Mathematical Modeling

Numerical methods

The implementation of mathematical modeling methods in engineering and manufacturing reduces the number of prototypes and their testing. While forecasting activity and risk assessment in economics and environmental science requires mathematical modeling. Furthermore, software implementation of any deterministic or stochastic model requires the use of computational methods.

The main focus area of our company is algorithm development and software implementation of the various computational mathematical methods, which are the following:

Multivariate conditional and unconditional optimization
Numerical solutions of partial differential equations
Numerical integration and differentiation
Solving systems of linear and nonlinear equations
Multivariate data approximation and interpolation
Statistical data analysis, including classification methods, factor and time series analyses.

Math equation solvers

Simmakers develops solutions for 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 can 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.