Готові списки джерел за темами / Method of fundamental solution

Добірка наукової літератури з теми "Method of fundamental solution"

Автор: Grafiati
Опубліковано: 10 грудня 2022
Оновлено: 28 січня 2023

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Статті в журналах з теми "Method of fundamental solution"

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Hrubá, M. "dCAPS method: advantages, troubles and solution." Plant, Soil and Environment 53, No. 9 (January 7, 2008): 417–20. http://dx.doi.org/10.17221/2293-pse.

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In our work, we focus on the evolutionary studies of sex chromosomes. As model organisms we use several species of the plant genus <i>Silene</i>. An important part of our research is represented by genetic mapping based on the assays of DNA length or sequence polymorphisms. Apart from the other methods we also use the dCAPS method, which is very useful for detection of the sequence polymorphisms (SNPs). This method is unique as it is able to detect SNPs that are not situated in any restriction site; a fundamental principle of this method is usage of primer designed with one or two mismatches that bring into the target sequence the mutation in vicinity of SNP. Using this method, we found out some improvements that can make analyses more cost-effective.
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2

Kitagawa, Takashi. "Asymptotic stability of the fundamental solution method." Journal of Computational and Applied Mathematics 38, no. 1-3 (December 1991): 263–69. http://dx.doi.org/10.1016/0377-0427(91)90175-j.

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3

GÁSPÁR, CSABA. "REGULARIZATION TECHNIQUES FOR THE METHOD OF FUNDAMENTAL SOLUTIONS." International Journal of Computational Methods 10, no. 02 (March 2013): 1341004. http://dx.doi.org/10.1142/s0219876213410041.

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A special regularization method based on higher-order partial differential equations is presented. Instead of using the fundamental solution of the original partial differential operator with source points located outside of the domain, the original second-order partial differential equation is approximated by a higher-order one, the fundamental solution of which is continuous at the origin. This allows the use of the method of fundamental solutions (MFS) for the approximate problem. Due to the continuity of the modified operator, the source points and the boundary collocation points are allowed to coincide, which makes the solution process simpler. This regularization technique is generalized to various problems and combined with the extremely efficient quadtree-based multigrid methods. Approximation theorems and numerical experiences are also presented.
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4

Wei, H., J. L. Zheng, J. Sladek, V. Sladek, and P. H. Wen. "Method of fundamental solution using Erdogan's solution: Static and dynamic." Engineering Analysis with Boundary Elements 148 (March 2023): 176–89. http://dx.doi.org/10.1016/j.enganabound.2022.12.035.

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5

Nath, D., and M. S. Kalra. "Solution of Grad–Shafranov equation by the method of fundamental solutions." Journal of Plasma Physics 80, no. 3 (February 19, 2014): 477–94. http://dx.doi.org/10.1017/s0022377814000026.

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In this paper we have used the Method of Fundamental Solutions (MFS) to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibria of tokamak plasmas with monomial sources. These monomials are the individual terms appearing on the right-hand side of the GS equation if one expands the nonlinear terms into polynomials. Unlike the Boundary Element Method (BEM), the MFS does not involve any singular integrals and is a meshless boundary-alone method. Its basic idea is to create a fictitious boundary around the actual physical boundary of the computational domain. This automatically removes the involvement of singular integrals. The results obtained by the MFS match well with the earlier results obtained using the BEM. The method is also applied to Solov'ev profiles and it is found that the results are in good agreement with analytical results.
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6

Hu, S. P., C. M. Fan, C. W. Chen, and D. L. Young. "Method of Fundamental Solutions for Stokes' First and Second Problems." Journal of Mechanics 21, no. 1 (March 2005): 25–31. http://dx.doi.org/10.1017/s1727719100000514.

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AbstractThis paper describes the applications of the method of fundamental solutions (MFS) as a mesh-free numerical method for the Stokes' first and second problems which prevail in the semi-infinite domain with constant and oscillatory velocity at the boundary in the fluid-mechanics benchmark problems. The time-dependent fundamental solutions for the semi-infinite problems are used directly to obtain the solution as a linear combination of the unsteady fundamental solution of the diffusion operator. The proposed numerical scheme is free from the conventional Laplace transform or the finite difference scheme to deal with the time derivative term of the governing equation. By properly placing the field points and the source points at a given time level, the solution is advanced in time until steady state solutions are reached. It is not necessary to locate and specify the condition at the infinite domain such as other numerical methods. Since the present method does not need mesh discretization and nodal connectivity, the computational effort and memory storage required are minimal as compared to the domain-oriented numerical schemes. Test results obtained for the Stokes' first and second problems show good comparisons with the analytical solutions. Thus the present numerical scheme has provided a promising mesh-free numerical tool to solve the unsteady semi-infinite problems with the space-time unification for the time-dependent fundamental solution.
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Liu, Chein-Shan, Zhuojia Fu, and Chung-Lun Kuo. "Directional Method of Fundamental Solutions for Three-dimensional Laplace Equation." Journal of Mathematics Research 9, no. 6 (November 8, 2017): 112. http://dx.doi.org/10.5539/jmr.v9n6p112.

