# 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.