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Relevant bibliographies by topics / Boundary integral equations

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Academic literature on the topic 'Boundary integral equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 March 2023

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Journal articles on the topic "Boundary integral equations"

1

Bruk, V. M. "BOUNDARY VALUE PROBLEMS FOR INTEGRAL EQUATIONS WITH OPERATOR MEASURES." Issues of Analysis 24, no. 1 (June 2017): 19–40. http://dx.doi.org/10.15393/j3.art.2017.3810.

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Morino, Luigi. "Boundary Integral Equations in Aerodynamics." Applied Mechanics Reviews 46, no. 8 (August 1, 1993): 445–66. http://dx.doi.org/10.1115/1.3120373.

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A review of the use of boundary integral equations in aerodynamics is presented, with the objective of addressing what has been accomplished and, even more, what remains to be done. The paper is limited to aerodynamics of aeronautical type, with emphasis on unsteady flows (incompressible and compressible, potential and viscous). For potential flows, both incompressible and compressible flows are considered; the issue of the boundary conditions on the wake and on the trailing edge are addressed in some detail (in particular, some unresolved issues related to the impulsive start are pointed out). For incompressible viscous flows, the use of boundary integral equations in the non-primitive variable formulation are addressed: the Helmholtz decomposition and a decomposition recently introduced (and here referred to as the Poincare´ decomposition) are presented, along with their relationship. The latter is used to examine the relationship between potential and attached viscous flows (in particular, it is shown how the Poincare´ representation, for vortex layers of infinitesimal thickness, reduces to the potential-flow representation). The extension to compressible flows is also briefly outlined and the relative advantages of the two decompositions are discussed. Throughout the paper the emphasis is on the derivation and the interpretation of the boundary integral equations; issues related to the discretization (ie, panel methods, boundary element methods) are barely addressed. For numerical results, which are not included here, the reader is referred to the original references.

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Vavasis, Stephen A. "Preconditioning for Boundary Integral Equations." SIAM Journal on Matrix Analysis and Applications 13, no. 3 (July 1992): 905–25. http://dx.doi.org/10.1137/0613055.

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Amini, S., and N. D. Maines. "Regularization of strongly singular integrals in boundary integral equations." Communications in Numerical Methods in Engineering 12, no. 11 (November 1996): 787–93. http://dx.doi.org/10.1002/(sici)1099-0887(199611)12:11<787::aid-cnm19>3.0.co;2-5.

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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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Sulym, Heorhiy, Iaroslav Pasternak, Mariia Smal, and Andrii Vasylyshyn. "Mixed Boundary Value Problem for an Anisotropic Thermoelastic Half-Space Containing Thin Inhomogeneities." Acta Mechanica et Automatica 13, no. 4 (December 1, 2019): 238–44. http://dx.doi.org/10.2478/ama-2019-0032.

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Abstract The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and the extended Stroh formalism which allows writing the general solution of thermoelastic problems in terms of certain analytic functions. In addition, with the help of it, it is possible to convert the volume integrals included in the equation into contour integrals, which, in turn, will allow the use of the method of boundary elements. For modelling of solids with thin inhomogeneities, a coupling principle for continua of different dimensions is used. Applying the theory of complex variable functions, in particular, Cauchy integral formula and Sokhotski–Plemelj formula, the Somigliana type boundary integral equations are constructed for thermoelastic anisotropic half-space. The obtained integral equations are introduced into the modified boundary element method. A numerical analysis of the influence of boundary conditions on the half-space boundary and relative rigidity of the thin inhomogeneity on the intensity of stresses at the inclusions is carried out.

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Bukanay, N. U., A. E. Mirzakulova, M. K. Dauylbayev, and K. T. Konisbayeva. "A boundary jumps phenomenon in the integral boundary value problem for singularly perturbed differential equations." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 98, no. 2 (June 30, 2020): 46–58. http://dx.doi.org/10.31489/2020m2/46-58.

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Jankowski, Tadeusz. "Differential equations with integral boundary conditions." Journal of Computational and Applied Mathematics 147, no. 1 (October 2002): 1–8. http://dx.doi.org/10.1016/s0377-0427(02)00371-0.

