Relevant bibliographies by topics / Localised boundary-domain integral equation

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Academic literature on the topic 'Localised boundary-domain integral equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 February 2022

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Journal articles on the topic "Localised boundary-domain integral equation"

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Chkadua, Otar, Sergey E. Mikhailov, and David Natroshvili. "Localized boundary-domain integral equation formulation for mixed type problems." Georgian Mathematical Journal 17, no. 3 (2010): 469–94. http://dx.doi.org/10.1515/gmj.2010.025.

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Abstract Some modifed direct localized boundary-domain integral equations (LBDIEs) systems associated with the mixed boundary value problem (BVP) for a scalar “Laplace” PDE with variable coefficient are formulated and analyzed. The main results established in the paper are the LBDIEs equivalence to the original variable-coefficient BVPs and the invertibility of the corresponding localized boundary-domain integral operators in appropriately chosen function spaces.
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Chkadua, Otar, Sergey E. Mikhailov, and David Natroshvili. "Singular localised boundary‐domain integral equations of acoustic scattering by inhomogeneous anisotropic obstacle." Mathematical Methods in the Applied Sciences 41, no. 17 (2018): 8033–58. http://dx.doi.org/10.1002/mma.5268.

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Rungamornrat, Jaroon, and Sakravee Sripirom. "Stress Analysis of Three-Dimensional Media Containing Localized Zone by FEM-SGBEM Coupling." Mathematical Problems in Engineering 2011 (2011): 1–27. http://dx.doi.org/10.1155/2011/702082.

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This paper presents an efficient numerical technique for stress analysis of three-dimensional infinite media containing cracks and localized complex regions. To enhance the computational efficiency of the boundary element methods generally found inefficient to treat nonlinearities and non-homogeneous data present within a domain and the finite element method (FEM) potentially demanding substantial computational cost in the modeling of an unbounded medium containing cracks, a coupling procedure exploiting positive features of both the FEM and a symmetric Galerkin boundary element method (SGBEM)
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Mikhailov, S. E., and I. S. Nakhova. "Mesh-based numerical implementation of the localized boundary-domain integral-equation method to a variable-coefficient Neumann problem." Journal of Engineering Mathematics 51, no. 3 (2005): 251–59. http://dx.doi.org/10.1007/s10665-004-6452-0.

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Keeler, J. S., B. J. Binder, and M. G. Blyth. "On the critical free-surface flow over localised topography." Journal of Fluid Mechanics 832 (October 26, 2017): 73–96. http://dx.doi.org/10.1017/jfm.2017.639.

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Flow over bottom topography at critical Froude number is examined with a focus on steady, forced solitary wave solutions with algebraic decay in the far field, and their stability. Using the forced Korteweg–de Vries (fKdV) equation the weakly nonlinear steady solution space is examined in detail for the particular case of a Gaussian dip using a combination of asymptotic analysis and numerical computations. Non-uniqueness is established and a seemingly infinite set of steady solutions is uncovered. Non-uniqueness is also demonstrated for the fully nonlinear problem via boundary-integral calcula
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Münch, Arnaud. "Optimal Internal Dissipation of a Damped Wave Equation Using a Topological Approach." International Journal of Applied Mathematics and Computer Science 19, no. 1 (2009): 15–38. http://dx.doi.org/10.2478/v10006-009-0002-x.

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Optimal Internal Dissipation of a Damped Wave Equation Using a Topological ApproachWe consider a linear damped wave equation defined on a two-dimensional domain Ω, with a dissipative term localized in a subset ω. We address the shape design problem which consists in optimizing the shape of ω in order to minimize the energy of the system at a given timeT. By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at timeTwith respect to the variation in ω. Expressed as a boundary integral on ∂ω, this derivative is then used as an advection velocity in a H
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Klettner, Christian A., and Ian Eames. "Momentum and energy of a solitary wave interacting with a submerged semi-circular cylinder." Journal of Fluid Mechanics 708 (August 10, 2012): 576–95. http://dx.doi.org/10.1017/jfm.2012.333.

