Application of the automatic code generation and symbolic computation techniques to numerical solution of PDE problems

Abstract A software package for the numerical solution of systems linear and nonlinear partial differential equations by grid methods is presented, which combines symbolic computations automatic code generation techniques. Discretization carried out finite volumes differences on two-dimensional three-dimensional regular rectangular grids. The algebraic obtained as a result discretization performed Newton’s method with employment third-party SLAE solvers. generated can exploit shared distributed memory parallelisms take advantage heterogeneous computations. results solutions two sample CFD problems fluid flow in cylindrical cavity filled electrically conductive liquid driven traveling rotating magnetic fields are presented.