Research Article

Morphing for faster computations with finite difference time domain algorithms

¹ Aix-Marseille Université, CNRS, Centrale Marseille, Institut Fresnel, 13013 Marseille, France
² UMI 2004 Abraham de Moivre-CNRS, Imperial College London, London SW7 2AZ, UK
³ Department of Mathematics, Imperial College London, London SW7 2AZ, UK
⁴ BTU Trust, 77700 Magny le Hongre, France

^* e-mail: ronald.aznavourian@fresnel.fr

Received: 23 July 2021
Accepted: 13 December 2021
Published online: 3 February 2022

Abstract

In the framework of wave propagation, finite difference time domain (FDTD) algorithms, yield high computational time. We propose to use morphing algorithms to deduce some approximate wave pictures of their interactions with fluid-solid structures of various shapes and different sizes deduced from FDTD computations of scattering by solids of three given shapes: triangular, circular and elliptic ones. The error in the L² norm between the FDTD solution and approximate solution deduced via morphing from the source and destination images are typically less than 1% if control points are judiciously chosen. We thus propose to use a morphing algorithm to deduce approximate wave pictures: at intermediate time steps from the FDTD computation of wave pictures at a time step before and after this event, and at the same time step, but for an average frequency signal between FDTD computation of wave pictures with two different signal frequencies. We stress that our approach might greatly accelerate FDTD computations as discretizations in space and time are inherently linked via the Courant–Friedrichs–Lewy stability condition. Our approach requires some human intervention since the accuracy of morphing highly depends upon control points, but compared to the direct computational method our approach is much faster and requires fewer resources. We also compared our approach to some neural style transfer (NST) algorithm, which is an image transformation method based on a neural network. Our approach outperforms NST in terms of the L² norm, Mean Structural SIMilarity, expected signal to error ratio.