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AbstractThe interaction of a weakly viscous solitary wave with a submerged semi-circular cylinder was examined using high-resolution two-dimensional numerical calculations. Two simulations were carried out: (a) as a baseline calculation, the propagation of a solitary wave over uniform depth; and (b) a solitary wave interacting with a submerged semi-circular cylinder. Large-scale simulations were performed to resolve the viscous boundary layers on the free surface, bottom and around the obstacle. Integral measures such as momentum and energy are analysed and compared against analytical approxim
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Vellingiri, Rajagopal, Dmitri Tseluiko, and Serafim Kalliadasis. "Absolute and convective instabilities in counter-current gas–liquid film flows." Journal of Fluid Mechanics 763 (December 11, 2014): 166–201. http://dx.doi.org/10.1017/jfm.2014.667.

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AbstractWe consider a thin liquid film flowing down an inclined plate in the presence of a counter-current turbulent gas. By making appropriate assumptions, Tseluiko & Kalliadasis (J. Fluid Mech., vol. 673, 2011, pp. 19–59) developed low-dimensional non-local models for the liquid problem, namely a long-wave (LW) model and a weighted integral-boundary-layer (WIBL) model, which incorporate the effect of the turbulent gas. By utilising these models, along with the Orr–Sommerfeld problem formulated using the full governing equations for the liquid phase and associated boundary conditions, we
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Chang, Chia-Hao, Ching-Sheng Huang, and Hund-Der Yeh. "Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers." Hydrology and Earth System Sciences 20, no. 3 (2016): 1225–39. http://dx.doi.org/10.5194/hess-20-1225-2016.

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Abstract. Most previous solutions for groundwater flow induced by localized recharge assumed either aquifer incompressibility or two-dimensional flow in the absence of the vertical flow. This paper develops a new three-dimensional flow model for hydraulic head variation due to localized recharge in a rectangular unconfined aquifer with four boundaries under the Robin condition. A governing equation describing spatiotemporal head distributions is employed. The first-order free-surface equation with a source term defining a constant recharge rate over a rectangular area is used to depict water t
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Chang, C. H., C. S. Huang, and H. D. Yeh. "Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers." Hydrology and Earth System Sciences Discussions 12, no. 11 (2015): 12247–80. http://dx.doi.org/10.5194/hessd-12-12247-2015.

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Abstract. Most previous solutions for groundwater flow induced by localized recharge assumed either aquifer incompressibility or two-dimensional flow in the absence of the vertical flow. This paper develops a new three-dimensional flow model for hydraulic head variation due to localized recharge in a rectangular unconfined aquifer with four boundaries under the Robin condition. A governing equation for describing the head distribution is employed. The first-order free surface equation with a source term defining a constant recharge rate over a rectangular area is used to depict water table mov
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Dissertations / Theses on the topic "Localised boundary-domain integral equation"

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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/LBDID
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Langdon, Stephen. "Domain embedding boundary integral equation methods and parabolic PDEs." Thesis, University of Bath, 1999. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299654.

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Atle, Andreas. "Numerical approximations of time domain boundary integral equation for wave propagation." Licentiate thesis, KTH, Numerical Analysis and Computer Science, NADA, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1682.

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<p>Boundary integral equation techniques are useful in thenumerical simulation of scattering problems for wave equations.Their advantage over methods based on partial di.erentialequations comes from the lack of phase errors in the wavepropagation and from the fact that only the boundary of thescattering object needs to be discretized. Boundary integraltechniques are often applied in frequency domain but recentlyseveral time domain integral equation methods are beingdeveloped.</p><p>We study time domain integral equation methods for thescalar wave equation with a Galerkin discretization of twod
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Fresneda-Portillo, Carlos. "Boundary-domain integral equation systems for the Stokes system with variable viscosity and diffusion equation in inhomogeneous media." Thesis, Brunel University, 2016. http://bura.brunel.ac.uk/handle/2438/14521.

