共查询到20条相似文献,搜索用时 15 毫秒
1.
A mathematical model of magnetotelluric sounding (MTS) is constructed for a layered medium with a nonhomogeneous inclusion.
The model is intended for marine studies. The problem is solved by the integral electric current method. A modified integral
current method is proposed capable of generating a solution with a small number of partitions of the nohomogeneity region.
The efficiency of the proposed method is demonstrated for H-polarized field. The behavior of apparent resistivity and magnetic parameter curves is investigated for marine MTS.
Translated from Prikladnaya Matematika i Informatika, No. 29, pp. 19–28, 2008. 相似文献
2.
M. S. Kruglyakov 《Computational Mathematics and Modeling》2010,21(1):30-40
We consider the direct problem of aerial electric sounding for a layered medium with a vertical cylindrical anomaly. We determine
the minimum size of the anomaly when it is indistinguishable from an infinite layer of the same conductivity. The integral
equation is solved by the integral current method. The concept of apparent conductivity is introduced for sounding problems
using a magnetic dipole. The calculations support the conjecture of the locality of aerial sounding and prove the high efficiency
of the integral current method for such problems. 相似文献
3.
We consider the direct problem of three-dimensional modeling of marine magnetotelluric sounding of nonhomogeneous media in
the presence of a vertical magnetic field component in the primary field. The problem is reduced to a system of volume integral
equations.
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Translated from Prikladnaya Matematika i Informatika, No. 27, pp. 46–53, 2007. 相似文献
4.
An algorithm is described for the two-dimensional inverse problem of magnetotelluric sounding with E-polarization, based on minimization of the Tikhonov smoothing functional by the Newton—Kantorovich method (linearization method). The method of integral equations is used in the algorithm to solve the direct problem of magnetotelluric sounding. An iterative method is constructed for the solution of the integral equation in the direct problem and a rate of convergence bound is derived for this method.Translated from Metody Matematicheskogo Modelirovaniya, Avtomatizatsiya Obrabotki Nablyudenii i Ikh Primeneniya, pp. 199–215, 1986. 相似文献
5.
N. I. Berezina V. I. Dmitriev N. A. Mershchikova 《Computational Mathematics and Modeling》2011,22(3):229-237
The article presents a quasi-one-dimensional method for solving the inverse problem of electromagnetic sounding. The quasi-one-dimensional
method is an iteration process that in each iteration solves a parametric one-dimensional inverse problem and a two-dimensional
direct problem. The solution results of these problems are applied to update the input values for the parametric one-dimensional
inverse problem in the next iteration. The method has been implemented for a two-dimensional inverse problem of magnetotelluric
sounding in a quasi-layered medium. 相似文献
6.
V. I. Dmitriev P. S. Belkin N. A. Mershchikova 《Computational Mathematics and Modeling》2005,16(4):289-300
The article computes the electromagnetic field on the surface of a layered medium with a local nonhomogeneity. The problem
is transformed from three- to two-dimensional and the singulari-ties are investigated using the integral equation method.
The proposed algorithm efficiently sim-ulates two-dimensional H-polarization fields by solving a system of integral equations. The method is particularly effective for solving inverse problems.
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Translated from Prikladnaya Matematika i Informatika, No. 18, pp. 5–16, 2004. 相似文献
7.
The two-dimensional magnetotelluric sounding inverse problem is solved by a quasi-one-dimensional method. A linearization
method is proposed for one-dimensional inverse problems. The appearance of false conducting structures in the solution of
the inverse problem is considered and some counter-measures are suggested. The quasi-one-dimensional method is applicable
to many-dimensional magnetotelluric sounding inverse problems if the electrical conductivity is a priori known to vary slowly
along the Earth’s surface.
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Translated from Prikladnaya Matematika i Informatika, No. 22, pp. 5–11, 2005. 相似文献
8.
The inverse problem of electromagnetic sounding of the shape of a conducting body is considered in the framework of the two-dimensional
model with E-polarization, assuming a cylindrical body of an arbitrary cross section embedded in a layered medium. The integral
equations are obtained for the case of an ideally conducting body and a body of finite conductivity. The linearization method
is applied to obtain an iterative method that finds a correction to the initial shape.
Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 96–103. 相似文献
9.
Solving a viscoelastic material boundary value problem provides the voltage, electric field and displacement current results to a certain class of electromagnetic problems. By means of the electromagnetic-viscoelastic analogy described herein, a solid mechanics finite element program can analyze a two-dimensional harmonic oscillation (constant frequency) electromagnetic problem for “lossy” dielectric materials. For this special class of electromagnetic field problems, the Maxwell equations reduce to a two-dimensional Laplace equation with complex coefficients. This form identically matches the viscoelasticity field equations.
This paper develops the electromagnetic-viscoelastic analogy from the basic governing field equations. The analogy is implemented in ABAQUS, a general solid mechanics finite element program. Simple one- and two-dimensional examples prove the accuracy and usefulness of the analogy. 相似文献
10.
V. F. Piven’ 《Differential Equations》2014,50(9):1182-1200
We study two-dimensional stationary and nonstationary boundary value problems of fluid filtration in an anisotropic inhomogeneous porous layer whose conductivity is modeled by a not necessarily symmetric tensor. For the velocity field, we introduce generalized singular Cauchy and Cauchy type integrals whose kernels are expressed via the leading solutions of the main equations and have a hydrodynamic interpretation. We obtain the limit values of a Cauchy type generalized integral (Sokhotskii-Plemelj generalized formulas). This permits one to develop a method for solving boundary value problems for the filtration velocity field. The idea of the method and its efficiency are illustrated for the boundary value problem of filtration in adjacent layers of distinct conductivities and the problem of the evolution of liquid interface. 相似文献
11.
