This is a MATLAB-based suite for 2-D numerical computing with the boundary element method on smooth geometries and open arcs.
deltaBEM achieves third order accuracy by using simple kernel evaluations with no assembly required. The potentials and operators of the Calderón Projector for Laplace, Helmholtz, as well as the steady state and time-harmonic linear elasticity equations are included. The package mimics the underlying Calderón Calculus at the discrete level so that most well-posed boundary integral equations can be discretized in a simple minded form.
The package deltaBEM is a collection of open source MATLAB files requiring no compilation. A front end is not provided. The user is expected to peruse the documented examples provided and modify them to write scripts that meet their needs. Potential users are welcome to download and use the code freely. We just request that any results obtained with the aid of deltaBEM acknowledge its use and cite the relevant papers. At present we only offer the functions needed for steady state and time-harmonic problems. However, the time-harmonic case has been programmed in a way that makes it easy to connect with Convolution Quadrature (CQ) routines for time domain simulations. Low order CQ routines will be added shortly to this site.
The deltaBEM suite has developed over the years thanks to the joint efforts of a number of people -ranging from faculty to undergraduate students- that have contributed with theoretical developments, computational implementation and lots of field/crash-testing. Here are the main contributors with affiliations at time of the release of the software:
- Francisco-Javier Sayas, University of Delaware (Coordinator)
- Victor Domínguez, Universidad Pública de Navarra, Spain
- Tonatiuh Sánchez-Vizuet, Graduate Student, University of Delaware
- Tianyu Qiu, Graduate Student, University of Delaware
- Matthew Hassell, Graduate Student, University of Delaware
- Sijiang Lu, Graduate Student, University of Delaware (Contributed 2011-2013)
Early ideas leading to the current configuration of deltaBEM appear in papers in collaboration with María-Luisa Rapún. Further development was done during summer research internships with freshmen graduate students Michael DePersio (2012, University of Delaware) and Douglas Freeman (2013, University of Delaware). Andrea Carosso, then a senior udergraduate student at the University of Delaware (currently a graduate student at UC-Boulder), participated during a summer program and an independent study course throughout the 2013 academic year.
Project website: https://team-pancho.github.io/deltaBEM
Team website: https://team-pancho.github.io