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.
In this work we consider parallel variational algorithms for solution of linear systems. Theoretical analysis explains the superlinear convergence rate for two step gradient descent method. A new modification of the algorithm is proposed. Results of computational experiments are given for a linear system of equations approximating 3D elliptic boundary value problem. All algorithms are implemented using parallel array object tool ParSol, then a parallel algorithm follows semi‐automatically from the serial one. Results of the scalability analysis are presented and the efficiency of the presented parallel algorithm is investigated experimentally.
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