I am trying to figure out how to construct a matrix for solving systems of linear equations with two dimensions of space and a dimension of time, but I do not know how to do this or begin visualizing such a matrix. The solution depends on all the data at all times less than the solved time so I can't cheat by simply updating a 2D matrix. For instance, it is very clear that a 2D matrix will look like this: http://www.eecs.berkeley.edu/~demmel/cs267/lecture17/DiscretePoisson.gif Do I add the third dimension directly below this, or to the right? or to the bottom right? I would assume to the bottom right since a system of equations which can be reduced to tridiagonal matrix will also be true for a 3D matrix. On the other hand, I do not how it would be possible to create a tridiagonal matrix with a 3D problem because you will refer to prior time levels when solving new time levels.