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We propose a simple extension of the two-dimensional method of fundamental solutions (MFS) to a two-dimensional like MFS for the numerical solution of the three-dimensional Laplace equation in an arbitrary interior domain. In the directional MFS (DMFS) the directors are planar orientations, which can take the geometric anisotropy of the problem domain into account, and more importantly the order of the logarithmic singularity with $\ln R$ of the new fundamental solution is reduced than that of the conventional three-dimensional fundamental solution with singularity $1/r$. Some numerical examples are used to validate the performance of the DMFS.
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8

Shidfar, A., and Z. Darooghehgimofrad. "Numerical solution of two backward parabolic problems using method of fundamental solutions." Inverse Problems in Science and Engineering 25, no. 2 (January 30, 2016): 155–68. http://dx.doi.org/10.1080/17415977.2016.1138947.

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Lin, Ji, C. S. Chen, and Chein-Shan Liu. "Fast Solution of Three-Dimensional Modified Helmholtz Equations by the Method of Fundamental Solutions." Communications in Computational Physics 20, no. 2 (July 21, 2016): 512–33. http://dx.doi.org/10.4208/cicp.060915.301215a.

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AbstractThis paper describes an application of the recently developed sparse scheme of the method of fundamental solutions (MFS) for the simulation of three-dimensional modified Helmholtz problems. The solution to the given problems is approximated by a two-step strategy which consists of evaluating the particular solution and the homogeneous solution. The homogeneous solution is approximated by the traditional MFS. The original dense system of the MFS formulation is condensed into a sparse system based on the exponential decay of the fundamental solutions. Hence, the homogeneous solution can be efficiently obtained. The method of particular solutions with polyharmonic spline radial basis functions and the localized method of approximate particular solutions in combination with the Gaussian radial basis function are employed to approximate the particular solution. Three numerical examples including a near singular problem are presented to show the simplicity and effectiveness of this approach.
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10

Chen, C. S., Xinrong Jiang, Wen Chen, and Guangming Yao. "Fast Solution for Solving the Modified Helmholtz Equation withthe Method of Fundamental Solutions." Communications in Computational Physics 17, no. 3 (March 2015): 867–86. http://dx.doi.org/10.4208/cicp.181113.241014a.

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AbstractThe method of fundamentalsolutions (MFS)is known as aneffective boundary meshless method. However, the formulation of the MFS results in a dense and extremely ill-conditioned matrix. In this paper we investigate the MFS for solving large-scale problems for the nonhomogeneous modified Helmholtz equation. The key idea is to exploit the exponential decay of the fundamental solution of the modified Helmholtz equation, and consider a sparse or diagonal matrix instead of the original dense matrix. Hence, the homogeneous solution can be obtained efficiently and accurately. A standard two-step solution process which consists of evaluating the particular solution and the homogeneous solution is applied. Polyharmonic spline radial basis functions are employed to evaluate the particular solution. Five numerical examples in irregular domains and a large number of boundary collocation points are presented to show the simplicity and effectiveness of our approach for solving large-scale problems.
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Дисертації з теми "Method of fundamental solution"

1

Poullikkas, Andreas. "The Method of Fundamental Solutions for the solution of elliptic boundary value problems." Thesis, Loughborough University, 1997. https://dspace.lboro.ac.uk/2134/27141.

