finite differencing of a PDE system
- To: mathgroup at smc.vnet.net
- Subject: [mg67629] finite differencing of a PDE system
- From: "Chris Chiasson" <chris at chiasson.name>
- Date: Sun, 2 Jul 2006 06:28:36 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Dear MathGroup, I have an elliptic system of first order linear partial differential equations that I would like to solve in the three Cartesian space dimensions. They represent elastic small strain on a longitudinally and uniformly loaded steel bar in tension. The discretization is a uniform \[Delta]x in all directions. I have run into two main problems. 1. The computer is going to use way too much memory if I use the Solve command on the equations. What are some good programmatic ways to create matrix formulations of a system of discretized PDEs in more than one space coordinate? The equation variables presently have three indices. I suppose these would need to be converted to one index for the matrix formulation. Also, it is likely that I will need to use sparse arrays. 2. The displacement and strain variables do not have any boundary conditions - they should be implicitly defined by the stress boundary conditions. I think it should be possible to determine the displacement on the free surfaces, because its partial derivatives appear in the equations that apply on the interior of the domain. However, the strain does not have any partial derivatives in the interior or boundary conditions on the exterior, how should I go about determining the value of the strain on the free surface nodes? Thanks for any input, -- http://chris.chiasson.name/