Abstract
In recent years there have been tremendous advances in the theoretical understanding of boundary integral equations for Maxwell problems. In particular, stable dual pairings of discretisation spaces have been developed that allow robust formulations of the preconditioned electric field, magnetic field and combined field integral equations. Within the BEM++ boundary element library we have developed implementations of these frameworks that allow an intuitive formulation of the typical Maxwell boundary integral formulations within a few lines of code. The basis for these developments is an efficient and robust implementation of Calderón identities together with a product algebra that hides and automates most technicalities involved in assembling Galerkin boundary integral equations. In this paper we demonstrate this framework and use it to derive very simple and robust software formulations of the standard preconditioned electric field, magnetic field and regularised combined field integral equations for Maxwell.
Highlights
The numerical simulation of electromagnetic wave scattering poses significant theoretical and computational challenges
Much effort in recent years has gone into the development of fast and robust boundary integral equation formulations to simulate a range of phenomena from the design and performance of antennas to radar scattering from large metallic objects
While there have been a range of important theoretical advances in recent years for the development of robust preconditioned boundary integral formulations for Maxwell, the computational implementation remains a challenge
Summary
The numerical simulation of electromagnetic wave scattering poses significant theoretical and computational challenges. Only a representation of the grid function in the dual space is available By extending this mechanism to operators, the concept of products of operators is defined in BEM++. For larger problems we are interested in iterative solvers and corresponding interfaces to GMRES and CG are provided We will use this operator concept extensively in this paper to formulate the different types of Maxwell integral equations. More details of the abstract implementation of operator algebras in BEM++ can be found in [7]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
