Relevant bibliographies by topics / Boundary integral method

Academic literature on the topic 'Boundary integral method'

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Published: 4 June 2021
Last updated: 31 January 2023

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Journal articles on the topic "Boundary integral method"

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Sládek, V., and J. Sládek. "Boundary integral method in magnetoelasticity." International Journal of Engineering Science 26, no. 5 (January 1988): 401–18. http://dx.doi.org/10.1016/0020-7225(88)90001-8.

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Benedetti, Ivano, Vincenzo Gulizzi, and Vincenzo Mallardo. "Boundary Element Crystal Plasticity Method." Journal of Multiscale Modelling 08, no. 03n04 (September 2017): 1740003. http://dx.doi.org/10.1142/s1756973717400030.

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A three-dimensional (3D) boundary element method for small strains crystal plasticity is described. The method, developed for polycrystalline aggregates, makes use of a set of boundary integral equations for modeling the individual grains, which are represented as anisotropic elasto-plastic domains. Crystal plasticity is modeled using an initial strains boundary integral approach. The integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations are discussed. Voronoi-tessellation micro-morphologies are discretized using nonstructured boundary and volume meshes. A grain-boundary incremental/iterative algorithm, with rate-dependent flow and hardening rules, is developed and discussed. The method has been assessed through several numerical simulations, which confirm robustness and accuracy.
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Setukha, A. V. "Method of Boundary Integral Equations with Hypersingular Integrals in Boundary-Value Problems." Journal of Mathematical Sciences 257, no. 1 (July 29, 2021): 114–26. http://dx.doi.org/10.1007/s10958-021-05475-3.

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Yu, Dehao, and Longhua Zhao. "Natural boundary integral method and related numerical methods." Engineering Analysis with Boundary Elements 28, no. 8 (August 2004): 937–44. http://dx.doi.org/10.1016/s0955-7997(03)00120-6.

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Cong, Wenxiang, and Ge Wang. "Boundary integral method for bioluminescence tomography." Journal of Biomedical Optics 11, no. 2 (2006): 020503. http://dx.doi.org/10.1117/1.2191790.

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Zakerdoost, Hassan, Hassan Ghassemi, and Mehdi Iranmanesh. "Solution of Boundary Value Problems Using Dual Reciprocity Boundary Element Method." Advances in Applied Mathematics and Mechanics 9, no. 3 (January 17, 2017): 680–97. http://dx.doi.org/10.4208/aamm.2014.m783.

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AbstractIn this work we utilize the boundary integral equation and the Dual Reciprocity Boundary Element Method (DRBEM) for the solution of the steady state convection-diffusion-reaction equations with variable convective coefficients in two-dimension. The DRBEM is a numerical method to transform the domain integrals into the boundary only integrals by using the fundamental solution of Helmholtz equation. Some examples are calculated to confirm the accuracy of the approach. The results obtained by the analytic solutions are in good agreement with ones provided by the DRBEM technique.
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Wen, Pi Hua, and M. H. Aliabadi. "Dynamic Crack Problems Using Meshless Method." Key Engineering Materials 525-526 (November 2012): 601–4. http://dx.doi.org/10.4028/www.scientific.net/kem.525-526.601.

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A Meshless Approximation Based on the Radial Basis Function (RBF) Is Developed for Analysis of Dynamic Crack Problems. A Weak Form for a Set of Governing Equations with a Unit Test Function Is Transformed into Local Integral Equations. A Completed Set of Closed Forms of the Local Boundary Integrals Are Obtained. as the Closed Forms of the Local Boundary Integrals Are Obtained, there Are No any Domain or Boundary Integrals to Be Calculated Numerically in this Approach.
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Ying, Wenjun, and Wei-Cheng Wang. "A Kernel-Free Boundary Integral Method for Variable Coefficients Elliptic PDEs." Communications in Computational Physics 15, no. 4 (April 2014): 1108–40. http://dx.doi.org/10.4208/cicp.170313.071113s.

