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.
Apie lygiagrečiuosius algoritmus, skirtus netiesinių difuzijos lygčių sprendimui ir jų naudojimą vaizdų filtravimui
Šiame darbe nagrinėjami lygiagretieji algoritmai, kurie skirti netiesinių nestacionarių difuzijos lygčių sprendimui. Pirmiausia yra suformuluoti netiesinių filtrų matematiniai modeliai. Šie uždaviniai aproksimuoti baigtinių tūrių schemomis. Lygiagretieji algoritmai konstruojami duomenų lygiagretumo metodu. Jie realizuoti autorių sukurtu ParSol programavimo įrankiu. Pateiktas trumpas šio įrankio aprašymas. Ištirtas lygiagrečiųjų algoritmų efektyvumas ir pateikti algoritmų išplečiamumo analizės rezultatai. Teorines išvados palygintos su skaičiavimo rezultatais. Netiesiniai difuziniai filtrai pritaikyti galvos kompiuterinių tomogramų filtravimui.
Čiegis, R., Jakušev, A., Krylovas, A., & Suboč, O. (2005). Parallel algorithms for solution of nonlinear diffusion problems in image smoothing. Mathematical Modelling and Analysis, 10(2), 155-172. https://doi.org/10.3846/13926292.2005.9637279
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.
