3-D ADI
 

i am formulating 3-D transient theraml analysis. the numerical scheme i am using, is alternating direct implicit (ADI).i ve divided the time step into three small steps of time 1/3. i am facing problem in writing the codes in c++. the size of matrix is becoming too large and it does not supporting the large array size. plese help me

Re: 3-D ADI
 

Hi Nitin,

i advise you to store your non-zero matrix's elements in a new small matrix in which you can conserves your memory storage

Noureddine

Re: 3-D ADI
 

As Djeghri pointed out, you should consider a compressed matrix storage strategy such as CSR, MSR, etc. You can refer to Saad's book on sparse linear systems which can be found here: http://www-users.cs.umn.edu/~saad/books.html

Re: 3-D ADI
 

Plz carrify my doubts regarding 2-D transient conduction in cylindrical coordinate. 1) how to implement the boundary conditions.? for the 1st half time step in r-direction, how will be the z-boundary conditions..in n+1/2 level or nth level

2)is there any stability criteria to b satisfied while using ADI scheme?

awaiting your valuable suggestions thanking you in advance hari

Re: 3-D ADI
 

transient ADI-schemes (2D Peaceman-Rachford, or 3D Douglas-Gunn) are "nearly" the same as the Crank-Nicholson-scheme. It can be regarded as a factorization of Crank-Nicholson.

So in numerical sense there is no stability criteria as for explicit schemes, but be aware of physical unresonable results (possibly not damped osciallations). Beacause of this check the timestep size (Friedrich-Levi-Courant condition).

Literature: Douglas J.; Gunn I. E., "A general formulation of alternating direction methods , part I: parabolic and hyperbolic problems", Numer.Anal. 19, 1982, p.871-885

Re: 3-D ADI
 

Also be aware that while the algorithm may have no stability limit, the splitting error can cause significant issues, particularly in 3D.

Re: 3-D ADI
 

thanks for ur valuable suggetion

my problem in 3D formulation is the large array size. currently no. of nodes in x direction=4 no. of nodes in y direction=15 no. of nodes in z direction=300 hence the total size of the matrix is 18000*18000 and there are three time step of 1/3 sec. in on complete cycle and i m calculating this matrix three times in one complete cycle [x-implicit,y-implicit,z-implicit]. plese help me

Re: 3-D ADI
 

Hi sharma

the advantage of ADI is to reduce the memory storage by building alternatively, an array with a size as grid number for each direction of your computational domain.

i advice you to see also the TDMA (3 sweep)like resolution, or you can resolve directly your problem without any array by point SOR.

good luck.