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We investigate the use of the Method of Fundamental Solutions (MFS) for the numerical solution of elliptic problems arising in engineering. In particular, we examine harmonic and biharmonic problems with boundary singularities, certain steady-state free boundary flow problems and inhomogeneous problems. The MFS can be viewed as an indirect boundary method with an auxiliary boundary. The solution is approximated by a linear combination of fundamental solutions of the governing equation which are expressed in terms of sources located outside the domain of the problem. The unknown coefficients in the linear combination of fundamental solutions and the location of the sources are determined so that the boundary conditions are satisfied in a least squares sense. The MFS shares the same advantages of the boundary methods over domain discretisation methods. Moreover, it is relatively easy to implement, it is adaptive in the sense that it takes into account sharp changes in the solution and/or in the geometry of the domain and it can easily incorporate complicated boundary conditions.
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2

Sundqvist, Per. "Numerical Computations with Fundamental Solutions." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5757.

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3

Dyhoum, Taysir Emhemed. "The method of fundamental solutions and MCMC methods for solving electrical tomography problems." Thesis, University of Leeds, 2016. http://etheses.whiterose.ac.uk/15552/.

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Electrical impedance tomography (EIT) is a non-intrusive and portable imaging technique which has been used widely in many medical, geological and industrial applications for imaging the interior electrical conductivity distribution within a region from the knowledge of the injected currents through attached electrodes and resulting voltages, or boundary potential and current flux. If the quantities involved are all real then EIT is called electrical resistance tomography (ERT). The work in this thesis focuses on solving inverse geometric problems in ERT where we seek detecting the size, the shape and the location of inner objects within a given bounded domain. These ERT problems are governed by Laplace’s equation subject either to the most practical and general boundary conditions, forming the socalled complete-electrode model (CEM), in two dimensions or to the more idealised boundary conditions in three-dimensions called the continuous model. Firstly, the method of the fundamental solutions (MFS) is applied to solve the forward problem of the two-dimensional complete-electrode model of ERT in simplyconnected and multiple-connected domains (rigid inclusion, cavity and composite bimaterial), as well as providing the corresponding MFS solutions for the three-dimensional continuous model. Secondly, a Bayesian approach and the Markov Chain Monte Carlo (MCMC) estimation technique are employed in combinations with the numerical MFS direct solver in order to obtain the inverse solution. The MCMC algorithm is not only used for reconstruction, but it also deals with uncertainty assessment issues. The reliability and accuracy of a fitted object is investigated through some meaningful statistical aspects such as the object boundary histogram and object boundary credible intervals.
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4

Bin-Mohsin, Bandar Abdullah. "The method of fundamental solutions for Helmholtz-type problems." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/4843/.

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The purpose of this thesis is to extend the range of application of the method fundamental solutions (MFS) to solve direct and inverse geometric problems associated with two- or three-dimensional Helmholtz-type equations. Inverse problems have become more and more important in various fields of science and technology, and have certainly been one of the fastest growing areas in applied mathematics over the last three decades. However, as inverse geometric problems typically lead to mathematical models which are ill-posed, their solutions are unstable under data perturbations and classical numerical techniques fail to provide accurate and stable solutions.
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5

Sedláček, Stanislav. "Aplikace metody hraničních prvků na některé problémy trhliny v blízkosti bi-materiálového rozhraní." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2012. http://www.nusl.cz/ntk/nusl-230134.

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There are many shape and other changes in the engineering constructions. These changes cause the concentration of the stress. There is a higher probability of the crack initiation in the vicinity of these stress concentrators. The problems of the crack can be solved nowadays only with help of sufficient numeric tools. The Boundary Element Method is one of the many numerical tools which offer the solution of some problems of the mechanics. The goal of this diploma thesis is to formulate boundary element method for the plane problem of the linear elasticity for izotropic material with different types of the stress concentrators.
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6

Bozkaya, Canan. "Boundary Element Method Solution Of Initial And Boundary Value Problems In Fluid Dynamics And Magnetohydrodynamics." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609552/index.pdf.

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In this thesis, the two-dimensional initial and boundary value problems invol-ving convection and diffusion terms are solved using the boundary element method (BEM). The fundamental solution of steady magnetohydrodynamic (MHD) flow equations in the original coupled form which are convection-diffusion type is established in order to apply the BEM directly to these coupled equations with the most general form of wall conductivities. Thus, the solutions of MHD flow in rectangular ducts and in infinite regions with mixed boundary conditions are obtained for high values of Hartmann number, M. For the solution of transient convection-diffusion type equations the dual reciprocity boundary element method (DRBEM) in space is combined with the differential quadrature method (DQM) in time. The DRBEM is applied with the fundamental solution of Laplace equation treating all the other terms in the equation as nonhomogeneity. The use of DQM eliminates the need of iteration and very small time increments since it is unconditionally stable. Applications include unsteady MHD duct flow and elastodynamic problems. The transient Navier-Stokes equations which are nonlinear in nature are also solved with the DRBEM in space - DQM in time procedure iteratively in terms of stream function and vorticity. The procedure is applied to the lid-driven cavity flow for moderate values of Reynolds number. The natural convection cavity flow problem is also solved for high values of Rayleigh number when the energy equation is added.
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7

Sun, Liecheng. "ANALYTICAL STRIP METHOD TO ANTISYMMETRIC LAMINATED PLATES." UKnowledge, 2009. http://uknowledge.uky.edu/gradschool_diss/715.

