Numerical simulation of the continuous media problems on hybrid computer systems

Четверушкин, Б. Н.; Шильников, Е. В.; Давыдов, Александр Александрович

doi:10.1016/j.advengsoft.2013.02.003

Cited by 7 publications

(2 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Taking the Pennes term from the (n + 1) layer one can obtain more soft condition of the stability without use of the implicit schemes, which become enough sophisticated in case of the irregular grids. In order to improve the stability of explicit scheme used in current study the flux relaxation method [2,3] is used. Instead of the direct numerical computation of equation (2.1) ((3.3) in the grid form) it is proposed to replace this one by the following parametric system:…”

Section: Numerical Computationmentioning

confidence: 99%

Numerical modeling and optimization of the cryosurgery operations

Kudryashov

Shilnikov

2015

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

Please cite this article as: N.A. Kudryashov, K.E. Shilnikov, Numerical modeling and optimization of the cryosurgery operations, Journal of Computational and Applied Mathematics (2015), http://dx.Abstract Numerical computation of the three dimensional problem of the freezing interface propagation during the cryosurgical impact coupled with the multi-objective optimization mechanism is used in order to improve the efficiency and safety of the cryosurgery operations performing. The heat transfer in soft tissue during the thermal exposure to low temperature is described by the Pennes bioheat model. The finite volume method combined with the control volume approximation of the heat fluxes is applied for the cryosurgery numerical modeling on the tumor tissue of a quite arbitrary shape. The flux relaxation approach is used for the stability improvement of the explicit finite difference schemes. The generalized method of effective traversals is proposed for the searching of the Pareto front segments as the multiobjective optimization problem solutions.

show abstract

Section: Numerical Computationmentioning

confidence: 99%

Numerical modeling and optimization of the cryosurgery operations

Kudryashov

Shilnikov

2015

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…In this context, a task of interest is to develop explicit schemes that admit nearly full parallelization. For parabolic equations, the hyperbolization technique is successfully used for this purpose [1][2][3][4][5][6][7][8][9][10][11][12], which makes it possible to relax the stability conditions for explicit algo rithms.…”

Section: Introductionmentioning

confidence: 99%