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AbstractThis work proposes a generalized boundary integral method for variable coefficients elliptic partial differential equations (PDEs), including both boundary value and interface problems. The method is kernel-free in the sense that there is no need to know analytical expressions for kernels of the boundary and volume integrals in the solution of boundary integral equations. Evaluation of a boundary or volume integral is replaced with interpolation of a Cartesian grid based solution, which satisfies an equivalent discrete interface problem, while the interface problem is solved by a fast solver in the Cartesian grid. The computational work involved with the generalized boundary integral method is essentially linearly proportional to the number of grid nodes in the domain. This paper gives implementation details for a second-order version of the kernel-free boundary integral method in two space dimensions and presents numerical experiments to demonstrate the efficiency and accuracy of the method for both boundary value and interface problems. The interface problems demonstrated include those with piecewise constant and large-ratio coefficients and the heterogeneous interface problem, where the elliptic PDEs on two sides of the interface are of different types.
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Koumoutsakos, P., and A. Leonard. "Improved boundary integral method for inviscid boundary condition applications." AIAA Journal 31, no. 2 (February 1993): 401–4. http://dx.doi.org/10.2514/3.11682.

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Moshaiov, A., and C. Vitooraporn. "Application of Boundary Integral Method to Continuous Plate Structures." Journal of Ship Research 34, no. 03 (September 1, 1990): 212–17. http://dx.doi.org/10.5957/jsr.1990.34.3.212.

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Ship hulls are composed of complex plate structures. Such structures can be analyzed by analytical as well as numerical methods. Here it is demonstrated that boundary integrals can be used to analyze such structures by a seminumerical method. Boundary integrals have been used for analyzing single plate bending problems, and only recently have attempts been made to extend their use to complex plate structures. In this paper the Direct Boundary Integral Method for bending of thin elastic plates is extended to analysis of the continuous plate structures. The concepts of compatibility and equilibrium conditions along the common boundary have been imposed in conjunction with a boundary element formulation for each panel. Several examples of loading conditions are presented and compared with analytical solutions. The excellent agreement achieved illustrates the effectiveness of the extended formulation.
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Dissertations / Theses on the topic "Boundary integral method"

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

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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 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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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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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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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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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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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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Books on the topic "Boundary integral method"

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Natural boundary integral method and its applications. Beijing: Science Press, 2002.

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Pomp, Andreas. The Boundary-Domain Integral Method for Elliptic Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0094576.

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Pomp, Andreas. The boundary-domain integral method for elliptic systems. Berlin: Springer, 1998.

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Bakr, A. A. The Boundary Integral Equation Method in Axisymmetric Stress Analysis Problems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-82644-3.

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The boundary integral equation method in axisymmetric stress analysis problems. Berlin: Springer-Verlag, 1986.

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Bakr, A. A. The Boundary Integral Equation Method in Axisymmetric Stress Analysis Problems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986.

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Bryan, Kurt. A Boundary integral method for an inverse problem in thermal imaging. Hampton, Va: ICASE, 1992.

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Bazhlekov, Ivan Blagoev. Non-singular boundary-integral method for deformable drops in viscous flows. Eindhoven: Technische Universiteit Eindhoven, 2003.

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Mendelson, Alexander. Analysis of mixed-mode crack propagation using the boundary integral method. [Washington, DC]: National Aeronautics and Space Administration, 1986.

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Canada. Defence Research Establishment Atlantic. Integral Method For the Calculation of Boundary Layer Growth on A Ship Hull. S.l: s.n, 1985.

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Book chapters on the topic "Boundary integral method"

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Hackbusch, Wolfgang. "The Boundary Element Method." In Integral Equations, 318–43. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9215-5_9.

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Hall, W. S. "Ordinary Integral Equations." In The Boundary Element Method, 1–38. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0784-6_1.

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Lutz, E., L. J. Gray, and A. R. Ingraffea. "Indirect Evaluation of Surface Stress in the Boundary Element Method." In Boundary Integral Methods, 339–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-85463-7_33.

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Tanaka, Masa, Y. Yamada, and M. Shirotori. "Computer Simulation of Duct Noise Control by the Boundary Element Method." In Boundary Integral Methods, 480–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-85463-7_47.

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Attaway, Dorothy C. "The Boundary Element Method for the Diffusion Equation: A Feasibility Study." In Boundary Integral Methods, 75–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-85463-7_7.

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Zagar, I., P. Skerget, and A. Alujevic. "Boundary Domain Integral Method for the Space Time Dependent Viscous Incompressible Flow." In Boundary Integral Methods, 510–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-85463-7_50.

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Miyake, S., M. Nonaka, and N. Tosaka. "An Integral Equation Method for Geometrically Nonlinear Bending Problem of Elastic Circular Arch." In Boundary Integral Methods, 349–58. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-85463-7_34.

