Reducing the two dimensional Green functions: Fourier mode decomposition
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| Författarna: | , |
|---|---|
| Materialtyp: | artículo original |
| Status: | Versión publicada |
| Utgivningstid: | 2020 |
| Beskrivning: | 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. |
| Land: | Portal de Revistas TEC |
| Organisation: | Instituto Tecnológico de Costa Rica |
| Repositorio: | Portal de Revistas TEC |
| Språk: | Inglés |
| OAI Identifier: | oai:ojs.pkp.sfu.ca:article/5078 |
| Länkar: | https://revistas.tec.ac.cr/index.php/tec_marcha/article/view/5078 |
| Nyckelord: | Green functions Fourier mode decomposition discrete representation stochastic gradient descent Funciones de Green descomposición en modos de Fourier representación discreta Gradient Descent estocástico |