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An Analytical Strip Method (ASM) for the analysis of stiffened and non-stiffened antisymmetric laminated composite plates is derived by considering the bending-extension coupling effect for bending, free vibration and buckling. A system of three equations of equilibrium, governing the general response of arbitrarily laminated composite plates, is reduced to a single eighth order partial differential equation in terms of a displacement function. The displacement function is solved in a single series form to determine the displacement, fundamental frequency, and buckling load of antisymmetric cross-ply and angle-ply laminated composite plates. The solution is applicable to rectangular plates with two opposite edges simply supported, while the other edges are simply supported, clamped, free, beam supported, or any combinations of these boundary conditions. This method overcomes the limitations of other analytical methods (Navier’s and Lévy’s), and provides an alternative to numerical, semi-numerical, and approximate methods of analysis. Numerical examples of bending, free vibration, and buckling of antisymmetric laminated composite plates are presented in tabular and graphical form. Whenever possible, the results of the present study are compared with those published in the literature and/or ANSYS solutions. The comparison firmly establishes that this method could be used for the analysis of antisymmetric laminated composite plates. Future research needs are identified for the aspects that have not been reached by the present study and others.
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8

Reeve, Thomas Henry. "The method of fundamental solutions for some direct and inverse problems." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4278/.

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We propose and investigate applications of the method of fundamental solutions (MFS) to several parabolic time-dependent direct and inverse heat conduction problems (IHCP). In particular, the two-dimensional heat conduction problem, the backward heat conduction problem (BHCP), the two-dimensional Cauchy problem, radially symmetric and axisymmetric BHCPs, the radially symmetric IHCP, inverse one and two-phase linear Stefan problems, the inverse Cauchy-Stefan problem, and the inverse two-phase one-dimensional nonlinear Stefan problem. The MFS is a collocation method therefore it does not require mesh generation or integration over the solution boundary, making it suitable for solving inverse problems, like the BHCP, an ill-posed problem. We extend the MFS proposed in Johansson and Lesnic (2008) for the direct one-dimensional heat equation, and Johansson and Lesnic (2009) for the direct one-phase one-dimensional Stefan problem, with source points placed outside the space domain of interest and in time. Theoretical properties, including linear independence and denseness, the placement of source points, and numerical investigations are included showing that accurate results can be efficiently obtained with small computational cost. Regularization techniques, in particular, Tikhonov regularization, in conjunction with the L-curve criterion, are used to solve the illconditioned systems generated by this method. In Chapters 6 and 8, investigating the linear and nonlinear Stefan problems, the MATLAB toolbox lsqnonlin, which is designed to minimize a sum of squares, is used.
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9

Bozkaya, Nuray. "Application Of The Boundary Element Method To Parabolic Type Equations." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12612074/index.pdf.

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In this thesis, the two-dimensional initial and boundary value problems governed by unsteady partial differential equations are solved by making use of boundary element techniques. The boundary element method (BEM) with time-dependent fundamental solution is presented as an efficient procedure for the solution of diffusion, wave and convection-diffusion equations. It interpenetrates the equations in such a way that the boundary solution is advanced to all time levels, simultaneously. The solution at a required interior point can then be obtained by using the computed boundary solution. Then, the coupled system of nonlinear reaction-diffusion equations and the magnetohydrodynamic (MHD) flow equations in a duct are solved by using the time-domain BEM. The numerical approach is based on the iteration between the equations of the system. The advantage of time-domain BEM are still made use of utilizing large time increments. Mainly, MHD flow equations in a duct having variable wall conductivities are solved successfully for large values of Hartmann number. Variable conductivity on the walls produces coupled boundary conditions which causes difficulties in numerical treatment of the problem by the usual BEM. Thus, a new time-domain BEM approach is derived in order to solve these equations as a whole despite the coupled boundary conditions, which is one of the main contributions of this thesis. Further, the full MHD equations in stream function-vorticity-magnetic induction-current density form are solved. The dual reciprocity boundary element method (DRBEM), producing only boundary integrals, is used due to the nonlinear convection terms in the equations. In addition, the missing boundary conditions for vorticity and current density are derived with the help of coordinate functions in DRBEM. The resulting ordinary differential equations are discretized in time by using unconditionally stable Gear'
s scheme so that large time increments can be used. The Navier-Stokes equations are solved in a square cavity up to Reynolds number 2000. Then, the solution of full MHD flow in a lid-driven cavity and a backward facing step is obtained for different values of Reynolds, magnetic Reynolds and Hartmann numbers. The solution procedure is quite efficient to capture the well known characteristics of MHD flow.
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10

