About BETL

BETL is a C++ template library for the discretisation of boundary integral operators. While it currently implements the discretisation of 3-dimensional boundary integral operators via Galerkin schemes its design principles allow also for the incorporation of other discretisation schemes such as, e.g., the still popular collocation methods.
Over the years this project has grown slightly bigger than it was originally expected. In its original form BETL was just intended to serve as set of methods with rather limited functionality for maintaining an existing industrial Boundary Element solver. Since then BETL has become a fully autonomous tool on which powerful Boundary Element applications can be build. BETL's strength lies in its use of well-known design principles in conjunction with state of the art C++ language features. This ensures the fast development of robust, extendable, and reliable numerical schemes and implementations which are somehow related to the discretisation of boundary integral operators.

Main features of BETL

BETL mainly aims on the discretisation of quite general boundary integral operators. The following list gives a rough overview on BETL's main features.

• Support of different element types
• 3-noded triangular elements
• 6-noded triangular elements
• 10-noded triangular elements
• 4-noded quadrilateral elements
• 8-noded quadrilateral elements
• 16-noded quadrilateral elements
• Lagrangian basis functions of constant, linear, quadratic, and cubic order for triangular as well as as for quadrilateral elements
• Raviart-Thomas- and Nedelec-type basis functions of lowest order for the 3-noded triangular element
• Laplace- and Helmholtz-type fundamental solutions
• A set of traces to compute
• single-layer potentials
• double-layer potentials
• hypersingular integral operators
• A set of integrators
• General integrators are based on formulas developed by S. Sauter and C. Schwab. They cover quite arbitrary weak- and strongly-singular integral kernels
• Semi-analytic integrators for the Laplace kernel on 3-noded triangular elements are based on routines which have been developed by O. Steinbach and his group
  
• Lean interfaces for sparse direct solvers such as UMFPACK, SuperLU, and Pardiso
• A simple-to-use interface for the incorporation of the AHMED library developed by M. Bebendorf
• An interface for using the Directional Fast Multipole Method as it has been developed by M. Messner, E. Darve, and M. Schanz (published as Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation).
• Natural semantics for linear algebra computations by using expression templates

What BETL is not designed for

Concerning Boundary Element Methods, there exist some topics which one might expect to be included into a library of this kind, but which, consequently, are not covered by BETL itself. Since BETL is solely dedicated to the computation of discrete boundary layer potentials, these topics do not fit into the library's design principles:

• There is no concept of boundary conditions implemented
• The software implements no Boundary Element Methods. However, BETL comes with a bunch of tutorials which explain how to embed BETL structures into some particular Boundary Element Methods in order to solve a certain boundary value problem

Documentation

If you are interested, please have a look at the documentation for further details about BETL. Currently, BETL's documentation is still under construction. Nevertheless, the documentation is already freely available and may be found under the following links.

• HTML-version
• pdf-version

The source code's Doxygen documentation will be also available.

Publications

• A BETL related talk: Söllerhaus Workshop, September 2012
• R. Hiptmair, L. Kielhorn: BETL — A generic boundary element template library, Tech. Rep. 2012-36, Seminar for Applied Mathematics, ETH Zürich (pdf, sources, meshes (33MB), aca settings)
  
• L. Kielhorn: Matrix-vector computations with BETL, Tech. Note, Seminar for Applied Mathematics, ETH Zürich (pdf)
• A BETL poster: Swiss Numerics Colloquium 2013 (pdf)

Obtaining BETL

BETL has originated from an industrial environment. This is the main reason why the license agreement prohibits any commercial use of this software. Despite this, BETL is free for academic use in research and teaching. Interested users are granted access to the subversion repository after their academic affiliation has been proven. For this, simply complete the license agreement and send it together with an attached copy of your academic affiliation via e-mail either to Lars Kielhorn or to Ralf Hiptmair.