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

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

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

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

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

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

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

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.