Čiegis, R.; Jakušev, A.; Krylovas, A.; Suboč, O. Parallel algorithms for solution of nonlinear diffusion problems in image smoothing. (English) Zbl 1073.65548 Math. Model. Anal. 10, No. 2, 155-172 (2005). Summary: We consider parallel algorithms for the solution of nonlinear parabolic partial differential equations. First mathematical models describing nonlinear diffusion filters are presented. The finite-volume method is used to approximate differential equations. Parallel algorithms are based on the domain decomposition method. The algorithms are implemented by using ParSol parallelization tool and a brief description of this tool is also presented. The efficiency of proposed parallel algorithms is investigated and results of the scalability analysis are given. Theoretical predictions are compared with results of computational experiments. Application of nonlinear diffusion filters for analysis of computer tomography images is discussed in the last section of the paper. Cited in 3 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35K55 Nonlinear parabolic equations 65Y05 Parallel numerical computation 76S05 Flows in porous media; filtration; seepage 76M20 Finite difference methods applied to problems in fluid mechanics Keywords:numerical examples; porous medium; finite differences; nonlinear diffusion filters; finite-volume method; domain decomposition method Software:Parsol PDFBibTeX XMLCite \textit{R. Čiegis} et al., Math. Model. Anal. 10, No. 2, 155--172 (2005; Zbl 1073.65548)