Pesce, Antonello. "Stochastic fundamental solutions for a class of degenerate SPDEs." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14559/.

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In this thesis, we look for a fundamental solution for a broad, possibly degenerate class of stochastic partial differential equations (SPDEs), whose deterministic part is a Kolmogorov equation with coefficients measurable in the time variable. We use a version of the It\^o-Wentzell formula to reduce the SPDE to a PDE, for which we extend the classic Levi's parametrix method to find a fundamental solution.
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Книги з теми "Method of fundamental solution"

1

Augustin, Matthias Albert. A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17079-4.

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2

Metod fundamentalʹnykh resheniĭ v geomekhanike dobychi nefti i gaza: Method of fundamental solutions in geomechanic of reservoirs and wells. Moskva: RUDN, 2013.

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3

1948-, Gray William G., ed. Numerical methods for differential equations: Fundamental concepts for scientific and engineering applications. Englewood Cliffs, N.J: Prentice Hall, 1992.

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4

Société française de chimie. Division de chimie physique. International Meeting. Chemical reactivity in liquids: Fundamental aspects. Edited by Moreau Michel and Turq Pierre. New York: Plenum Press, 1988.

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5

Clerck, Marcel de. The operational seminar: A training method to foster development. Geneva: InternationalBureau of Education, 1990.

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6

Martynov, G. A. Fundamental theory of liquids: Method of distribution functions. Bristol: A. Hilger, 1992.

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7

Hartley, T. T. A solution to the fundamental linear fractional order differential equation. [Cleveland, Ohio]: National Aeronautics and Space Administration, Lewis Research Center, 1998.

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8

Gokalp, Mulayim Zia. The fundamental problems of Turkish cooperatives and proposals for their solution. Istanbul: Friedrich Ebert Foundation, 1990.

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9

Clark, R. W. A new iterative matrix solution procedure for three-dimensional panel methods. New York: AIAA, 1985.

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10

Logg, Anders, Kent-Andre Mardal, and Garth Wells, eds. Automated Solution of Differential Equations by the Finite Element Method. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23099-8.

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Частини книг з теми "Method of fundamental solution"

1

Partridge, P. W., C. A. Brebbia, and L. C. Wrobel. "Other Fundamental Solutions." In The Dual Reciprocity Boundary Element Method, 223–65. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-3690-7_6.

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2

Evensen, Geir, Femke C. Vossepoel, and Peter Jan van Leeuwen. "Maximum a Posteriori Solution." In Springer Textbooks in Earth Sciences, Geography and Environment, 27–33. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-96709-3_3.

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AbstractWe will now introduce a fundamental approximation used in most practical data-assimilation methods, namely the definition of Gaussian priors. This approximation simplifies the Bayesian posterior, which allows us to compute the maximum a posteriori (MAP) estimate and sample from the posterior pdf. This chapter will introduce the Gaussian approximation and then discuss the Gauss–Newton method for finding the MAP estimate. This method is the starting point for many of the data-assimilation algorithms discussed in the following chapters.
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3

Svanadze, Merab. "Fundamental Solutions in Elasticity." In Potential Method in Mathematical Theories of Multi-Porosity Media, 25–56. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28022-2_2.

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4

Fujitani, Y. "Analysis of the Elastic Fundamental Solution by Finite Element Method." In Computational Mechanics ’88, 421–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-61381-4_102.

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5

Gáspár, Csaba. "A Fast and Stable Multi-Level Solution Technique for the Method of Fundamental Solutions." In Meshfree Methods for Partial Differential Equations IX, 19–42. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15119-5_2.

