Theoretical considerations in numerical analysis in view of modeling a pulsatile magnetoactive pump for medical circulatory support

Abstract

This paper presents theoretical considerations on numerical modelling of magnetic fields in view of modeling a pulsatile magnetoactive pump based on the use of flexible magnetic material. To some extent, this publication fills a gap in the literature of numerical methods: the comparisons and analyses of some results obtained from the 'old' FDS, the 'popular' FEM. The authors, in previous publications, have presented numerical results that can be now considered as numerical facts. This contribution presents theoretical considerations from which the comparisons of the numerical results obtained from a strong formulation using finite difference schemes (FDS) and a weak formulation using finite element method (FEM) can be interpreted.Index Terms--Boundary value problems, continuity conditions at interface, finite difference methods, finite element methods, magnetic field, weak formulation, strong formulation, pulsatile magnetoactive pump, medical circulatory support. (13) into equation (12) produces the partial derivative of A I,J with respect to y in the air: J I J I J I J I J I Substitution of equation