expected quadratic L2-convergence. Later, a Petrov-Galerkin approach was proposed, where the trial functions were tensor products of piecewise linear and piecewise constant splines. The resulting approximative scheme is stable and convergent. The analysis has been carried out in the cases of the single layer heat operator and the hypersingular heat operator. The rate of the convergence with respect to the L2-norm is also here of suboptimal order.

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Zarco, Mark Albert. "Solution of soil-structure interaction problems by coupled boundary element-finite element method." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/38298.

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Esterhuizen, Jacob J. B. "The evaluation of embankment stresses by coupled boundary element - finite element method." Thesis, Virginia Tech, 1993. http://hdl.handle.net/10919/42954.

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Numerical methods and specifically the finite element method have improved significantly since their introduction in the 60's. These advances were mainly in: 1) introducing higher-order elements, 2) developing effective solution schemes, 3) developing sophisticated means of modeling the constitutive behavior of geotechnical materials, and 4) introducing iteration techniques to model material non-linearity. This thesis, on the other hand, deals with the topic of modeling the boundary conditions of the finite element problem. Typically, the boundary conditions will be approximated by specifying displacement constraints. such as restraining the bottom boundary of the finite element mesh against displacements in the horizontal and vertical directions (x- and y-directions). Where bedrock or dense residual soils underlie the soft foundation soil at a relatively shallow depth, this is a good assumption. However. when soft soil is encountered for large depths, the assumption of zero movement constraints for a mesh boundary at a shallower depth than the actual bedrock will result in a serious underestimation of stresses and displacements. By coupling boundary elements to the finite elements and using them to model the infinite extent of the foundation soil, a more realistic answer is obtained. Employing the coupled boundary element - finite element method, four cases were analyzed and the results compared to values of the pure finite element method. The results show that the coupled method indeed yielded higher stress- and displacement-values, indicating that the pure finite element method underestimates stresses and displacements when modeling very deep soils.

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Nesemann, Leo [Verfasser]. "Finite element and boundary element methods for contact with adhesion / Leo Nesemann." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2011. http://d-nb.info/1013365542/34.

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Chidgzey, Steven R. "Advances in the development of the scaled boundary method for applications in fracture mechanics." University of Western Australia. School of Civil and Resource Engineering, 2007. http://theses.library.uwa.edu.au/adt-WU2007.0176.

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[Truncated abstract] The scaled boundary method is a powerful, though undervalued, computational analysis method. The complex mathematics of the original derivation of the method has rendered it unattractive to researchers. However, the method has proven more efficient than conventional computational analysis methods for problems involving unbounded domains and for problems involving stress singularities. The advantages of the scaled boundary method in dealing with stress singularities make it uniquely suited to the analysis of fracture mechanics problems. This study will extend the capabilities of the scaled boundary method, exploring fracture mechanics applications in particular. Only benchmark elastostatic fracture mechanics problems are analysed as the focus of this work is the development of the scaled boundary method. It will be demonstrated that the intimidating mathematics of the method can be distilled into an elegant method which offers considerable advantages when used in the analysis of crack problems. This thesis will argue that the advantages of the scaled boundary method make it more valuable than is generally perceived and that coming to grips with the sometimes intimidating method is worthwhile. In this study, a significant contribution is made to the development of the scaled boundary method with a number of advances. The scaled boundary method is used to determine the higher order terms in asymptotic crack tip fields. The higher order terms play an important role in characterising the behaviour of cracked structures, but can only be evaluated analytically for a few simple cases. The higher order terms for a number of crack configurations are calculated using the scaled boundary method. Excellent agreement with results obtained from the literature is demonstrated. A penalty formulation is developed for use with a recently developed solution procedure for the scaled boundary method. The new solution procedure is based on the theory of matrix functions and the real Schur decomposition. ... A study is presented of error estimation and adaptivity procedures for use with the scaled boundary method when a reduced set of base functions is used. The error estimation procedure based on the superconvergent patch recovery technique and the error estimation procedure based on reference solutions are modified for use with the scaled boundary method when a reduced set of base functions is used. The use of a reduced set of base functions in an adaptivity procedure for the scaled boundary method is trialled. Adaptivity based solely on the set of base functions is shown to be inefficient. In contrast, the judicious use of a reduced set of base functions is shown to improve the overall efficiency of other adaptivity procedures.

