Difference between revisions of "Poisson equation, solving with DFT"
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Primary authors of this description:[[Участник:Виктор Степаненко|V.M.stepanenko]], [[Участник:Evgeny Mortikov|E.V.Mortikov]], [[Участник:VadimVV|Vad.V.Voevodin]] ([[#Описание локальности данных и вычислений|section 2.2]]) | Primary authors of this description:[[Участник:Виктор Степаненко|V.M.stepanenko]], [[Участник:Evgeny Mortikov|E.V.Mortikov]], [[Участник:VadimVV|Vad.V.Voevodin]] ([[#Описание локальности данных и вычислений|section 2.2]]) | ||
| − | == | + | == Properties and structure of the algorithm == |
| − | === | + | === General description of the algorithm === |
| − | + | ||
| + | The Poisson equation for the multidimensional space has the form | ||
| + | <math> | ||
| + | \sum_{i=1}^{N}\frac{\partial^2 \phi}{\partial x_i^2}=f,~\mathbf{x}\in D. | ||
| + | </math> | ||
| + | |||
| + | Here, <math>D \in \mathbb{R}^N</math> is the domain in which the solution <math>\phi(\mathbf{x})</math> is defined, and <math>\mathbf{x}=(x_1,...,x_N)^T</math> is the vector of independent variables. The Poisson equation is supplemented by the boundary conditions | ||
| + | <math> | ||
| + | B(\phi)=F, \mathbf{x} \in \Gamma(D), | ||
| + | </math> | ||
Revision as of 23:13, 3 February 2016
Primary authors of this description:V.M.stepanenko, E.V.Mortikov, Vad.V.Voevodin (section 2.2)
1 Properties and structure of the algorithm
1.1 General description of the algorithm
The Poisson equation for the multidimensional space has the form [math] \sum_{i=1}^{N}\frac{\partial^2 \phi}{\partial x_i^2}=f,~\mathbf{x}\in D. [/math]
Here, [math]D \in \mathbb{R}^N[/math] is the domain in which the solution [math]\phi(\mathbf{x})[/math] is defined, and [math]\mathbf{x}=(x_1,...,x_N)^T[/math] is the vector of independent variables. The Poisson equation is supplemented by the boundary conditions [math] B(\phi)=F, \mathbf{x} \in \Gamma(D), [/math]
