The goal of this page is to make these problems available so as to provide a set of test problems that solver developers can use to compare their performance results, both convergence rates and solve times, with other solver methods and implementations on several challenging problems in elasticity. The performance results of my multigrid solvers, on these problems, can be found from papers available on my home page.

These problems are provided in the form of simple ASCII text files with
the finite element problem. These files are in FEAP
format, and contain the finite element mesh (coordinates and element
connectivities) and boundary conditions (identification of Dirichlet boundary
conditions, and non-zero boundary values). All non-zero boundary
values are provide as nodal quantities (eg, pressure loads have already
been distributed to the nodes). The stiffness matrices are also provided
in Matlab format (ie, a list of triples < i j A_{ij} >).
For problems with non-zero Dirichlet boundary conditions, a right hand
side vector "__b__" and an approximate solution vector "__x__",
solved to 6 digits of accuracy of the residual in most cases (ie, |A__x__-__b__|
/ |__b__| < 10^{-6}), is also provided. These vectors
are in plain ASCII text format and can be read by Matlab. All of
these meshes have either all trilinear hexahedra elements, all four node
quadrilateral shell elements, or all linear tetrahedra elements.
These problems are all 3D.

This table provides a list of problems with some of their pertinent
properties and links to the problems themselves. Some of these problems
are available in larger sized (ie, the problem is parameterized), if you
are interested in other version of these problems you can contact me from
my homage. My "Evaluation" paper on home
page. has more details about the materials, loading, etc. for these
problems along with performance results for my multigrid solvers.

Test problem name | Degrees of freedom (other versions available on request) | Thin body features | Large jumps in material coefficients | Incompressible materials | Scalable version available | Shell Elements |

Cone | 21,600 | X | . | . | . | . |

Beam-column | 34,460 | X | . | . | . | . |

Plate | 33K (2K-2M) | . | . | . | X | X |

Wing | 22K (5K-2.2M) | . | . | . | X | X |

Cylinder with large cutouts | 13K (13K-2.5M) | . | . | . | X | X |

Cantilever | 62,208 | . | X | X | . | . |

Sphere in a cube | 25K (170 - 7.5M) | . | X | X | X | . |

Concentric Spheres in cube | 80K (80K - 76M) | . | X | X | X | . |