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Schippers, H. "Multigrid methods for boundary integral equations." Numerische Mathematik 46, no. 3 (September 1985): 351–63. http://dx.doi.org/10.1007/bf01389491.

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Maczynski, J. "Boundary integral equations and reinforced bodies." Engineering Analysis with Boundary Elements 3, no. 3 (September 1986): 166–72. http://dx.doi.org/10.1016/0955-7997(86)90005-6.

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Dissertations / Theses on the topic "Boundary integral equations"

1

Ivanyshyn, Olha. "Nonlinear boundary integral equations in inverse scattering." Lichtenberg (Odw.) Harland Media, 2007. http://d-nb.info/988643316/04.

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Ivanyshyn, Olha. "Nonlinear boundary integral equations in inverse scattering /." Fischbachtal, Odenw : HARLAND media, 2008. http://deposit.d-nb.de/cgi-bin/dokserv?id=3104928&prov=M&dok_var=1&dok_ext=htm.

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Harbrecht, Helmut, and Reinhold Schneider. "Wavelet based fast solution of boundary integral equations." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600649.

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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 which yields quasi-sparse system matrices. These matrices can be compressed such that the complexity for solving a boundary integral equation scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. Based on the wavelet Galerkin scheme we present also an adaptive algorithm. By numerical experiments we provide results which demonstrate the performance of our algorithm.

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Yuen, P. K. "Bivariational methods and their application to integral equations." Thesis, University of Bradford, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376696.

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

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

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Dahmen, Wolfgang, Helmut Harbrecht, and Reinhold Schneider. "Compression Techniques for Boundary Integral Equations - Optimal Complexity Estimates." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600464.

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In this paper matrix compression techniques in the context of wavelet Galerkin schemes for boundary integral equations are developed and analyzed that exhibit optimal complexity in the following sense. The fully discrete scheme produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that is proven to stay proportional to the number of unknowns. Key issues are the second compression, that reduces the near field complexity significantly, and an additional a-posteriori compression. The latter one is based on a general result concerning an optimal work balance, that applies, in particular, to the quadrature used to compute the compressed stiffness matrix with sufficient accuracy in linear time. The theoretical results are illustrated by a 3D example on a nontrivial domain.

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

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

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10

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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Books on the topic "Boundary integral equations"

1

Hsiao, George C., and Wolfgang L. Wendland. Boundary Integral Equations. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71127-6.

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Hsiao, George C., and Wolfgang L. Wendland. Boundary Integral Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-68545-6.

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Linkov, A. M. Boundary Integral Equations in Elasticity Theory. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-015-9914-6.

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Boundary integral equations in elasticity theory. Dordrecht: Kluwer Academic Publishers, 2002.

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Amini, S. Regularisation of strongly singular integrals in boundary integral equations. Salford: University of Salford Department of Mathematics and Computer Science, 1995.

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A, Dzhuraev. Methods of singular integral equations. Harlow, Essex, England: Longman Scientific and Technical, 1992.

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Maz’ya, Vladimir G., and Alexander A. Soloviev. Boundary Integral Equations on Contours with Peaks. Edited by Tatyana Shaposhnikova. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0171-9.

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8

G, Maz'ya V., and Nikol'skii S. M, eds. Analysis IV: Linear and boundary integral equations. Berlin: Springer-Verlag, 1991.

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Strongly elliptic systems and boundary integral equations. Cambridge: Cambridge University Press, 2000.

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A, Soloviev Alexander, Shaposhnikova Tatyana, and SpringerLink (Online service), eds. Boundary Integral Equations on Contours with Peaks. Basel: Birkhäuser Basel, 2010.

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Book chapters on the topic "Boundary integral equations"

1

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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Hsiao, George C., and Wolfgang L. Wendland. "Boundary Integral Equations." In Boundary Integral Equations, 25–94. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71127-6_2.

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Maz’ya, V. G. "Boundary Integral Equations." In Analysis IV, 127–222. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58175-5_2.

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Schatz, Albert H., Vidar Thomée, and Wolfgang L. Wendland. "Boundary Integral Equations." In Mathematical Theory of Finite and Boundary Element Methods, 223–38. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-7630-8_3.

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Atkinson, Kendall, and Weimin Han. "Boundary Integral Equations." In Texts in Applied Mathematics, 551–81. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-0458-4_13.