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The importance of the Stokes system stems from the fact that the Stokes system is the stationary linearised form of the Navier Stokes system [Te01, Chapter1]. This linearisation is allowed when neglecting the inertial terms at a low Reinolds numbers Re << 1. The Stokes system essentially models the behaviour of a non - turbulent viscous fluid. The mixed interior boundary value problem related to the compressible Stokes system is reduced to two different BDIES which are equivalent to the original boundary value problem. These boundary-domain integral equation systems (BDIES) can be expressed in
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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 co
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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 co
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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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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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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 equa
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Dély, Alexandre. "Computational strategies for impedance boundary condition integral equations in frequency and time domains." Thesis, Ecole nationale supérieure Mines-Télécom Atlantique Bretagne Pays de la Loire, 2019. http://www.theses.fr/2019IMTA0135.

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L'équation intégrale du champ électrique (EFIE) est très utilisée pour résoudre des problèmes de diffusion d'ondes électromagnétiques grâce à la méthode aux éléments de frontière (BEM). En domaine fréquentiel, les systèmes matriciels émergeant de la BEM souffrent, entre autres, de deux problèmes de mauvais conditionnement : l'augmentation du nombre d'inconnues et la diminution de la fréquence entrainent l'accroissement du nombre de conditionnement. En conséquence, les solveurs itératifs requièrent plus d'itérations pour converger vers la solution, voire ne convergent pas du tout. En domaine te
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Book chapters on the topic "Localised boundary-domain integral equation"

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Qamar, M. A., R. T. Fenner, and A. A. Becker. "Application of the Boundary Integral Equation (Boundary Element) Method to Time Domain Transient Heat Conduction Problems." In Boundary Integral Methods. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-85463-7_43.

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Chkadua, O., S. E. Mikhailov, and D. Natroshvili. "Analysis of Some Localized Boundary–Domain Integral Equations for Transmission Problems with Variable Coefficients." In Integral Methods in Science and Engineering. Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8238-5_10.

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Beshley, Andriy, Roman Chapko, and B. Tomas Johansson. "A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients." In Trends in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04459-6_47.

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Ando, Ryosuke. "On Applications of Fast Domain Partitioning Method to Earthquake Simulations with Spatiotemporal Boundary Integral Equation Method." In Mathematical Analysis of Continuum Mechanics and Industrial Applications II. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6283-4_8.

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Hsiao, George C., Ernst P. Stephan, and Wolfgang L. Wendland. "An integral equation formulation for a boundary value problem of elasticity in the domain exterior to an arc." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0076269.

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Amangaliyeva, Meiramkul M., Muvasharkhan T. Jenaliyev, Minzilya T. Kosmakova, and Murat I. Ramazanov. "On the Solvability of Nonhomogeneous Boundary Value Problem for the Burgers Equation in the Angular Domain and Related Integral Equations." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67053-9_12.

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Aigulim, Bayegizova, and Dadayeva Assiyat. "Boundary Integral Equations of no Stationary Boundary Value Problems for the Klein-Gordon Equation." In Mathematical Theorems - Boundary Value Problems and Approximations. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.91693.

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The non-stationary boundary value problems for Klein-Gordon equation with Dirichlet or Neumann conditions on the boundary of the domain of definition are considered; a uniqueness of boundary value problems is proved. Based on the generalized functions method, boundary integral equations method is developed to solve the posed problems in strengths of shock waves. Dynamic analogs of Green’s formulas for solutions in the space of generalized functions are obtained and their regular integral representations are constructed in 2D and 3D over space cases. The singular boundary integral equations are obtained which resolve these tasks.
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Lee, Jungki. "Volume Integral Equation Method (VIEM)." In Advances in Computers and Information in Engineering Research, Volume 2. ASME, 2021. http://dx.doi.org/10.1115/1.862025_ch4.

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A number of analytical techniques are available for the stress analysis of inclusion problems when the geometries of inclusions are simple (e.g., cylindrical, spherical or ellipsoidal) and when they are well separated [9, 41, 52]. However, these approaches cannot be applied to more general problems where the inclusions are anisotropic and arbitrary in shape, particularly when their concentration is high. Thus, stress analysis of heterogeneous solids or analysis of elastic wave scattering problems in heterogeneous solids often requires the use of numerical techniques based on either the finite element method (FEM) or the boundary integral equation method (BIEM). However, these methods become problematic when dealing with elastostatic problems or elastic wave scattering problems in unbounded media containing anisotropic and/or heterogeneous inclusions of arbitrary shapes. It has been demonstrated that the volume integral equation method (VIEM) can overcome such difficulties in solving a large class of inclusion problems [6,10,20,21,28–30]. One advantage of the VIEM over the BIEM is that it does not require the use of Green’s functions for anisotropic inclusions. Since the elastodynamic Green’s functions for anisotropic media are extremely difficult to calculate, the VIEM offers a clear advantage over the BIEM. In addition, the VIEM is not sensitive to the geometry or concentration of the inclusions. Moreover, in contrast to the finite element method, where the full domain needs to be discretized, the VIEM requires discretization of the inclusions only.
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Conference papers on the topic "Localised boundary-domain integral equation"

