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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
 Interiorpoint methods
 Algorithmic issues: search directions, line search, trustregion, 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, minmax 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 multidomain mesh generation
 Refinement and coarsening of simplicial meshes
 Triangular and tetrahedral mesh generation techniques: Delaunaybased, gridbased, octreebased, and advancing front;
 Mesh improvement: vertex smoothing and element transformations
 Geometric primitives and numerical robustness
 Interpolation, including barycentric and mean value coordinates.
