

2007 year, number 2
V. P. Il’in
Institute of Computational Mathematics and Mathematical Geophysics, SB RAS Novosibirsk, Russia, Email:ilin@sscc.ru
Pages: 99111
Abstract >>
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

M. I. Ivanov^{1}, V. A. Kateshov^{1}, I. A. Kreme^{1}r, and M. V. Urev^{2}
^{1}Centre RITM Corporation, Novosibirsk, Russia, Email: Kremer@aoritm.co ^{2}Institute of Computational Mathematics and Mathematical Geophysics, SB RAS Novosibirsk, Russia, Email: urev@nmsf.sscc.ru
Pages: 112120
Abstract >>
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

M. I. Ivanov^{1}, V. A. Kateshov^{1}, I. A. Kremer^{1}, and M. V. Urev^{2}
^{1}Centre RITM Corporation, Novosibirsk, Russia, Email: Kremer@aoritm.com ^{2}Institute of Computational Mathematics and Mathematical Geophysics, SB RAS Novosibirsk, Russia, Email: urev@nmsf.sscc.ru
Pages: 121130
Abstract >>
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.

M. G. Persova^{1}, Yu. G. Soloveichik^{1}, G. M. Trigubovich^{2}, M. V. Abramov^{1}, and A. V. Zinchenko^{1}
^{1}Novosibirsk State Technical University Novosibirsk, Russia, Email: solov@fpm.ami.nstu.ru ^{2}Siberian Research Institute of Geology, Geophysics, and Mineral Resources, Novosibirsk, Russia, Email: tgm@sniiggims.ru
Pages: 131138
Abstract >>
Based on threedimensional 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.

M. G. Persova, Yu. G. Soloveichik, E. V. Khitsenko, M. G. Tokareva, and Yu. V. Trakimus
Novosibirsk State Technical University Novosibirsk, Russia, Email: solov@fpm.ami.nstu.ru
Pages: 139146
Abstract >>
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 finiteelement 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.

V. P. Il’in^{1} and S. G. Pudov^{2}
^{1}Institute of Computational Mathematics and Mathematical Geophysics, SB RAS Novosibirsk, Russia, Email: ilin@sscc.ru ^{2}Technological Design Institute of Digital Technique, SB RASNovosibirsk, Russia, Email: pudov@dote.ru
Pages: 147152
Abstract >>
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.

S. G. Pudov
Technological Design Institute of Digital Technique, SB RASNovosibirsk, Russia, Email: pudov@dote.ru
Pages: 153158
Abstract >>
A preconditioned semiconjugate 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. M. Matsekh^{1} and E. P. Shurina^{2}
^{1}Los Alamos National Laboratory, Los Alamos, USA Email: matsekh@lanl.gov ^{2}Novosibirsk State Technical University, Novosibirsk, Russia ^{2}Institute of Computational Technologies, SB RAS Novosibirsk, Russia, Email: shurina@online.sinor.ru
Pages: 159169
Abstract >>
A new implementation of the Godunovinverse iteration, that is, inverse iteration with guaranteed accuracy, is presented. A new implementation of the Cullum

E. P. Shurina^{1}, O. V. Nechaeva^{2}, and O. V. Nechaev^{2}
^{1}The Novosibirsk State Technical University, Novosibirsk, Russia, Email: shurina@online.sinor.ru ^{2}Looch Research and Production Association for Geophysical Equipment, Novosibirsk, Russia, Email: howl@ngs.ru
Pages: 170176
Abstract >>
A mixed variational problem formulation is proposed to find the electric field as a solution to a secondorder differential equation and the magnetic flux density vector as a solution to a firstorder differential equation.

Y. L. Gurieva
Institute of Computational Mathematics and Mathematical Geophysics, SB RASNovosibirsk, Russia, Email: yana@lapasrv.sscc.ru
Pages: 177181
Abstract >>
The semiconjugate residual algorithm is applied to solving a threedimensional Navier

A. V. Petukhov
Institute of Computational Mathematics and Mathematical Geophysics, SB RAS Novosibirsk, Russia, Email: mnu@ngs.ru
Pages: 182191
Abstract >>
Numerical methods for solving 3D mixed boundaryvalue problems for a Helmholtz complex equation describing electromagnetic fields with the timeharmonic dependence are presented. Divergencefree barycentric finite volume approximations on tetrahedral grids are proposed. Computation of the local balance matrices and assembling of the global matrix are based on elementbyelement technologies. A preconditioned semiconjugate residual method is described for iterative solving the resulting real system of linear algebraic equations with a nonsymmetric sparse highorder matrix. Results of numerical experiments for a series of model problems on a sequence of refined grids are presented. The results demonstrate the secondorder accuracy of the grid solutions and the high convergence rate of the iterative processes

V. M. Sveshnikov
Institute of Computational Mathematics and Mathematical Geophysics, SB RASNovosibirsk, Russia, Email: victor@lapasrv.sscc.ru
Pages: 192197
Abstract >>
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.

I. A. Shmakov
Institute of Computational Mathematics and Mathematical Geophysics, SB RASNovosibirsk, Russia, Email: i_shmakov@ngs.ru
Pages: 198203
Abstract >>
The finite volume method is considered for numerical solving the onedimensional 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 underrelaxation method. The secondorder convergence of the method is illustrated by results of numerical experiments

