Parallel forming of preconditioners based on the approximation of the Sherman-Morrison inversion formula

Исследуются возможности ускорения предобусловленных методов бисопряженных градиентов (BiCGStab, Bi-Conjugate Gradient Stabilized) с предобусловливателем на основе аппроксимации обращения матрицы по формуле Шермана-Моррисона. Рассмотрена новая форма параллельного алгоритма, использующая матрично-векторные произведения при формирования матриц предобусловливателя. Показана эффективность распараллеливания наиболее ресурсоемких операций этого предобусловливателя на графических процессорах. Acceleration of preconditioned bi-conjugate gradient stabilized (BiCGStab) methods with preconditioners based on the matrix approximation by the Sherman-Morrison inversion formula is studied. A new form of the parallel algorithm using matrix-vector products to generate preconditioning matrices is proposed. A parallelization efficiency of the most resource-intensive operations of such preconditioners on multi-core central and graphics processing units (CPUs and GPUs) is shown.

A PARALLEL MULTIRATE ALGORITHM FOR THE NUMERICAL INTEGRATION OF SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS

The new approach to calculate dynamic behavior of large-scale systems, separated on subsystems is presented. Parallelization efficiency of computing process is described.

Analysis of the diffusion influence on the bubble dynamics in an acoustic field

A diffusion problem for a spherically symmetric gas bubble in a liquid in an isotropic acoustic field is considered. The problem is solved both for a single bubble and for a bubble in a monodisperse cluster. A numerical method for solving the diffusion problem is developed. For the oscillating part of the diffusion problem the numerical experiments have been carried out for different amplitudes of the external pressure. A comparison is made between the calculation results obtained by the approximation theory and the numerical method presented. The effect of taking into account the mass change on the bubble dynamics is studied. For extensive parametric research the algorithm is paralleled and the parallelization efficiency is evaluated.