Universal numerical algorithms and their software implementation

Parallel Numerical Algorithms and Software

Numerical Implementation of Gradient Algorithms

A numerical method for computational implementation of gradient dynamical systems is presented. The method is based upon the development of geometric integration numerical methods, which aim at preserving the dynamical properties of the original ordinary differential equation under discretization. In particular, the proposed method belongs to the class of discrete gradients methods, which subst...

Numerical Linear Algebra Algorithms and Software

Reconstruction Algorithms for Positron Emission Tomography and Single Photon Emission Computed Tomography and their Numerical Implementation

The modern imaging techniques of Positron Emission Tomography and of Single Photon Emission Computed Tomography are not only two of the most important tools for studying the functional characteristics of the brain, but they now also play a vital role in several areas of clinical medicine, including neurology, oncology and cardiology. The basic mathematical problems associated with these techniq...

Numerical Algorithms of the Lawrence-Doniach Model for Layered Superconductors and their Parallel Implementation

The Lawrence{Doniach model is often used for studying vortex dynamics in su-perconductors which exhibit a layered structure. In solving these model equations numerically, the added degrees of complexity due to the coupling and nonlinearity of the model often warrant the extensive use of high-performance computers for their solution. Approaches for reducing the complexity of the Lawrence{Doniach...