Reducing the two dimensional Green functions: Fourier mode decomposition

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Juan Pablo Mallarino-Robayo
Alejandro Ferrero-Botero

Abstract

Often we encounter high dimensional differential equations. A clever representation of a generalized solution could be procured in certain cases using Green functions. We show how this representation could be achieved and via a clever Fourier mode decomposition for the particular disc case resulting in a highly correlated set of functions that transforming into a discrete representation – via a classical second order finite difference approximation – can be ultimately represented as a linear equation for matrices embedding all boundary conditions in the structure of such objects. The resulting problem could be solved using stochastic gradient descent with an additional on-the-fly optimization reducing required computation resources substantially.

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How to Cite
Mallarino-Robayo, J. P., & Ferrero-Botero, A. (2020). Reducing the two dimensional Green functions: Fourier mode decomposition. Tecnología En Marcha Journal, 33(5), Pág. 66–73. https://doi.org/10.18845/tm.v33i5.5078
Section
Artículo científico