The Iterative Solver in ADINA for 3D Models

In the News of April 30, 2006 we demonstrated already the use of the new iterative solver in ADINA for the analysis of solids. This solver has been released in ADINA 8.4. It can be very effective when considering 3D large models, in linear and nonlinear analyses, including contact.

The solver is used with the higher-order brick and tetrahedral elements in ADINA (but these element meshes may also contain other elements). The higher-order brick and tetrahedral elements need frequently be used to predict stresses accurately. We illustrate the effectiveness of the solver on a one processor machine in the example considered below.

• Cube modeled with 27-node brick elements, linear static analysis, one step

• Use of 3D-iterative solver and sparse solver for different mesh densities

• Runs made on HP-UX Itanium computer, 1 processor, 8 GB RAM; all runs made in-core for ease of illustration

Cube modeled with 27-node brick elements, fixed at the top and
subjected to gravity loading

Plots of normalized CPU time vs. number of DOFs for sparse solver
and 3D-iterative solver

Plots of memory used vs. number of DOFs for sparse solver and 3D-iterative solver

While we consider here a mesh of equal sized 27-node elements, the iterative solver works on fully unstructured meshes, see e.g. the News of April 30, 2006. The case of 27-node elements is severe. There is significant coupling between elements and hence the bandwidth is large.

The important points to notice are that for the iterative solver

• the solution time increases practically linearly with the number of DOFs

• the memory used increases practically linearly with the number of DOFs

• both quantities are much smaller than when using the direct sparse solver.

This makes it possible to estimate quite accurately the CPU time and memory required for a solution, when using the iterative solver.

Of course, the memory used and the solution time for the sparse solver become rapidly very large as the number of DOFs increases and the ADINA out-of-core solution with parallel processing need be used.

For further information and some nonlinear analyses using the iterative solver, see the News of April 30, 2006.