### Abstract

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 Par-Sol 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.

Original language | English |
---|---|

Pages (from-to) | 155-172 |

Number of pages | 18 |

Journal | Mathematical Modelling and Analysis |

Volume | 10 |

Issue number | 2 |

Publication status | Published - 2005 |

Externally published | Yes |

### Fingerprint

### Keywords

- Finite-volume method
- Nonlinear diffusion filters
- Parallel algorithms

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Modelling and Analysis*,

*10*(2), 155-172.

**Parallel algorithms for solution of nonlinear diffusion problems in image smoothing.** / Čiegis, R.; Jakušev, A.; Krylovas, A.; Suboč, O.

Research output: Contribution to journal › Article

*Mathematical Modelling and Analysis*, vol. 10, no. 2, pp. 155-172.

}

TY - JOUR

T1 - Parallel algorithms for solution of nonlinear diffusion problems in image smoothing

AU - Čiegis, R.

AU - Jakušev, A.

AU - Krylovas, A.

AU - Suboč, O.

PY - 2005

Y1 - 2005

N2 - 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 Par-Sol 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.

AB - 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 Par-Sol 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.

KW - Finite-volume method

KW - Nonlinear diffusion filters

KW - Parallel algorithms

UR - http://www.scopus.com/inward/record.url?scp=24944528130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944528130&partnerID=8YFLogxK

M3 - Article

VL - 10

SP - 155

EP - 172

JO - Mathematical Modelling and Analysis

JF - Mathematical Modelling and Analysis

SN - 1392-6292

IS - 2

ER -