Elliptic Fields


Boundary Element Method (BEM) Solvers

The 3D solvers used and developed within the Elfi-Project are based on the Boundary Element Method.


Casopt is a derivate of the Polopt solver initiated by Zoran Andjelic in the early 1980s [3.1] and continued at TU Munich within the Polopt-Project. The name Casopt originates from an EU project that has been performed significantly later between 2009 and 2013 as a cooperation of Technical Universities Munich, Graz and the University of Cambridge coordinated by ABB Corporate Research Switzerland.
The Casopt solver is based on the old Polopt version from 1990s that has been used as a reference solver to perform benchmarking of new BEM solvers developed in scope of the Casopt project. The results of benchmarking have been summarized in [3.2]. The Casopt solver has limited performance since it does not make use of new numerical techniques like compression of the fully populated matrix or clustering of far field regions. However, it is supposed to be sufficient for the research and educational purposes, which are currently the target of the Elfi platform. The main purpose of including the the Casopt-solver in the Elfi-package is to provide a reliable reference solver for benchmarking (the same purpose as in the Casopt-Project). The new solvers being developed within the Casopt-Project are beyond the scope of the Elfi-Project. More information can be obtained from the following links or by contacting the developers: A new feature of the Casopt solver is the surface charging computation based on the saturation boundary condition formulated according to [3.4]. Its implementation and integration into the Casopt solver has been finalized within the Elfi-project.


Elfi-Venus is a new development within the Elfi-project started in 2021. The main motivation is creation of a new C/C++ code that can be efficiently handled in academic environment. The new code should enable researchers, working on future formulations and performance improvements, to reference the components of Elfi-Venus as a library. Currently, referencing (reusing) the existing components of the Fortran Casopt code is very difficult (or almost impossible). The Elfi-Venus will include all experience gained during more than 40 years of working with the 3D electrostatic codes mentioned above as well as the codes developed within the Venus-Project. An implementation of the region-oriented BEM formulation specified in [3.5] is also planned. A special focus is on extending the model size, which is in case of Casopt limited to the range of 100000, but should grow to more than 1 Million (it is the dimension of a fully populated BEM matrix !). Such large models can be now created in modern CAD systems when computing detailed representations of industrial devices. A cloud computing service will be available for Elfi-Venus solver.

Features of the Casopt solver

Features of the Elfi-Venus solver

Most features of the Casopt-solver will be available for Elfi-Venus. An additional feature is the cloud computing option, which enables computation of models with dimensions significantly larger than 100000. Anther extension is implementation quasistatic fields. Conductive fields as well as region-oriented and thin layer formulations will become a subject of follow-up projects. Elfi-Venus is planned to become the main 3D solver of the Elfi-package.


[3.1] Z. Andjelic, A contribution to the BEM for calculation and optimization of 3D electrostatic fields, Ph.D. Thesis, Faculty of Electrical Engineering, University of Zagreb 1984.

[3.2] T. Müller, Techniques for adapting industrial simulation software for power devices and networks to multi- and many-core architectures, Ph.D. Thesis, Faculty of Computer Science, Technical University Munich 2014.

[3.3] D. Amann, A. Blaszczyk, G. Of, and O. Steinbach, Simulation of floating potentials in industrial applications by boundary element methods, Journal of Mathematics in Industry, Springer Open, 2014.

[3.4] A. Blaszczyk, T. Christen, H. K. Meyer, M. Schueller, Surface charging formulations for engineering applications. Validation by experiments and transient models, Scientific Computing in Electrical Engineering, SCEE 2018, Taormina, Springer Nature 2020.

[3.5] A. Blaszczyk, Region-oriented BEM formulation for numerical computations of electric fields, Scientific Computing in Electrical Engineering, SCEE 2008, Espoo, Finland, Springer series Mathematics in Industry, Heidelberg 2010.

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