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Atkinson, Kendall, and Weimin Han. "Boundary Integral Equations." In Texts in Applied Mathematics, 405–35. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-0-387-21526-6_12.

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Hsiao, George C., and Wolfgang L. Wendland. "Integral Equations on $$\Gamma $$ $$\subset $$ $$IR$$ 3 Recast as Pseudodifferential Equations." In Boundary Integral Equations, 619–73. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71127-6_10.

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Hsiao, George C., and Wolfgang L. Wendland. "Pseudodifferential Operators as Integral Operators." In Boundary Integral Equations, 479–538. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71127-6_8.

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Hsiao, George C., and Wolfgang L. Wendland. "Boundary Integral Equations on Curves in $$IR$$ 2." In Boundary Integral Equations, 675–718. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71127-6_11.

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Hsiao, George C., and Wolfgang L. Wendland. "Sobolev Spaces." In Boundary Integral Equations, 159–205. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71127-6_4.

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Conference papers on the topic "Boundary integral equations"

1

Wen, Guo-chun, Zhen Zhao, Jian-ke Lu, Zong-yi Hou, Wei Lin, De-qian Pu, and Er-qian Rong. "Integral Equations and Boundary Value Problems." In International Conference on Integral Equations and Boundary Value Problems. WORLD SCIENTIFIC, 1990. http://dx.doi.org/10.1142/9789814539630.

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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, 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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Lu, Jian Ke, Guo Chun Wen, Zhen Zhao, Zong-Yi Hou, Wei Lin, and Guang-Wu Yang. "Boundary Value Problems, Integral Equations and Related Problems." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812793881.

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Yas'ko, M. "Boundary integral representation for time-harmonic Maxwell’s equations." In 2008 International Conference on Mathematical Methods in Electromagnetic Theory (MEET). IEEE, 2008. http://dx.doi.org/10.1109/mmet.2008.4580989.

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HARBRECHT, HELMUT, and REINHOLD SCHNEIDER. "WAVELET BASED FAST SOLUTION OF BOUNDARY INTEGRAL EQUATIONS." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702548_0008.

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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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Beghein, Yves, Kristof Cools, and Daniel De Zutter. "Accurate temporal discretization of time domain boundary integral equations." In 2012 IEEE Antennas and Propagation Society International Symposium and USNC/URSI National Radio Science Meeting. IEEE, 2012. http://dx.doi.org/10.1109/aps.2012.6349028.

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Saillard, M. "Boundary integral equations for time-harmonic rough surface scattering." In 6th International SYmposium on Antennas, Propagation and EM Theory, 2003. Proceedings. 2003. IEEE, 2003. http://dx.doi.org/10.1109/isape.2003.1276730.

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Marussig, Benjamin, Jürgen Zechner, Gernot Beer, and Thomas-Peter Fries. "INTEGRATION OF DESIGN AND ANALYSIS THROUGH BOUNDARY INTEGRAL EQUATIONS." In VII European Congress on Computational Methods in Applied Sciences and Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2016. http://dx.doi.org/10.7712/100016.2275.5812.

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Reports on the topic "Boundary integral equations"

1

Taus, Matthias, Gregory J. Rodin, and Thomas J. Hughes. Isogeometric Analysis of Boundary Integral Equations. Fort Belvoir, VA: Defense Technical Information Center, April 2015. http://dx.doi.org/10.21236/ada620024.

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Martinsson, P. G., and V. Rokhlin. A Fast Direct Solver for Boundary Integral Equations in Two Dimensions. Fort Belvoir, VA: Defense Technical Information Center, December 2003. http://dx.doi.org/10.21236/ada635871.

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Kong, W. Y., J. Bremer, and V. Rokhlin. An Adaptive Fast Direct Solver for Boundary Integral Equations in Two Dimensions. Fort Belvoir, VA: Defense Technical Information Center, August 2009. http://dx.doi.org/10.21236/ada555115.

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Bremer, J., V. Rokhlin, and I. Sammis. Universal Quadratures for Boundary Integral Equations on Two-Dimensional Domains with Corners. Fort Belvoir, VA: Defense Technical Information Center, November 2009. http://dx.doi.org/10.21236/ada555117.

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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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