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Peng, Xuan. "Isogeometric boundary element methods for linear elastic fracture mechanics." Thesis, Cardiff University, 2016. http://orca.cf.ac.uk/92543/.

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We develop in this work a procedure for obtaining the fatigue life of complex structures directly from Computer-Aided Design (CAD) data, without any mesh generation or regeneration as the cracks evolve. The method relies on a standard isogeometric boundary element method (IGABEM) where the same basis functions are used to both describe the geometry of the component and approximate the displacement and traction fields. The contributions of this work include: (1) Dual boundary integral equations have been applied to model 2D/3D fracture problems in the framework of IGA and that such simulations require no meshing or remeshing in the conventional sense; (2) Graded knot insertion and partition of unity enrichment have been used to capture the stress singularity around the crack tip. The contour-integral based methods and the virtual crack closure integral method are adopted to extract stress intensity factors in the framework of IGABEM; (3) Modifications on the singularity subtraction technique for (hyper-)singular integration are proposed to enhance the quadrature on distorted elements which commonly arise in IGA; (4)ANURBS-based geometry modification algorithm is developed to simulate fatigue crack growth in 2D/3D. smooth crack trajectory and crack front are obtained; (5) An implementation on trimmed NURBS is realized based on a localized double mapping method to perform the quadrature on trimmed elements. A phantom element method is subsequently proposed to model the surface crack (breaking crack) problem and the displacement discontinuity can be introduced without any reparametrization on the original patch.

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Vartiainen, Markku Juhani. "Singular boundary element methods for the hyperbolic wave equation." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621821.

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雷哲翔 and Zhexiang Lei. "Time domain boundary element method & its applications." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31233703.

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Lei, Zhexiang. "Time domain boundary element method & its applications /." [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13570365.

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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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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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Arjunon, Sivakkumar. "P-version refinement studies in the boundary element method a dissertation presented to the faculty of the Graduate School, Tennessee Technological University /." Click to access online, 2009. http://proquest.umi.com/pqdweb?index=19&sid=2&srchmode=1&vinst=PROD&fmt=6&startpage=-1&clientid=28564&vname=PQD&RQT=309&did=1786737301&scaling=FULL&ts=1250860988&vtype=PQD&rqt=309&TS=1250861000&clientId=28564.

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Silveira, Richard John. "A dual boundary and finite element method for fluid flow." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708272.

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Tang, W. "A generalized approach for transforming domain integrals into boundary integrals in boundary element methods." Thesis, University of Southampton, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378981.

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Chu, Chin-keung. "Parallel computation for time domain boundary element method /." Hong Kong : University of Hong Kong, 1999. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20565574.

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Weggler, Lucy Verfasser], and Sergej [Akademischer Betreuer] [Rjasanow. "High order boundary element methods / Lucy Weggler. Betreuer: Sergej Rjasanow." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2012. http://d-nb.info/1051586801/34.

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Bolton, Matthew Robert. "Acoustic scattering using boundary element methods with application to colloids." Thesis, University of East Anglia, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.514206.

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Berger, Hans-Uwe. "Inverse Problems in Soft Tissue Elastography using Boundary Element Methods." Thesis, University of Canterbury. Mechanical Engineering, 2009. http://hdl.handle.net/10092/4413.

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Elastography is an emerging functional imaging technique of current clinical research interest due to a direct relation between mechanical material parameters, especially the tissue stiffness, and tissue pathologies such as cancer. Digital Image Elasto-Tomography (DIET) is a new method that aims to develop elastographic techniques and create a simplified, improved breast cancer screening process. The elastic material information of breast tissue is reconstructed in the DIET concept from mechanically excited steady-state harmonic motion observed on the surface of the breast. While this inversion process has been traditionally approached using finite element methods, this surface-orientated problem is naturally suited to the use of Boundary Element Methods (BEMs) requiring the discretization only on the surface of the domain and on the interface of a potential inclusion. As only approximate information is available about breast tissue material parameters, this thesis presents the development of BEM based inverse problem algorithms suitable for the reconstruction of all material parameters in a proportionally damped isotropic linear elastic solid, where only the material density is known. The highly nonlinear identification process of a potential inclusion is treated through the combination of a systematic Grid-Search with gradient descent techniques. This algorithm is extended to a three-step algorithm that performs a background material parameter estimation before the subsequent identification of an inclusion and thus provides a confident indication for the differentiation between cancerous and healthy breast tissue. The development of these algorithms is illustrated by several simulation studies highlighting important reconstruction behaviors relevant to the elastographic inverse problem. A first experimental test on a silicon based breast phantom is presented.

