The CUDA implementation of the method of lines for the curvature dependent flows

Title:

The CUDA implementation of the method of lines for the curvature dependent flows

Creator:

Oberhuber, Tomáš, Suzuki, Atsushi, and Žabka, Vítězslav

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c36dcaa2-c250-4d4e-94b7-e1259976a62e
uuid:c36dcaa2-c250-4d4e-94b7-e1259976a62e

Subject:

GPGPU, CUDA, parallel algorithms, light performance computing, differential geometry, mean-curvature flow, Willmore flow, Rnge-Kutta method, method of lines, explicit scheme, and complementary finite volume method

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the integration time step. We implement this solver on CPU but also on GPU using the CUDA toolkit. We demonstrate that the mean-curvature flow can be successfully approximated in single precision arithmetic with the speed-up almost 17 on the Nvidia GeForce GTX 280 card compared to Intel Core 2 Quad CPU. On the same card, we obtain the speed-up 7 in double precision arithmetic which is necessary for the fourth order problem - the Willmore flow of graphs. Both speed-ups were achieved without affecting the accuracy of the approximation. The article is structured in such way that the reader interested only in the implementation of the Runge-Kutta-Merson solver on the GPU can skip the sections containing the mathematical formulation of the problems.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[251]-272

Source:

Kybernetika | 2011 Volume:47 | Number:2

Harvested from:

CDK

Metadata only:

false