Square domain with Re(x+iy)ⁿ boundary conditions

Neumann Problem with thermal conductivities 1 and 2.
All computations done on a 200*200=40000 rectangular element mesh.

Dirichlet Problemwith thermal conductivities 1 and 2.
All computations done on a 200*200=40000 rectangular element mesh.

Neumann Problem with thermal conductivities 1 and 20.
All computations done on a 200*200=40000 rectangular element mesh.

Neumann Problem with thermal conductivities 1 and 20.
All computations done with Matlab on a 21000 triangular element mesh.

Neumann Problem with thermal conductivities 0.5 and 10.
All computations done on a 200*200=40000 rectangular element mesh.
Updated! (08/28/08 5:03:00pm ET)

Neumann Problem with thermal conductivities 0.5 and 10 and different initial material configurations.
Updated! (11/17/08 11:54:00pm ET)

Steklov eigenfunctions for the square

Neumann Problem with thermal conductivities 1 and 10
All computations done on a 200*200=40000 rectangular element mesh.
Updated (03/28/09 7:25:00pm ET)

Neumann Problem with thermal conductivities 1 and 10
All computations done on a 400*400=160000 rectangular element mesh.
Updated (04/06/09 11:00:00pm ET)

Neumann Problem with thermal conductivities 1 and 20
All computations done on a 400*400=160000 rectangular element mesh.
Updated (04/08/09 11:40:00am ET)

Rectangular domain with cosine boundary conditions

Neumann Problem with thermal conductivities 0.5 and 10 and cosine boundary condition.
All computations done on a 160*1000=160000 rectangular element mesh.
Updated! (01/22/08)

Neumann Problem with thermal conductivities 1 and 10 and cosine boundary condition.
All computations done on a 160*1000=160000 rectangular element mesh.
Updated! (02/27/08 11:04:22pm ET)

Using the optimal designs of n=5,10,50,1000 with different boundary conditions.

The computations (01/04/2008) with coefficient matrix



The computations done on a 600*3750=2,250,000 element mesh (01/16/2008) with coefficient matrix


Updated! (01/22/08)

The computations done on a 300*1875=562,500 element mesh (02/28/2008) with coefficient matrix


Updated! (02/28/08 2:42:45pm ET)

Comparison of 3 cases with lambda=1 (02/28/2008)
Updated! (02/28/08 4:41:15pm ET)

The computations done on a 300*1875=562,500 element mesh (03/03/2008) with coefficient matrix


The corresponding 2 phase material has alpha=0.5 and beta=10. The pictures are for n=10.
Updated! (03/03/08 10:43:19am ET)

Comparison of 3 cases with lambda=0.44 (03/03/2008)
Updated! (03/03/08 9:54:33am ET)

Neumann Problem with thermal conductivities 1 and 10 and cosine boundary condition and A in objective functional.
All computations done on a 160*1000=160000 rectangular element mesh.
Updated! (08/13/08 09:35:45pm ET)

Neumann Problem with thermal conductivities 0.5 and 10 and cosine boundary condition and A in objective functional.
All computations done on a 160*1000=160000 rectangular element mesh.
Updated! (08/27/08 12:32:00pm ET)