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NOVELINO, LARISSA SIMOES. "APPLICATION OF FAST MULTIPOLE TECHNIQUES IN THE BOUNDARY ELEMENT METHODS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=37003@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Este trabalho visa à implementação de um programa de elementos de contorno para problemas com milhões de graus de liberdade. Isto é obtido com a implementação do Método Fast Multipole (FMM), que pode reduzir o número de operações, para a solução de um problema com N graus de liberdade, de O(N(2)) para O(NlogN) ou O(N). O uso de memória também é reduzido, por não haver o armazenamento de matrizes de grandes dimensões como no caso de outros métodos numéricos. A implementação proposta é baseada em um desenvolvimento consistente do convencional, Método de colocação dos elementos de contorno (BEM) – com conceitos provenientes do Hibrido BEM – para problemas de potencial e elasticidade de larga escala em 2D e 3D. A formulação é especialmente vantajosa para problemas de topologia complicada ou que requerem soluções fundamentais complicadas. A implementação apresentada, usa um esquema para expansões de soluções fundamentais genéricas em torno de níveis hierárquicos de polos campo e fonte, tornando o FMM diretamente aplicável para diferentes soluções fundamentais. A árvore hierárquica dos polos é construída a partir de um conceito topológico de superelementos dentro de superelementos. A formulação é inicialmente acessada e validada em termos de um problema de potencial 2D. Como resolvedores iterativos não são necessários neste estágio inicial de simulação numérica, podese acessar a eficiência relativa à implementação do FMM.
This work aims to present an implementation of a boundary element solver for problems with millions of degrees of freedom. This is achieved through a Fast Multipole Method (FMM) implementation, which can lower the number of operations for solving a problem, with N degrees of freedom, from O(N(2)) to O(NlogN) or O(N). The memory usage is also very small, as there is no need to store large matrixes such as required by other numerical methods. The proposed implementations are based on a consistent development of the conventional, collocation boundary element method (BEM) - with concepts taken from the variationally-based hybrid BEM - for large-scale 2D and 3D problems of potential and elasticity. The formulation is especially advantageous for problems of complicated topology or requiring complicated fundamental solutions. The FMM implementation presented in this work uses a scheme for expansions of a generic fundamental solution about hierarchical levels of source and field poles. This makes the FMM directly applicable to different kinds of fundamental solutions. The hierarchical tree of poles is built upon a topological concept of superelements inside superelements. The formulation is initially assessed and validated in terms of a simple 2D potential problem. Since iterative solvers are not required in this first step of numerical simulations, an isolated efficiency assessment of the implemented fast multipole technique is possible.

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Reinarz, Anne. "Sparse space-time boundary element methods for the heat equation." Thesis, University of Reading, 2015. http://centaur.reading.ac.uk/49315/.

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The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(hₓ-(d-1)), when the solution of the linear system is performed with linear complexity. We show that the discretisation with a wavelet basis leads to a numerically sparse matrix. Further, we show that this matrix can be compressed without losing accuracy of the underlying Galerkin scheme. This matrix compression reduces the number of non-zero matrix entries from O(N2) to O(N). Thus, we can indeed solve the linear system in linear time. It has been shown theoretically that using sparse grid methods leads to considerably higher convergence rates in the energy norm of the problem. In this work we will show that the convergence can be further improved for some choices of polynomial degrees by using more general sparse grid spaces. We also give numerical results to verify the theoretical bounds from [Chernov, Schwab, 2013].

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Peake, Michael John. "Enriched and isogeometric boundary element methods for acoustic wave scattering." Thesis, Durham University, 2014. http://etheses.dur.ac.uk/10655/.

