Richard Liska

Learn More
The support operator method designs mimetic finite difference schemes by first constructing a discrete divergence operator based on the divergence theorem, and then defining the discrete gradient operator as the adjoint operator of the divergence based on the Gauss theorem connecting the divergence and gradient operators, which remains valid also in the(More)
The article deals with automation of the process of numerical solving of partial differential equations systems (PDES) by means of computer algebra. For solving PDES the finite difference method is applied. The computer algebra system REDUCE and the numerical programming language FORTRAN are used in the methodology presented, its main aim being to speed up(More)
A new optimization-based synchronized flux-corrected conservative interpolation (remap-ping) of mass and momentum for arbitrary Lagrangian–Eulerian hydro methods is described. Fluxes of conserved variables – mass and momentum – are limited in a synchronous way to preserve local bounds of primitive variables – density and velocity. In numerical simulations(More)
The paper deals with the formalization of the basic operator method for construction of difference schemes for the numerical solving of partial differential eq~ua-tions. The strength of the basic operator method lies on the fact that it produces fully conservative difference schemes. The difference mesh can be non-orthogonal but has to be logically(More)
Some large scale physical computations require algorithms performing symbolic computations with a particular class of algebraic formulas in a numerical code. Developing and implementing such algorithms in a numerical programming language is a tedious and error prone task. The algorithms can be developed in a computer algebra system and their correctness can(More)