2-Dimensional Poisson Problem (Poisson Problem)

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Revision as of 11:22, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2-Dimensional Poisson Problem (Poisson Problem)}} == Description == Given $f$, solve for $u$ in the 2-dimensional Poisson equation: $u_{xx} + u_{yy} = f(x,y)$ == Related Problems == Related: 3-Dimensional Poisson Problem == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | ...")
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Description

Given $f$, solve for $u$ in the 2-dimensional Poisson equation:

$u_{xx} + u_{yy} = f(x,y)$

Related Problems

Related: 3-Dimensional Poisson Problem

Parameters

No parameters found.

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
5-point star Cramer's rule 1945 $O({4}^{(n^{2})})$ $O({4}^{(n^{2})})$ for sure, $O(n^{2})$ possibly??? (if super conservative) Exact Deterministic
5-point Gauss elimination 1945 $O(n^{4})$ $O(n^{4})$ Exact Deterministic
5-point Gauss Seidel iteration 1945 $O(n^{4} logn)$ $O(n^{2})$? Exact Deterministic
5-point SOR iteration 1954 $O(n^{3} logn)$ $O(n^{2})$? Exact Deterministic
5-point ADI iteration 1955 $O(n^{2} log^{2}n)$ $O(n^{2})$? Exact Deterministic
9-point SOR iteration 1956 $O(n^{3})$ $O(n^{2})$? Exact Deterministic
9-point Tensor product 1964 $O(n^{3})$ $O(n^{2})$? Exact Deterministic Time
9-point ADI iteration 1965 $O(n^{2} logn)$ $O(n^{2})$? Exact Deterministic
5-point FFT 1965 $O(n^{2} logn)$ $O(n^{2})$? Exact Deterministic
9-point ADI iteration + smooth guess 1969 $O(n^{2} logn)$ $O(n^{2})$? Exact Deterministic
5-point cyclic reduction 1970 $O(n^{2} logn)$ $O(n^{2})$? Exact Deterministic
9-point FFT 1978 $O(n^{2} logn)$ $O(n^{2})$? Exact Deterministic

Time Complexity graph

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Space Complexity graph

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Pareto Decades graph

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