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This thesis concerns numerical acoustic wave scattering analysis. Such problems have been solved with computational procedures for decades, with the boundary element method being established as a popular choice of approach. However, such problems become more computationally expensive as the wavelength of an incident wave decreases; this is because capturing the oscillatory nature of the incident wave and its scattered field requires increasing numbers of nodal variables. Authors from mathematical and engineering backgrounds have attempted to overcome this problem using a wide variety of procedures. One such approach, and the approach which is further developed in this thesis, is to include the fundamental character of wave propagation in the element formulation. This concept, known as the Partition of Unity Boundary Element Method (PU-BEM), has been shown to significantly reduce the computational burden of wave scattering problems. This thesis furthers this work by considering the different interpolation functions that are used in boundary elements. Initially, shape functions based on trigonomet- ric functions are developed to increase continuity between elements. Following that, non-uniform rational B-splines, ubiquitous in Computer Aided Design (CAD) soft- ware, are used in developing an isogeometric approach to wave scattering analysis of medium-wave problems. The enriched isogeometric approach is named the eXtended Isogeometric Boundary Element Method (XIBEM). In addition to the work above, a novel algorithm for finding a uniform placement of points on a unit sphere is presented. The algorithm allows an arbitrary number of points to be chosen; it also allows a fixed point or a bias towards a fixed point to be used. This algorithm is used for the three-dimensional acoustic analyses in this thesis. The new techniques developed within this thesis significantly reduce the number of degrees of freedom required to solve a problem to a certain accuracy—this reduc- tion is more than 70% in some cases. This reduces the number of equations that have to be solved and reduces the amount of integration required to evaluate these equations.

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朱展強 and Chin-keung Chu. "Parallel computation for time domain boundary element method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31220678.

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Fronk, Thomas Harris. "Fully-coupled fluid-structure analysis of a baffled rectangular orthotropic plate using the boundary element and finite element methods." Diss., This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-07282008-134729/.

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Zhang, Hui. "Image-based boundary element computation of three-dimensional potential problems." Online access for everyone, 2008. http://www.dissertations.wsu.edu/Thesis/Summer2008/h_zhang_072308.pdf.

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KEUM, BANGYONG. "ANALYSIS OF 3-D CONTACT MECHANICS PROBLEMS BY THE FINITE ELEMENT AND BOUNDARY ELEMENT METHODS." University of Cincinnati / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1054815631.

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Bayliss, Martin. "The numerical modelling of elastomers." Thesis, Cranfield University, 2003. http://hdl.handle.net/1826/87.

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This thesis reports onreview and research work carried out on the numerical analysis of elastomers. The two numerical techniques investigated for this purpose are the finite and boundary element methods. The finite element method is studied so that existing theory is used to develop a finite element code both to review the finite element method as applied to the stress analysis of elastomers and to provide a comparison of results and numerical approach with the boundary element method. The research work supported on in this thesis covers the application of the boundary element method to the stress analysis of elastomers. To this end a simplified regularization approach is discussed for the removal of strong and hypersingularities generated in the system on non-linear boundary integral equations. The necessary programming details for the implementation of the boundary element method are discussed based on the code developed for this research. Both the finite and boundary element codes developed for this research use the Mooney-Rivlin material model as the strain energy based constitutive stress strain function. For validation purposes four test cases are investigated. These are the uni-axial patch test, pressurized thick wall cylinder, centrifugal loading of a rotating disk and the J-Integral evaluation for a centrally cracked plate. For the patch test and pressurized cylinder, both plane stress and strain have been investigated. For the centrifugal loading and centrally cracked plate test cases only plane stress has been investigated. For each test case the equivalent results for an equivalent FEM program mesh have been presented. The test results included in this thesis prove that the FE and BE derivations detailed in this work are correct. Specifically the simplified domain integral singular and hyper-singular regularization approach was shown to lead to accurate results for the test cases detailed. Various algorithm findings specific to the BEM implementation of the theory are also discussed.

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Ben, Hamdin Hanya Abdusalam Mohamed. "Boundary element and transfer operator methods for multi-component wave systems." Thesis, University of Nottingham, 2012. http://eprints.nottingham.ac.uk/12446/.

