Open Thesis

Stencil Operators for block-structured grids

Advisor:   Dr.-Ing. Rainer Hartmann, M. Sc.

UGblocks is a 3D c++ library for numerical expressions on unstructured grid. The unstructured domain is partitioned into structured elements with a locally regular grids:

  • hexahedrons (3D)
  • rectangles (2D)

UGblocks provides numerous operators for solving partial differential equations for finite element analysis (FEM). Operations are evaluated by the use of expression templates.

Recommended knowledge:

  • background in c++ and templates
  • numerical linear algebra
  • preferable parallel programming with MPI


  • numerical simulation of laser beams
  • Parallel solvers for large scale sparse problems

Differential operators store local stiffness matrices for each node of the regular grid. Evaluating differential expressions with constant coefficients implies applying the same local stiffness matrices in the inner region of a structured element.

The scope of a possible thesis is to figure out regions with identical local stiffness matrices. Then nine-point (2D) and 27-point (3D) stencil operators provide a memory efficient (one stencil per element) and performance optimized multiplication of stiffness matrix times variable.
Boundary points are evaluated locally for each element and finally synchronized.


  • Rainer Hartmann
  • Prof. Christoph Pflaum