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Nakayama, Tsukasa, and Hiroaki Tanaka. "A Numerical Method for the Analysis of Nonlinear Sloshing in Circular Cylindrical Containers." In Boundary Integral Methods, 359–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-85463-7_35.

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Buresti, G., G. Lombardi, and L. Polito. "Analysis of the Interaction Between Lifting Surfaces by Means of a Non-Linear Panel Method." In Boundary Integral Methods, 125–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-85463-7_12.

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Annigeri, Balkrishna S., and William D. Keat. "Two and Three Dimensional Crack Growth Using the Surface Integral and Finite Element Hybrid Method." In Boundary Integral Methods, 45–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-85463-7_4.

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Conference papers on the topic "Boundary integral method"

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Galybin, A. N., and Sh A. Mukhamediev. "Integral equations for elastic problems posed in principal directions: application for adjacent domains." In BOUNDARY ELEMENT METHOD 2006. Southampton, UK: WIT Press, 2006. http://dx.doi.org/10.2495/be06006.

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Litynskyy, Svyatoslav, and Yuriy Muzy. "Boundary elements method for some triangular system of boundary integral equations." In 2009 International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED). IEEE, 2009. http://dx.doi.org/10.1109/diped.2009.5306941.

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DiPaola, Milo, and David J. Willis. "A Rotating Reference Frame, Integral Boundary Layer Method." In 46th AIAA Fluid Dynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2016. http://dx.doi.org/10.2514/6.2016-3974.

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Vico, Felipe, Miguel Ferrando-Bataller, Eva Antonino-Daviu, and Marta Cabedo-Fabres. "A New Quadrature Method for Singular Integrals of Boundary Integral Equations in Electromagnetism." In 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting. IEEE, 2020. http://dx.doi.org/10.1109/ieeeconf35879.2020.9330434.

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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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Ravnik, Jure, A. Susnjara, Jan Tibuat, Dragan Poljak, and M. Cvetkovic. "Stochastic Boundary-Domain Integral Method for heat transfer simulations." In 2019 4th International Conference on Smart and Sustainable Technologies (SpliTech). IEEE, 2019. http://dx.doi.org/10.23919/splitech.2019.8783026.

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Bang, Seungbae, Kirill Serkh, Oded Stein, and Alec Jacobson. "A Hybrid Boundary Element and Boundary Integral Equation Method for Accurate Diffusion Curves." In SA '22: SIGGRAPH Asia 2022. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3550340.3564233.

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Litynskyy, Svyatoslav, Yuriy Muzychuk, and Anatoliy Muzychuk. "Boundary integral equations method in boundary problems for unbounded triangular system of elliptical equations." In 2009 International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED). IEEE, 2009. http://dx.doi.org/10.1109/diped.2009.5306940.

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Antonijevic, Sinisa, and Dragan Poljak. "Some optimizations of the Galerkin-Bubnov Integral Boundary Element Method." In 2013 21st International Conference on Applied Electromagnetics and Communications (ICECom). IEEE, 2013. http://dx.doi.org/10.1109/icecom.2013.6684736.

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Manning, Robert E., Ian Ballinger, and Mack Dowdy. "Fast Boundary Integral Method for Slosh and Microgravity Fluid Dynamics." In 53rd AIAA/SAE/ASEE Joint Propulsion Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2017. http://dx.doi.org/10.2514/6.2017-4664.

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Reports on the topic "Boundary integral method"

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Chang, Sanchi S., and Tatsuo Itoh. The Boundary-Integral Method for Planar Microstrip Circuits. Fort Belvoir, VA: Defense Technical Information Center, December 1988. http://dx.doi.org/10.21236/ada203715.

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Cruse, T. A., and E. Z. Polch. Nonlinear Fracture Mechanics Analysis with Boundary Integral Method. Fort Belvoir, VA: Defense Technical Information Center, May 1986. http://dx.doi.org/10.21236/ada173216.

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Schultz, W. W., and S. W. Hong. Solution of Potential Problems Using an Overdetermined Complex Boundary Integral Method. Fort Belvoir, VA: Defense Technical Information Center, January 1988. http://dx.doi.org/10.21236/ada250816.

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Garzon, M., D. Adalsteinsson, L. Gray, and J. A. Sethian. Wave breaking over sloping beaches using a coupled boundary integral-level set method. Office of Scientific and Technical Information (OSTI), December 2003. http://dx.doi.org/10.2172/840733.

