Starting diary file "diary-2016-03-07.txt" on Mon Mar 07 2016 12:25 PM.

edit mydiffusion.m
edit B.m
edit U0.m
edit S.m

Dcoeff = .01; k = 100; dt = .01; t_end = 3.0;

U = mydiffusion(Dcoeff, @S, @B, @U0, k, dt, t_end, 1);
Hit space to begin simulation.

A2 = laplacian2d_sparse1(k);
nnz(A2)
ans =
       49600
spy(A2)

A2 = laplacian2d_dense(3)
A2 =
     4    -1     0    -1     0     0     0     0     0
    -1     4    -1     0    -1     0     0     0     0
     0    -1     4     0     0    -1     0     0     0
    -1     0     0     4    -1     0    -1     0     0
     0    -1     0    -1     4    -1     0    -1     0
     0     0    -1     0    -1     4     0     0    -1
     0     0     0    -1     0     0     4    -1     0
     0     0     0     0    -1     0    -1     4    -1
     0     0     0     0     0    -1     0    -1     4

edit laplacian2d_dense

A2 = laplacian2d_dense(k);
whos
  Name            Size                   Bytes  Class     Attributes

  A2          10000x10000            800000000  double              
  ...

tic; A2 = laplacian2d_dense(k);toc;
Elapsed time is 1.894549 seconds.

A2 = laplacian2d_dense(3)
A2 =
     4    -1     0    -1     0     0     0     0     0
    -1     4    -1     0    -1     0     0     0     0
     0    -1     4     0     0    -1     0     0     0
    -1     0     0     4    -1     0    -1     0     0
     0    -1     0    -1     4    -1     0    -1     0
     0     0    -1     0    -1     4     0     0    -1
     0     0     0    -1     0     0     4    -1     0
     0     0     0     0    -1     0    -1     4    -1
     0     0     0     0     0    -1     0    -1     4
A = sparse(A2)
A =
   (1,1)        4
   (2,1)       -1
   (4,1)       -1
   (1,2)       -1
   (2,2)        4
   (3,2)       -1
   (5,2)       -1
   (2,3)       -1
   (3,3)        4
   (6,3)       -1
   (1,4)       -1
   (4,4)        4
   (5,4)       -1
   (7,4)       -1
   (2,5)       -1
   (4,5)       -1
   (5,5)        4
   (6,5)       -1
   (8,5)       -1
   (3,6)       -1
   (5,6)       -1
   (6,6)        4
   (9,6)       -1
   (4,7)       -1
   (7,7)        4
   (8,7)       -1
   (5,8)       -1
   (7,8)       -1
   (8,8)        4
   (9,8)       -1
   (6,9)       -1
   (8,9)       -1
   (9,9)        4

edit laplacian2d_sparse1

clear A2
tic; A2 = laplacian2d_sparse1(k);toc
Elapsed time is 2.038455 seconds.

whos
  Name            Size                Bytes  Class     Attributes

  A2          10000x10000            873624  double    sparse    
  ...

tic; A2 = laplacian2d_sparse1(200);toc
Elapsed time is 30.416937 seconds.

whos
  Name            Size                 Bytes  Class     Attributes

  A2          40000x40000            3507224  double    sparse    
  Dcoeff          1x1                      8  double              
  dt              1x1                      8  double              
  k               1x1                      8  double              
  t_end           1x1                      8  double              

B = laplacian2d_sparse3(4);
full(B)
ans =
  Columns 1 through 11
     4    -1     0     0    -1     0     0     0     0     0     0
    -1     4    -1     0     0    -1     0     0     0     0     0
     0    -1     4    -1     0     0    -1     0     0     0     0
     ...

A = laplacian2d_sparse1(4);
nnz(A-B)
ans =
     0

tic; A2 = laplacian2d_sparse1(k);toc
Elapsed time is 2.048772 seconds.
tic; A2 = laplacian2d_sparse3(k);toc

Elapsed time is 2.040239 seconds.
tic; A2 = laplacian2d_sparse3(k);toc

tic; A2 = laplacian2d_sparse3(200);toc
Elapsed time is 30.680980 seconds.

tic; A2 = laplacian2d_sparse3(k);toc
Elapsed time is 2.054608 seconds.

tic; A2 = laplacian2d_sparse2(k);toc
Elapsed time is 0.093778 seconds.

tic; A2 = laplacian2d_sparse2(k);toc
Elapsed time is 0.092867 seconds.

edit laplacian2d_sparse2.m

tic; A2 = laplacian2d_kron(k);toc
Elapsed time is 0.054639 seconds.

clear B
tic; U = mydiffusion(Dcoeff, @S, @B, @U0, k, dt, t_end, 0); toc;
Elapsed time is 11.655917 seconds.

profile on
tic; U = mydiffusion(Dcoeff, @S, @B, @U0, k, dt, t_end, 0); toc;
Elapsed time is 13.568836 seconds.

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