BETL2 is a C++ template library providing a framework for the
implementation of low-order piecewise polynomial boundary element and
finite element Galerkin discretization of boundary value problems
as they arise in various physical and engineering
applications. Prominent examples are, e.g., electrostatic or thermal
models as well as the scattering of acoustic and electromagnetic
BETL2 implements a slightly modified and extended
interface for handling meshes. It heavily uses template programming
to achieve flexibility with minimal runtime overhead.
This ensures the fast development of
robust, extendable, and reliable numerical schemes and implementations
which for the discretization of boundary value problems.
While BETL2 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
Main features of BETL
BETL mainly aims on the discretisation of quite general boundary
integral operators and volume variational formulations.
The following list gives a rough overview on
BETL's main features.
Support of hybrid 2D and 3D meshes somprising various element types
Lagrangian basis functions of constant, linear,
quadratic, and cubic order for many element types
Raviart-Thomas- and Nedelec-type basis functions up to quadratic
Laplace- and Helmholtz-type fundamental solutions
Galerkin discretization of various integral operators for scalar 2nd-order
elliptic boundary value problems and Maxwell's equations in frequency domain.
Computation of entries of Galerkin matrices for boundary integral operators:
General integrators are based on formulas developed by S.
Sauter and C. Schwab. They
cover quite arbitrary weak- and strongly-singular integral
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
A simple-to-use interface for the incorporation of the AHMED
library developed by M.
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
R. Hiptmair, L. Kielhorn: BETL — A generic boundary element
template library, Tech. Rep. 2012-36, Seminar for Applied
Mathematics, ETH Zürich (pdf,
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)
BETL has originated from an industrial environment and is also used for
commercial projects. This is the
main reason why the license agreement prohibits any
commercial use of this software. Despite this, BETL2 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
Kielhorn or to Ralf