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In this thesis, exact and semiclassical approaches are derived for predicting wave energy distributions in coupled cavities with variable material properties. These approaches are attractive because they can be extended to more complex built-up systems. For the exact treatment, we describe a multi-component boundary element method. We point out that depending on the boundary conditions and the number of interfaces between sub-components, it may be advantageous to use a normal derivative method to set up the integral kernels. We describe how the arising hypersingular integral kernels can be reduced to weakly singular integral and then using the piecewise constant collocation method. The normal derivative method can be used to minimise the number of weakly-singular integrals thus leading to BEM formulations which are easier to handle. The second component of this work concerns a novel approach for finding an exact formulation of the transfer operator. This approach is demonstrated successfully for a disc with boundary conditions changing discontinuously across the boundary. Such an operator captures the diffraction effects related to the change of boundary conditions. So it incorporates boundary effects such as diffraction and surface waves. A comparison between the exact results from the BEM against the exact transfer operator shows good agreement between both categories. Such an exact operator converges to the semiclassical Bogomolny transfer operator in the semiclassical limit. Having seen how the exact transfer operator behaves for a unit disc, a similar approach is adapted for the coupled cavity configuration resulting in the semiclassical transfer operator. Our formulation for the transfer operator is applicable not only for the quantization of a system, but also to recover the Green function.

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Lindkvist, Gaute. "Indirect boundary element methods for modelling bubbles under three dimensional deformation." Thesis, Deaprtment of Engineering Systems and Management, 2009. http://hdl.handle.net/1826/3098.

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The nonlinear behaviour of gas and vapour bubbles is a complex phenomenon which plays a signi cant role in many natural and man-made processes. For example, bubbles excited by an acoustic eld play important roles in lithotripsy, drug delivery, ultrasonic imaging, surface cleaning and give rise to the phenomenon of sonoluminescence (light emission from a bubble excited by sound). In such contexts, the oscillation of even a single bubble is not yet fully understood, let alone the behaviour of multiple bubbles interacting with each other. An essential part of understanding such problems is un- derstanding the complex and sometimes unpredictable coupling between the oscillation of the bubble volume and the bubble shape, a problem requiring experimental research, theoretical work and numerical studies. In this Thesis we focus on numerical simulation of a single gas bubble oscillating in a free liquid. Previously, such numerical simulations have al- most exclusively assumed axisymmetry and small amplitude oscillations. To avoid these assumptions we build upon and extend previous boundary ele- ment methods used for three dimensional simulations of other bubble prob- lems. We use high order elements and parallel processing to yield an indirect boundary element method capable of capturing ne surface e ects on three dimensional bubbles subjected to surface tension, over extended periods of time. We validate the method against the classical Rayleigh-Plesset equation for spherical oscillation problems before validating the indirect boundary el- ement method and the method used by Shaw (2006), against each other, on several small amplitude axisymmetric oscillation problems. We then proceed to study near-resonant non-axisymmetric shape oscillations of order 2 and 4 and the e ect these oscillations have on higher order modes, with a level of detail we believe has not been achieved in a non-axisymmetric study before. We also con rm some predictions made by Pozrikidis' on resonant interac- tions between the second order modes and the volume mode in addition. Finally we study the spherical instability of a bubble trapped in a uniform acoustic eld, demonstrating, as expected, that instabilities show up in all resonant shape modes, including non-axisymmetric ones.

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Druma, Calin. "Formulation of steady-state and transient potential problems using boundary elements." Ohio : Ohio University, 1999. http://www.ohiolink.edu/etd/view.cgi?ohiou1175886094.

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Golan, Lawrence P. "Thermal analysis of sliding contact systems using the boundary element method." Thesis, This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-11242009-020117/.

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Sheng, Ni. "Trefftz boundary and polygonal finite element methods for piezoelectric and ferroelectric analyses." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B31483434.

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Sheng, Ni, and 盛妮. "Trefftz boundary and polygonal finite element methods for piezoelectric and ferroelectric analyses." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B31483434.

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Cooke, Tristrom Peter. "Some problems in anisotropic elasticity /." Title page, contents and summary only, 1998. http://web4.library.adelaide.edu.au/theses/09PH/09phc773.pdf.

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Moody, R. O. "The numerical solution of moving-boundary problems using moving-finite-element methods." Thesis, University of Reading, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383463.

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Geraci, Giorgio. "Boundary element methods for cohesive thermo-mechanical damage and micro-cracking evolution." Thesis, Imperial College London, 2018. http://hdl.handle.net/10044/1/63826.

