2-Dimensional Poisson Problem (Poisson Problem)
Revision as of 10:22, 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 |- | ...")
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 |