Open AccessVisual Analysis of the Exact Solution of a Heat Equation
Author(s) -
Himanshu Agarwal
Publication year - 2019
Publication title -
international journal of innovative technology and exploring engineering
Language(s) - English
Resource type - Journals
ISSN - 2278-3075
DOI - 10.35940/ijitee.i8576.078919
Subject(s) - interpolation (computer graphics) , similarity (geometry) , image (mathematics) , visualization , sampling (signal processing) , peak signal to noise ratio , image quality , mathematics , image scaling , computer science , artificial intelligence , noise (video) , computer vision , algorithm , image processing , filter (signal processing)
The solution of the two-dimensional heat equation is represented as images. The considered heat equation is 2 2 2 2 . U U U t x y , 0 1, 0 1 x y . The Boundary conditions are U y t U y t (0, , ) 0, (1, , ) 0, U x t ( ,0, ) 0, and U x t ( ,1, ) 0 and the initial condition is U x y x y ( , ,0) sin 4 cos 4 . The images provide quick but approximate insights to the solution. Approximation by image visualization depends on many factors such as the display device, human eye factors, image resolution (sampling rate and bit depth of the image), and image resize methods. We have provided images for different time t and different resolutions We have studied the impact of different sampling rate and different image resize methods on the quality of the images. User study is performed for qualitative inspection and peak signal to noise ratio (PSNR) is used as a quantitative measure of the relative similarity in images with respect to different sampling rate and time t . Qualitative inspection and PSNR follow the same trend. Further, Qualitative inspection confirms that the quality of approximation of solution by image visualization improves with increase in sampling rate. Moreover, lanczos3 is the best interpolation method to resize the images.