Numerical methods

Language

Implementation of mathematical modeling methods in engineering and manufacturing allows to reduce the number of prototypes and their testing. Forecasting activity and risk asessment in economics and environmental science at present can’t go without mathematical modeling methods. At the same time, software implementation of any deterministic or stochastic mathematical model requires the use of computational mathematical methods.

In connection with this, the main area of our company is the algorithmization and software implementation of the various computational mathematical methods, which are the following:

• multivariate conditional and unconditional optimization;
• numerical solution of differential equations in partial derivatives;
• numerical integration and differentiation;
• systems of linear and nonlinear algebraic equations solving;
• multivariate data approximation and interpolation ;
• statistical data analysis, including classification methods, factor and time series analyses.

Math equation solvers

Solutions in the following mathematical areas: Optimization/Minimization/Maximization, Linear Algebra, Quadrature/Integration, Partial Differential Equations, Approximation, Interpolation/Extrapolation, Roots and Zeros, Nonlinear Functions, Special Functions, Differential Equations, Eigensystems, Random Numbers, Integral Equations, Spectrum Analysis, Statistics, Utility Functions, Matrix and Vector Mathematics.

Numerical optimization

Finite element and finite difference methods;

Sequential unconstrained minimization;

Reduced gradient methods;

Sequential quadratic programming;

Interior-point methods;

Algorithmic Issues: search directions, line search, trust-region, merit functions, filter methods, conjugate gradients, factorization, convex set, convex functions, starting points, jamming.

Мesh generations

Various mesh techniques could be applied:

Delaunay triangulations and constrained Delaunay triangulations;

Optimal triangulations, such as Delaunay, min-max angle, and minimum weight triangulations;

Contouring algorithms for isosurfaces;

Curve and surface reconstruction from point sets;

Parameterization, simplification, and editing of surface meshes;

Quadrilateral, hexahedral, pyramidal, wedge, tetrahedral and mixed mesh element generations;

Unstructured or multi-domain mesh generation;

Refinement and coarsening of simplicial meshes;

Triangular and tetrahedral mesh generation techniques: Delaunay-based, grid-based, octree-based, and advancing front;

Mesh improvement: vertex smoothing and element transformations;

Geometric primitives and numerical robustness;

Interpolation, including barycentric and mean value coordinates.