Intuition behind the the bandwidth of a diagonal matrix in a boundary value problem
Let be the following boundary value problem :
begin{align} -Delta u(x,u) & = f(x,y) quad text{for} quad 0leq x leq 5 quad text{and} quad 0 leq y leq 1 \ u(x,y) & = 0 quad text{for }(x,y) text{ on boundary} end{align}
using grid sizes $h_x = frac{5}{501}$ and $h_y = frac{1}{101}$. On the grdi points $u_{i,j} = u(ih, jh)$ use a finite differenc stencil. The grid will consist of 500 points on $x$-direction and 100 points in $y$-direction.
The question of problem is to determine the nodes in the $x$-direction first and then determine the size (1) and semi-bandwidth (2) of the resulting matrix. (3) Deterermine the number of FLOPS using a banded Cholesky solver
The answers are:
(1): $N = N_1 cdot N_2 = 500 cdot 100$
(2): $b = 500$
(3): $frac{1}{2}b^2N = frac{1}{2}500^2cdot 50'000 = 2.5cdot 10^8$
My question is: can somebody explain what is the intuition behind the fact that the bandwidth is 500?
pde finite-differences
asked Nov 25 at 20:47
ecjb
1298
add a comment |
Let be the following boundary value problem :
begin{align} -Delta u(x,u) & = f(x,y) quad text{for} quad 0leq x leq 5 quad text{and} quad 0 leq y leq 1 \ u(x,y) & = 0 quad text{for }(x,y) text{ on boundary} end{align}
using grid sizes $h_x = frac{5}{501}$ and $h_y = frac{1}{101}$. On the grdi points $u_{i,j} = u(ih, jh)$ use a finite differenc stencil. The grid will consist of 500 points on $x$-direction and 100 points in $y$-direction.
The question of problem is to determine the nodes in the $x$-direction first and then determine the size (1) and semi-bandwidth (2) of the resulting matrix. (3) Deterermine the number of FLOPS using a banded Cholesky solver
The answers are:
(1): $N = N_1 cdot N_2 = 500 cdot 100$
(2): $b = 500$
(3): $frac{1}{2}b^2N = frac{1}{2}500^2cdot 50'000 = 2.5cdot 10^8$
My question is: can somebody explain what is the intuition behind the fact that the bandwidth is 500?
pde finite-differences
asked Nov 25 at 20:47
ecjb
1298
add a comment |
Let be the following boundary value problem :
begin{align} -Delta u(x,u) & = f(x,y) quad text{for} quad 0leq x leq 5 quad text{and} quad 0 leq y leq 1 \ u(x,y) & = 0 quad text{for }(x,y) text{ on boundary} end{align}
using grid sizes $h_x = frac{5}{501}$ and $h_y = frac{1}{101}$. On the grdi points $u_{i,j} = u(ih, jh)$ use a finite differenc stencil. The grid will consist of 500 points on $x$-direction and 100 points in $y$-direction.
The question of problem is to determine the nodes in the $x$-direction first and then determine the size (1) and semi-bandwidth (2) of the resulting matrix. (3) Deterermine the number of FLOPS using a banded Cholesky solver
The answers are:
(1): $N = N_1 cdot N_2 = 500 cdot 100$
(2): $b = 500$
(3): $frac{1}{2}b^2N = frac{1}{2}500^2cdot 50'000 = 2.5cdot 10^8$
My question is: can somebody explain what is the intuition behind the fact that the bandwidth is 500?
pde finite-differences
asked Nov 25 at 20:47
ecjb
1298
Let be the following boundary value problem :
begin{align} -Delta u(x,u) & = f(x,y) quad text{for} quad 0leq x leq 5 quad text{and} quad 0 leq y leq 1 \ u(x,y) & = 0 quad text{for }(x,y) text{ on boundary} end{align}
using grid sizes $h_x = frac{5}{501}$ and $h_y = frac{1}{101}$. On the grdi points $u_{i,j} = u(ih, jh)$ use a finite differenc stencil. The grid will consist of 500 points on $x$-direction and 100 points in $y$-direction.
The question of problem is to determine the nodes in the $x$-direction first and then determine the size (1) and semi-bandwidth (2) of the resulting matrix. (3) Deterermine the number of FLOPS using a banded Cholesky solver
The answers are:
(1): $N = N_1 cdot N_2 = 500 cdot 100$
(2): $b = 500$
(3): $frac{1}{2}b^2N = frac{1}{2}500^2cdot 50'000 = 2.5cdot 10^8$
My question is: can somebody explain what is the intuition behind the fact that the bandwidth is 500?
pde finite-differences
pde finite-differences
asked Nov 25 at 20:47
ecjb
1298
asked Nov 25 at 20:47
ecjb
1298
asked Nov 25 at 20:47
ecjb
1298
asked Nov 25 at 20:47
ecjb
1298
asked Nov 25 at 20:47
ecjb
1298
1298
add a comment |
add a comment |
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