Home – Home – Jornals – Avtometriya 2007 number 2

Topical issues of parallelizing computational methods and technologies for implementing the main mathematical modeling stages in solving a wide range of large applied problems are considered. Computation

Some issues of modeling stationary electromagnetic fields for 3D regions including inhomogeneous conducting media are considered. The problems are formulated in terms of potentials. It is proposed to solve the problems by a subdomain iteration method. A model example illustrates the convergence of the proposed method

Some issues of calculating the unstationary electromagnetic fields in 3D media with a piecewise homogeneous conductivity are considered. Potential statements of the problems in the time domain are used. An approach to solving this kind of problems is proposed. The computational stability of the method at late times is verified on a model example.

Based on three-dimensional mathematical modeling of nonstationary electromagnetic fields with a source in the form of an ungrounded current loop, two technologies are compared: areal electromagnetic sounding with a fixed source and remote sensors and profile survey with a coaxial device (the latter has already found numerous applications). Advantages of sounding with the use of remote sensors for electromagnetic field recording are demonstrated by examples of solving two problems.

Possibilities are studied of finding deep features, based on the measurements of an unsteady electric field in a cased well located far from another cased well with a vertical electric line exciting the field. The study is performed by means of finite-element modeling developed by the authors. The results obtained confirm the presence of information on the exploratory prospect in the recorded signals. Methods of extraction of this information from experimental data are discussed.

Iterative solving SLAE with nonsymmetric square real matrices by means of the robust modified method of generalized conjugate residuals and the hierarchical family of algorithms for incomplete matrix decomposition into triangular multipliers is considered. Special features of software algorithms based on symbolic factorization of matrices stored in a sparse row format are described. Experimental numerical results are given for a representative series of model problems. They demonstrate comparative efficiency of the methods.

A preconditioned semi-conjugate residual algorithm for solving systems of algebraic equations with a nonsymmetric square matrix is presented. Most of the calculations in the algorithm is accounted for vector operations whose number grows quadratically with the number of stored directing vectors. A parallel implementation of the algorithm is studied experimentally, the Eisenstat modification being chosen as the preconditioning. An algorithm for parallelizing matrix operations is presented for special problems.

A new implementation of the Godunov-inverse iteration, that is, inverse iteration with guaranteed accuracy, is presented. A new implementation of the Cullum

A mixed variational problem formulation is proposed to find the electric field as a solution to a second-order differential equation and the magnetic flux density vector as a solution to a first-order differential equation.

The semi-conjugate residual algorithm is applied to solving a three-dimensional Navier

Numerical methods for solving 3D mixed boundary-value problems for a Helmholtz complex equation describing electromagnetic fields with the time-harmonic dependence are presented. Divergence-free barycentric finite volume approximations on tetrahedral grids are proposed. Computation of the local balance matrices and assembling of the global matrix are based on element-by-element technologies. A preconditioned semi-conjugate residual method is described for iterative solving the resulting real system of linear algebraic equations with a nonsymmetric sparse high-order matrix. Results of numerical experiments for a series of model problems on a sequence of refined grids are presented. The results demonstrate the second-order accuracy of the grid solutions and the high convergence rate of the iterative processes

A new approach to the method of iterations on subdomains without intersection is proposed. Its distinction is that the Dirichlet condition is established at the boundary at all iterations on subdomains. The convergence of the approach is numerically analyzed using an example of solving a model problem.

The finite volume method is considered for numerical solving the one-dimensional horizontal unstationary problem of drying a homogeneous layer of mowed grass in the Cartesian coordinate system. The time derivative is discretized by the parametric scheme and the nonlinear algebraic system is solved by the iterative under-relaxation method. The second-order convergence of the method is illustrated by results of numerical experiments