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Cao, Yusong, William W. Schultz, and Robert F. Beck. Three-Dimensional Desingularized Boundary Integral Methods for Potential Problems. Fort Belvoir, VA: Defense Technical Information Center, February 1990. http://dx.doi.org/10.21236/ada251151.

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Shani, Uri, Lynn Dudley, Alon Ben-Gal, Menachem Moshelion, and Yajun Wu. Root Conductance, Root-soil Interface Water Potential, Water and Ion Channel Function, and Tissue Expression Profile as Affected by Environmental Conditions. United States Department of Agriculture, October 2007. http://dx.doi.org/10.32747/2007.7592119.bard.

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Constraints on water resources and the environment necessitate more efficient use of water. The key to efficient management is an understanding of the physical and physiological processes occurring in the soil-root hydraulic continuum.While both soil and plant leaf water potentials are well understood, modeled and measured, the root-soil interface where actual uptake processes occur has not been sufficiently studied. The water potential at the root-soil interface (yᵣₒₒₜ), determined by environmental conditions and by soil and plant hydraulic properties, serves as a boundary value in soil and plant uptake equations. In this work, we propose to 1) refine and implement a method for measuring yᵣₒₒₜ; 2) measure yᵣₒₒₜ, water uptake and root hydraulic conductivity for wild type tomato and Arabidopsis under varied q, K⁺, Na⁺ and Cl⁻ levels in the root zone; 3) verify the role of MIPs and ion channels response to q, K⁺ and Na⁺ levels in Arabidopsis and tomato; 4) study the relationships between yᵣₒₒₜ and root hydraulic conductivity for various crops representing important botanical and agricultural species, under conditions of varying soil types, water contents and salinity; and 5) integrate the above to water uptake term(s) to be implemented in models. We have made significant progress toward establishing the efficacy of the emittensiometer and on the molecular biology studies. We have added an additional method for measuring ψᵣₒₒₜ. High-frequency water application through the water source while the plant emerges and becomes established encourages roots to develop towards and into the water source itself. The yᵣₒₒₜ and yₛₒᵢₗ values reflected wetting and drying processes in the rhizosphere and in the bulk soil. Thus, yᵣₒₒₜ can be manipulated by changing irrigation level and frequency. An important and surprising finding resulting from the current research is the obtained yᵣₒₒₜ value. The yᵣₒₒₜ measured using the three different methods: emittensiometer, micro-tensiometer and MRI imaging in both sunflower, tomato and corn plants fell in the same range and were higher by one to three orders of magnitude from the values of -600 to -15,000 cm suggested in the literature. We have added additional information on the regulation of aquaporins and transporters at the transcript and protein levels, particularly under stress. Our preliminary results show that overexpression of one aquaporin gene in tomato dramatically increases its transpiration level (unpublished results). Based on this information, we started screening mutants for other aquaporin genes. During the feasibility testing year, we identified homozygous mutants for eight aquaporin genes, including six mutants for five of the PIP2 genes. Including the homozygous mutants directly available at the ABRC seed stock center, we now have mutants for 11 of the 19 aquaporin genes of interest. Currently, we are screening mutants for other aquaporin genes and ion transporter genes. Understanding plant water uptake under stress is essential for the further advancement of molecular plant stress tolerance work as well as for efficient use of water in agriculture. Virtually all of Israel’s agriculture and about 40% of US agriculture is made possible by irrigation. Both countries face increasing risk of water shortages as urban requirements grow. Both countries will have to find methods of protecting the soil resource while conserving water resources—goals that appear to be in direct conflict. The climate-plant-soil-water system is nonlinear with many feedback mechanisms. Conceptual plant uptake and growth models and mechanism-based computer-simulation models will be valuable tools in developing irrigation regimes and methods that maximize the efficiency of agricultural water. This proposal will contribute to the development of these models by providing critical information on water extraction by the plant that will result in improved predictions of both water requirements and crop yields. Plant water use and plant response to environmental conditions cannot possibly be understood by using the tools and language of a single scientific discipline. This proposal links the disciplines of soil physics and soil physical chemistry with plant physiology and molecular biology in order to correctly treat and understand the soil-plant interface in terms of integrated comprehension. Results from the project will contribute to a mechanistic understanding of the SPAC and will inspire continued multidisciplinary research.
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