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Manolis, G. D., and C. G. Panagiotopoulos. "Velocity-based boundary integral equation formulation in the time domain." In BEM/MRM 2009. WIT Press, 2009. http://dx.doi.org/10.2495/be090241.

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Cheng-Yi Tian, Yan Shi, and Long Li. "Hybridized discontinuous Galerkin time domain method with boundary integral equation method." In 2016 Progress in Electromagnetic Research Symposium (PIERS). IEEE, 2016. http://dx.doi.org/10.1109/piers.2016.7734317.

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AVIGAL, M., and J. E. STEINBERG. "BOUNDARY INTEGRAL METHOD FOR THE LAPLACE EQUATION IN A SLIT DOMAIN." In Proceedings of the Fourth International Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814291071_0065.

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Hu, Fang Q. "Further development of a time domain boundary integral equation method for aeroacoustic scattering computations." In 20th AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-3194.

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Hu, Fang Q., and Michelle E. Pizzo. "On the assessment of acoustic scattering and shielding by time domain boundary integral equation solutions." In 22nd AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics, 2016. http://dx.doi.org/10.2514/6.2016-2779.

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Rodio, Michelle E., Fang Q. Hu, and Douglas M. Nark. "Investigating the Numerical Stability of a Time-Domain Boundary Integral Equation with Impedance Boundary Condition for Simulating Sound Absorption of Lined Bodies." In 25th AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-2416.

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Hu, Fang Q., Michelle E. Pizzo, and Douglas M. Nark. "A new formulation of time domain boundary integral equation for acoustic wave scattering in the presence of a uniform mean flow." In 23rd AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics, 2017. http://dx.doi.org/10.2514/6.2017-3510.

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Ma, Jianfeng, Joshua David Summers, and Paul F. Joseph. "Meshless Integral Method for Analysis of Elastoplastic Geotechnical Materials." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29069.

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The meshless integral method based on regularized boundary equation [1][2] is extended to analyze elastoplastic geotechnical materials. In this formulation, the problem domain is clouded with a node set using automatic node generation. The sub-domain and the support domain related to each node are also generated automatically using algorithms developed for this purpose. The governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain and the moving least-squares approximation is employed for meshless function approximation. The geotechnical materials a
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Ma, Jianfeng, Joshua David Summers, and Paul F. Joseph. "Application of Meshless Integral Method to Metal Forming." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29066.

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In this paper, the meshless integral method based on the regularized boundary integral equation [1] is applied to analyze the metal forming processes characteristic with large deformation. Using Green-Naghdi’s theory, the updated Lagrangian governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain. The meshless function approximation is implemented by using the moving least-squares approximation. In Green-Naghdi’s theory, the Green-Lagrange strain is decomposed into the elastic part and plastic part and a J2 elastoplastic constitutive relation is us
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Kulish, Vladimir, and Kirill V. Poletkin. "An Analytical Solution of the Generalized Phase-Lagging Equation for Ultra-Fast Heat Transfer in One-Dimensional Semi-Infinite Domain." In ASME 2012 Third International Conference on Micro/Nanoscale Heat and Mass Transfer. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/mnhmt2012-75210.

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The paper presents an integral solution of the generalized one-dimensional phase-lagging heat equation with the convective term. The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of non-integer orders). Confluent hyper-geometric functions, known as Whittaker’s functions, appear in the course of the solution procedure, upon applying the Laplace transform to the original transport equation. The analytical solution of the problem is written in the integral form and provides a relationship between the loc
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