Fast Fourier transform method for partial differential equations, case study: The 2-D diffusion equation
The authors consider the 2D constant coefficient diffusion equation in a rectangle (say with first kind boundary conditions). They develop the idea to apply the fast Fourier transform (FFT) in x and y direction to the initial data, to multiply by the n-th power (if the solution at n t is desired) of the transfer function and once more to use FFT to get the numerical result. The arguments in favour of this process are: it does not depend on n (in the sense that the mentioned n-th power can be calculated through exponentials) and hence the solution at n t can be obtained in one step; the difference between explicit and implicit schemes disappears (and the highest order method may be selected; all single parts of this process (FFT, vector multiply) are executable by corresponding hardware. Some timing results of experiments using such equipment are cited.
scientific article; zbMATH DE number 4072310
scientific article