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6

Howell, John R., M. Pinar Mengüç, Kyle Daun, and Robert Siegel. "Fundamental Radiative Transfer Relations and Approximate Solution Methods." In Thermal Radiation Heat Transfer, 489–534. Seventh edition. | Boca Raton : CRC Press, 2021. | Revised edition of: Thermal radiation heat transfer / John R. Howell, M. Pinar Mengüç, Robert Siegel. Sixth edition. 2015.: CRC Press, 2020. http://dx.doi.org/10.1201/9780429327308-11.

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7

Augustin, Matthias Albert. "Methods of Fundamental Solutions in Poroelasticity." In A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs, 91–114. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17079-4_5.

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8

Gáspár, Csaba. "Some Regularized Versions of the Method of Fundamental Solutions." In Meshfree Methods for Partial Differential Equations VI, 181–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32979-1_12.

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Poullikkas, Andreas, Andreas Karageorghis, and Georgios Georgiou. "The Method of Fundamental Solutions in Three-Dimensional Elastostatics." In Parallel Processing and Applied Mathematics, 747–55. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-48086-2_83.

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Kompiš, V., and J. Búry. "Hybrid-Trefftz Finite Element Formulations Based on The Fundamental Solution." In IUTAM Symposium on Discretization Methods in Structural Mechanics, 181–87. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4589-3_21.

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Тези доповідей конференцій з теми "Method of fundamental solution"

1

Muzik, Juraj. "GROUNDWATER FLOW SOLUTION USING METHOD OF FUNDAMENTAL SOLUTIONS." In 16th International Multidisciplinary Scientific GeoConference SGEM2016. Stef92 Technology, 2016. http://dx.doi.org/10.5593/sgem2016/b11/s02.102.

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2

Chen, W., and F. Z. Wang. "A method of fundamental solution without fictitious boundary." In BEM/MRM 2009. Southampton, UK: WIT Press, 2009. http://dx.doi.org/10.2495/be090101.

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3

ROUBIDES, PASCAL. "THE FUNDAMENTAL SOLUTION METHOD FOR ELLIPTIC BOUNDARY VALUE PROBLEMS." In Proceedings of the International Conference (ICCMSE 2003). WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704658_0119.

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4

Erdo¨nmez, Cengiz, and Hasan Saygın. "Conduction Heat Transfer Problem Solution Using the Method of Fundamental Solutions With the Dual Reciprocity Method." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72566.

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Анотація:
The method of fundamental solutions (MFS) is first proposed in 1964 by Kupradze and theoretical basis of this method is constructed at the end of 1980’s. As a meshless method, no domain meshing is required for MFS. Fundamental solutions are used to solve problems without coping with the singularity on the boundary because of the fictitious boundary defined containing the domain of the problem. In this paper effectiveness of the MFS will be introduced by two test problem for the homogeneous and inhomogeneous modified helmholtz equations. In-homogeneous terms are approximated by using the method of particular solutions through the dual reciprocity method. The conduction heat transfer problem is defined and transformed to the corresponding elliptic partial differential equation by using finite difference and the method of lines method which gives an inhomogeneous helmholtz equation. Then the problem is solved iteratively by using the MFS. Two test problem are solved by both the finite element method (FEM) and MFS and compared in the figures. It can be seen that as a meshless method, MFS gives very good results for the test problems. The thermal shock problem presented here also gives accurate solutions by using MFS and agrees well with the FEM solution.
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5

Fei Zhao, Wuyi Yu, Maoqing Li, and Xin Li. "Volumetric texture synthesis using fundamental solution methods." In Education (ICCSE). IEEE, 2009. http://dx.doi.org/10.1109/iccse.2009.5228135.

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6

Buryachenko, Valeriy A. "Method of Fundamental Solution in Thermoelasticity of Random Structure Matrix Composites." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86515.

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One considers linear thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of non-canonical (i.e. non-ellipsoidal) shape. The representations of the effective properties (effective moduli, thermal expansion, and stored energy) are expressed through the statistical averages of the interface polarization tensors (generalizing the initial concepts, see e.g. [1] and [2]) introduced apparently for the first time. The new general integral equations connecting the stress and strain fields in the point being considered with the stress and strain fields in the surrounding points are obtained for the random fields of heterogeneities. The method is based on a recently developed centering procedure where the notion of a perturbator is introduced in terms of boundary interface integrals estimated by the method of fundamental solution for a single inclusion inside the infinite matrix. This enables one to reconsider basic concepts of micromechanics such as effective field hypothesis, quasi-crystalline approximation, and the hypothesis of ellipsoidal symmetry. The results of this reconsideration are quantitatively estimated for some modeled composite reinforced by aligned homogeneous heterogeneities of non canonical shape. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.
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TSEPOURA, K. G., S. V. TSINOPOULOS, S. PAPARGYRI-BESKOU, and D. POLYZOS. "STATIC FUNDAMENTAL SOLUTION IN 3-D GRADIENT ELASTICITY." In Proceedings of the Fifth International Workshop on Mathematical Methods in Scattering Theory and Biomedical Technology. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777140_0023.