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In this thesis, Boundary Element Methods (BEM) are developed for micro-mechanic cohesive non linear problems. Modelling of intergranular and transgranular damage and micro-cracking evolution in polycrystalline materials is presented for different physical engineering problems and loading conditions: mechanical and thermo-mechanical applications are considered in the context of micromechanics. Throughout the thesis the different models are based on a multi-region boundary element approach combined with the dual boundary element formulation. The polycrystalline microstructures are generated with Voronoi tessellations, which well represent statistically the morphology of multi-grain materials; the formulation is able to consider the stochastic effect of each grain’s crystal anisotropy within the whole aggregate. Linear cohesive laws are used for assessing initiation and propagation of damage on intergranular and transgranular surfaces; moreover different physical assumptions on the cohesive models are investigated in order to guarantee energetic independence between mode I and II of fracture as well as inter- and trans-granular damage. Transgranular surfaces are introduced during the numerical simulation, so that the benefits of BEM are maintained and any internal damage propagation is not affected by initial discretization: the nucleation is based on a stress criterion. Upon cohesive failure, non linear frictional contact analysis is introduced. The effect of thermal loading is then introduced to model stress generation and damage propagation due to steady state and transient thermal loading. The cohesive model is updated to take into account the new thermal fields. Damage dependent Fourier’s law is implemented to model cohesive surfaces as heat barriers. Investigations on the effect of grain size, critical fracture energies and loading conditions are done. The presented formulations are shown to provide efficient modelling of the aforementioned engineering applications and their accuracy is compared throughout the thesis with analytical, numerical and experimental findings, where available.

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Ullah, Baseer. "Structural topology optimisation based on the boundary element and level set methods." Thesis, Durham University, 2014. http://etheses.dur.ac.uk/10659/.

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The research work presented in this thesis is related to the development of structural optimisation algorithms based on the boundary element and level set methods for two and three-dimensional linear elastic problems. In the initial implementation, a stress based evolutionary structural optimisation (ESO) approach has been used to add and remove material simultaneously for the solution of two-dimensional optimisation problems. The level set method (LSM) is used to provide an implicit description of the structural geometry, which is also capable of automatically handling topological changes, i.e. holes merging with each other or with the boundary. The classical level set based optimisation methods are dependent on initial designs with pre-existing holes. However, the proposed method automatically introduces internal cavities utilising a stress based hole insertion criteria, and thereby eliminates the use of initial designs with pre-existing holes. A detailed study has also been carried out to investigate the relationship between a stress and topological derivative based hole insertion criteria within a boundary element method (BEM) and LSM framework. The evolving structural geometry (i.e. the zero level set contours) is represented by non-uniform rational b-splines (NURBS), providing a smooth geometry throughout the optimisation process and completely eliminating jagged edges. The BEM and LSM are further combined with a shape sensitivity approach for the solution of minimum compliance problems in two-dimensions. The proposed sensitivity based method is capable of automatically inserting holes during the optimisation process using a topological derivative approach. In order to investigate the associated advantages and disadvantages of the evolutionary and sensitivity based optimisation methods a comparative study has also been carried out. There are two advantages associated with the use of LSM in three-dimensional topology optimisation. Firstly, the LSM may readily be applied to three-dimensional space, and it is shown how this can be linked to a 3D BEM solver. Secondly, the holes appear automatically through the intersection of two surfaces moving towards each other. Therefore, the use of LSM eliminates the need for an additional hole insertion mechanism as both shape and topology optimisation can be performed at the same time. A complete algorithm is proposed and tested for BEM and LSM based topology optimisation in three-dimensions. Optimal geometries compare well against those in the literature for a range of benchmark examples.

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Shah, Jimit. "Vibro-Acoustic Studies on Damped Panels Using Finite and Boundary Element Methods." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1420207337.

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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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金吳根 and Wugen Jin. "Trefftz method and its application in engineering." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1991. http://hub.hku.hk/bib/B31232255.

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Jin, Wugen. "Trefftz method and its application in engineering /." [Hong Kong : University of Hong Kong], 1991. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13009540.

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Zhao, Kezhong. "A domain decomposition method for solving electrically large electromagnetic problems." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1189694496.

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Dissertations / Theses on the topic 'Boundary element methods'

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