Visualization of solution of heat equation by different interpolation methods
Vikas Kumar Pandey, Himanshu Agarwal, Amrish Kumar Aggarwal · AIP conference proceedings · 2020
Images are used to analyse the solution of two dimensional heat equation. A remarkable observation is that image of the solution detected an ambiguity in existing solution. Therefore better solution is proposed. The images are formed at three different sampling rates of 1000 × 1000, 100 × 100 and 10 × 10 pixels per unit for the space variables. Peak Signal to Noise Ratio (PSNR) is used as quantitative measure for relative analysis of two images and images are shown to the users for the analysis of solution. It has been observed that both analysis by using the images of sampling rate of 1000 × 1000 are rational with the mathematical solution. Average computation time (in seconds) to form a solution image of sampling rates of 1000 × 1000, 100 × 100 and 10 × 10 are approximately 100, 1 and 0.01 respectively. Different interpolation methods namely nearest, bilinear, bicubic, lanczos2 and lanczos3 are used to upscale and compare the images of sampling rate of 100 × 100 and 10 × 10 with 1000 × 1000. Average PSNR and computation time to upscale an image of sampling rate of 100 × 100 and 10 × 10 are 40 dB, 20 dB and 0.02 seconds, 0.02 seconds respectively for lanczos3 interpolation. It is observed that visual information of images of sampling rate of 1000 × 1000 and 100 × 100 are very close and computation time to form the images of sampling rate of 100 × 100 is very less as compared to 1000 × 1000.