Parallel algorithms for solution of nonlinear diffusion problems in image smoothing

In this work we consider parallel algorithms for solution of nonlinear parabolic PDEs. 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. Šiame darbe nagrinejami lygiagretieji algoritmai, kurie skirti netiesiniu nestacionariu difuzijos lygčiu sprendimui. Pirmiausia yra suformuluoti netiesiniu filtru matematiniai modeliai. Šie uždaviniai aproksimuoti baigtiniu tūriu schemomis. Lygiagretieji algoritmai konstruojami duomenu lygiagretumo metodu. Jie realizuoti autoriu sukurtu ParSolprogramavimo irankiu. Pateiktas trumpas šio irankio aprašymas. Ištirtas lygiagrečiuju algoritmu efektyvumas ir pateikti algoritmu išplečiamumo analizes rezultatai. Teorines išvados palygintos su skaičiavimo rezultatais. Netiesiniai difuziniai filtrai pritaikyti galvos kompiuteriniu tomogramu filtravimui. First Published Online: 14 Oct 201

A generalized domain decomposition paradigm for parallel incomplete LU factorization preconditionings

Incomplete LU (ILU) factorizations are popular preconditioning techniques for solving large linear systems that arise in scientific computations. We propose a (generalized) domain decomposition-based approach that leads to almost perfect speed-up with respect to standard ILU. Experimental results and theoretical spectral condition number are reported for two-dimensional problems. © 2001 Elsevier Science B.V.SCOPUS: ar.jinfo:eu-repo/semantics/publishe