Electromagnetics and Acoustics Group

Electromagnetics and Acoustics Group (EAG) focuses on simulations of wave propagation problems, including acoustics, electromagnetics, elastodynamics and various coupled problems. The main simulation tool is the hp-adaptive finite and boundary element methods where both element size h and polynomial order p vary locally to capture solution singularities or boundary layers. Both parameters h and p are determined in a fully automatic mode driven by an adaptive strategy aiming at minimization of the energy norm of the discretization error, or error in a specific quantity of interest. The hp-adaptive strategy produces a sequence of grids delivering exponential convergence, enabling solution of challenging problems with large material contrasts and dynamic range.

Sample applications are illustrated below. They include simulations of electromagnetic and sonic logging tools, analysis of unwanted noise in streamers, computation of Radar Cross Sections for objects with sharp edges and vertices, simulations of acoustic waves in the Human Head and others.

The last few years witnessed a very intensive development of theory and software behind our hp-adaptive Finite Elements technology. The theory of Projection-Based Interpolation providing a basis for automatic hp-adaptivity has been completed with recent breakthroughs on exis- tenceof polynomial preserving extension operators for all spaces forming the exact sequence. The theoretical work was done in collaboration with Annalisa Buffa, Weiming Cao, Martin Costabel, Monique Dauge, Jay Gopalakrishanan and Joachim Schoeberl.

The theory and hp codes have been documented in a two-volume book on “Computing with hp-Adaptive Finite Elements,” published by Chapman and Hall/CRS Press.