TchebyFlow Technology

TchebyFlow technology leverages on mathematical Theory of Approximation (Chebyshev, 19th Century). Exploiting the full calculation power of the 21st-Century technologies, it guarantees the exponential convergence of numerical results with the grid refinement, a grid whose structure is unique. No more worry about choosing the « right » grid, structured or not, made of triangles or else, no more worry about grid local refinement as it is the case with all the traditional methods (finite elements, finite volumes, finite differences). Furthermore, numerical discretization of mathematical model is 100%-Fidelity with the model. There is no introduction of ad-hoc numerical tricks or supplementary ad-hoc models (upwind, …). As a result, TchebyFlow delivers a numerical solution which is completely free from any bias (artificial viscosity, erroneous flux conditions on the boundaries, …). It is THE solution to the mathematical model. It’s unique.

TchebyFlow solves integro-differential equations with SPACE-TIME global approach: What is happening anywhere at any time depends on everything elsewhere, before and after.

Technology is suitable for both non-periodic & periodic functions. SPACE-TIME polynomial expansion transforms a derivative into a full & ill-conditioned matrix. This leads to extremely efficient differential solvers thanks to TchebyFlow know-how. No more Past-Present-Future concept No more Time Marching consideration.

By nature, TchebyFlow technology guarantees THE numerical solution with 100%-confidence. Solutions are obtained from ultra-fast & 100%-fidelity TchebyFlow solvers. Any multi-scale (simultaneously macro/micro/nano) behavior is particularly perfectly resolved, in thermic, fluidic, acoustics, mechanics & vibratory mechanics, electro-magnetism, chemistry, electro-chemistry.

Technology results from 50-year scientific career path. It leans on unique & optimal solving methods, enriched by a library of generic technological bricks.