Specialized Web Portal for Solving Problems on Multiprocessor Computing Systems

A system for remote calculations called “Specialized web portal for solving problems on multiprocessor computing systems” has been developed and installed at the Department of Ill-Posed Problems of Analysis and Applications of the Institute of Mathematics and Mechanics UrB RAS. The parallel algorithms have been incorporated into this system to solve the inverse gravity problem of lateral density reconstruction, the structural inverse gravity and magnetic problem of the contact surfaces reconstruction, and solving SLAEs with block-tridiagonal matrices in geoelectrics problems

Calculation of Relaxation Spectra from Stress Relaxation Measurements

Application of stress on materials increases the energy of the system. After removal of stress, macromolecules comprising the material shift towards equilibrium to minimize the total energy of the system. This process occurs through molecular rearrangements or “relaxation” during which macromolecules attain conformations of a lower energetic state. The time, however, that is required for these rearrangements can be short or long depending on the interactions between the macromolecular species that consist the material. When rearrangements occur faster than the time of observation (experimental timescale) then molecular motion is observed (flow) and the material is regarded as viscou

Algorithms for solving inverse geophysical problems on parallel computing systems

For solving inverse gravimetry problems, efficient stable parallel algorithms based on iterative gradient methods are proposed. For solving systems of linear algebraic equations with block-tridiagonal matrices arising in geoelectrics problems, a parallel matrix sweep algorithm, a square root method, and a conjugate gradient method with preconditioner are proposed. The algorithms are implemented numerically on a parallel computing system of the Institute of Mathematics and Mechanics (PCS-IMM), NVIDIA graphics processors, and an Intel multi-core CPU with some new computing technologies. The parallel algorithms are incorporated into a system of remote computations entitled "Specialized Web-Portal for Solving Geophysical Problems on Multiprocessor Computers." Some problems with "quasi-model" and real data are solved. © 2013 Pleiades Publishing, Ltd

Multistage Homotopy Analysis Method for Solving Nonlinear Integral Equations

In this paper, we present an efficient modification of the homotopy analysis method (HAM) that will facilitate the calculations. We then conduct a comparative study between the new modification and the homotopy analysis method. This modification of the homotopy analysis method is applied to nonlinear integral equations and mixed Volterra-Fredholm integral equations, which yields a series solution with accelerated convergence. Numerical illustrations are investigated to show the features of the technique. The modified method accelerates the rapid convergence of the series solution and reduces the size of work