V. I. Dmitriev 《Computational Mathematics and Modeling》1997,8(3):270-277
We consider the inverse sounding problem for a stratified medium using the variable magnetic field of a loop. A uniqueness
theorem and a theorem ensuring stable determination of the integral conductivity of the medium are proved. An algorithm is
proposed for the solution of the inverse problem based on a transformation from the time domain to the frequency domain.
Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 87–95. 相似文献
12.
A numerical solution method for two-dimensional electromagnetic field problems is presented using the B-spline finite-element expression based on polar coordinates. The technique has two main advantages: (1) to avoid the truncation errors at some curved boundaries and (2) to improve the accuracy of singular boundary-value problems with a sharp corner. The B-spline finite-element formulation in polar coordinates is derived and its numerical applications are illustrated by an eddy current problem and several waveguide eigenvalue problems. 相似文献
13.
A sensitive issue in numerical calculations for exterior flow problems, e.g.around airfoils, is the treatment of the far field boundary conditions on a computational domain which is bounded. In this paper we investigate this problem for two-dimensional transonic potential flows with subsonic far field flow around airfoil profiles. We take the artificial far field boundary in the subsonic flow region. In the far field we approximate the subsonic potential flow by the Prandtl-Glauert linearization. The latter leads via the Green representation theorem to a boundary integral equation on the far field boundary. This defines a nonlocal boundary condition for the interior ring domain. Our approach leads naturally to a coupled finite element/boundary element method for numerical calculations. It is compared with local boundary conditions. The error analysis for the method is given and we prove convergence provided the solution to the analytic transonic flow problem around the profile exists.
14.
K. V. Brushlinskii P. A. Ignatov 《Computational Mathematics and Mathematical Physics》2010,50(12):2071-2081
The mathematical apparatus of plasmastatics, which includes the MHD equilibrium equation and steady-state Maxwell equations,
is reduced, in two-dimensional problems arising due to symmetry, to a single scalar second-order elliptic equation with a
nonlinear right-hand side known as the Grad-Shafranov equation. In this paper, we numerically solve a series of boundary value
problems for this equation that model equilibrium plasma configurations in the magnetic field of the belt-like galathea trap
in a cylinder with two plasma embedded conductors. The mathematical model is outlined, the results of calculations of the
magnetic field and plasma pressure in the cylinder depending on the parameters of the problem are presented, and the main
integral characteristics of the trap are calculated. The existence and uniqueness of the solution is discussed; the limiting
values of the maximal pressure at which there exists a solution of the equilibrium problem are found. 相似文献
15.
The spectral method is considered for solving the direct and inverse problems of vertical electrical sounding (VES) in two-dimensional
quasi-layered media. The behavior of the anomalous potential spectrum is analyzed. An example is presented applying the spectral
method to solve the inverse VES problem.
Translated from Prikladnaya Matematika i Informatika, No. 2, pp. 34–43, 1999. 相似文献
16.
Alain L. Fymat 《Applied mathematics and computation》1979,5(1):23-39
The remote sensing of environmental particulate pollutants, particularly their size distribution, frequently leads to the solution of first-kind Fredholm integral equations. The corresponding physical kernel tends to smooth the behavior of the required function for all values of the dependent variable. Thus, the problem is ill posed and needs regularization by the introduction of constraints on the solution (closure condition). However, under physically realistic conditions, the original problem can be transformed so that it presents a unique and stable solution. One such condition is the so-called anomalous-diffraction approximation, for which we provide two alternate inversion formulae. We derive a new inversion formula (see our theorem) which generalizes that of Cooke and which also provides, as a special case, one of Titchmarsh's formulae. We propose a unifying viewpoint for a number of known integral inversion formulae, including those of Fox (his first theorem), Hardy, Hankel, Titchmarsh, Cooke, and our own, along with the mutual interrelationships that exist between them (Fig. 1 and Table 1). One solution to the particulate sounding problem is then obtained from a direct application of our formula [Eq. (25)]. An alternate solution is likewise obtained by applying Titchmarsh's formula (II) [Eq. (27)]. Both solutions can be independently recovered from Fox's first theorem, although under somewhat more restrictive conditions. They are shown to be identical, and to provide the unique solution to the remote sensing problem considered. 相似文献
17.
P. S. Belkin V. I. Dmitriev 《Moscow University Computational Mathematics and Cybernetics》2008,32(3):115-124
A method of solution of the inverse magnetotelluric sounding problem is considered. The method uses the known frequency-dependent magnetic field on the Earth’s surface. The magnetic field on the Earth’s surface is found with the help of a special technique from the known impedance on the Earth’s surface. The method is applied to solve typical inverse problems and provides for efficient determination of final solutions. 相似文献
18.
V. V. Dyakin V. Ya. Raevskii O. V. Umergalina 《Computational Mathematics and Mathematical Physics》2009,49(1):172-182
A direct magnetostatic problem for magnets with a finite-size inclusion is considered in an integrodifferential form. An approach is used that, under certain conditions, reduces the problem to a single integral equation on a two-dimensional manifold-the inclusion surface. As an important illustrative example, finite formulas are derived to compute the resulting field of a magnetic half-space with a spherical cavity in an arbitrary external field. 相似文献
19.
20.
A. V. Manzhirov 《Journal of Applied Mathematics and Mechanics》1985,49(6):777-782
A two-dimensional integral equatin appearing in axisymraetric contact problems for bodies with complex rheology is studied. A method of constructing the solution of this equation in proposed, based on inspecting the non-classical spectral properties of an integral operator. A contact problem for a non-uniformly aging viscoelastic foundation is solved as an example. 相似文献