Finite element market

Finite element test problems in elasticity for linear equation solvers

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 Aij >).  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, |Ax-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 .





Cylinder with large cutouts


Sphere in a cube

Concentric Spheres in cube