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Parallel algorithms for solution of nonlinear diffusion problems in image smoothing. (English) Zbl 1073.65548

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.

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

Software:

Parsol
PDFBibTeX XMLCite