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Wu, Li-na, Hai-e. Wei, and Quan Jiang. "Fast algorithm for the method of fundamental solution subjected to symmetry problems." In 2012 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA 2012). IEEE, 2012. http://dx.doi.org/10.1109/spawda.2012.6464094.

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Ten, K. M. "The Electrical VES Method for Solution of a Fundamental Problem of Exploratory Geophysics." In Saint Petersburg 2008. Netherlands: EAGE Publications BV, 2008. http://dx.doi.org/10.3997/2214-4609.20146916.

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Karageorghis, A., G. Fairweather, and P. A. Martin. "RECENT ADVANCES IN THE METHOD OF FUNDAMENTAL SOLUTIONS." In Proceedings of the 1st Asian Workshop on Meshfree Methods. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812778611_0005.

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Звіти організацій з теми "Method of fundamental solution"

1

Friedman, A. Partially-Corrected Euler Method for Solution of ODE's. Office of Scientific and Technical Information (OSTI), September 2007. http://dx.doi.org/10.2172/922092.

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2

Burke, G. J. Evaluation of the discrete complex-image method for a NEC-like moment-method solution. Office of Scientific and Technical Information (OSTI), January 1996. http://dx.doi.org/10.2172/201799.

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3

Schiesser, W. E. Method of lines solution of the Korteweg-de Vries equation. Office of Scientific and Technical Information (OSTI), June 1993. http://dx.doi.org/10.2172/64337.

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4

Striuk, Andrii M. Software engineering: first 50 years of formation and development. [б. в.], December 2018. http://dx.doi.org/10.31812/123456789/2880.

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The article analyzes the main stages of software engineering (SE) development. Based on the analysis of materials from the first SE conferences (1968-1969), it was determined how the software crisis prompted scientists and practitioners to join forces to form an engineering approach to programming. Differences in professional training for SE are identified. The fundamental components of the training of future software engineers are highlighted. The evolution of approaches to the design, implementation, testing and documentation of software is considered. The system scientific, technological approaches and methods for the design and construction of computer programs are highlighted. Analysis of the historical stages of the development of SE showed that despite the universal recognition of the importance of using the mathematical apparatus of logic, automata theory and linguistics when developing software, it was created empirically without its use. The factor that led practitioners to turn to the mathematical foundations of an SE is the increasing complexity of software and the inability of empirical approaches to its development and management to cope with it. The training of software engineers highlighted the problem of the rapid obsolescence of the technological content of education, the solution of which lies in its fundamentalization through the identification of the basic foundations of the industry. It is determined that mastering the basics of computer science is the foundation of vocational training in SE.
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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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Jerome L.V. Lewandowski. A Marker Method for the Solution of the Damped Burgers' Equatio. Office of Scientific and Technical Information (OSTI), November 2005. http://dx.doi.org/10.2172/934517.

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Weber, F. A., L. B. Da Silva, T. W. Jr Barbee, D. Ciarlo, and M. Mantler. Quantitative XRFA of carbon in a special matrix by the fundamental parameter method. Office of Scientific and Technical Information (OSTI), May 1996. http://dx.doi.org/10.2172/264594.

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Sharan, M., E. J. Kansa, and S. Gupta. Application of multiquadric method for numerical solution of elliptic partial differential equations. Office of Scientific and Technical Information (OSTI), January 1994. http://dx.doi.org/10.2172/10156506.

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Hajghassem, Mona, Eric C. Cyr, and Denis Ridzal. A time-parallel method for the solution of PDE-constrained optimization problems. Office of Scientific and Technical Information (OSTI), December 2015. http://dx.doi.org/10.2172/1430466.

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10

Jerome L.V. Lewandowski. Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method. Office of Scientific and Technical Information (OSTI), January 2005. http://dx.doi.org/10.2172/836622.

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