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

Abstract

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