Maxwell's equations; perturbation approach; boundary element method; uncertainty quantification; H-matrix; H-matrix arithmetic; electromagnetism
Dölz Jürgen, Harbrecht Helmut, Multerer Michael D. (2019), On the Best Approximation of the Hierarchical Matrix Product, in SIAM Journal on Matrix Analysis and Applications
, 40(1), 147-174.
Dölz Jürgen, Kurz Stefan, Schöps Sebastian, Wolf Felix (2019), Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples, in SIAM Journal on Scientific Computing
, 41(5), B983-B1010.
Dölz Jürgen, Kurz Stefan, Schöps Sebastian, Wolf Felix (2018), An Overview of Isogeometric Boundary Element Methods for Acoustic and Electromagnetic Scattering Problems, in PAMM
, 18(1), e201800100-e201800100.
A major effort has been undertaken in recent years to model physical phenomena under uncertain input data, and specifically uncertainty in the shape of components coming for example from tolerances in production processes. While in recent years the mathematical background has been well understood for elliptic problems and efficient simulation and solution algorithms are available, the quantification of uncertainty coming from uncertain shapes in electromagnetism is nowadays mainly done by generic sampling and quadrature methods, which require a lot of computing power. The perturbation approach has proven to be a valuable and more efficient method to quantify uncertainty for small perturbations of the shape in case of elliptic equations, and recent work shows that H-matrices are an ideal tool to cope with rough correlations in this approach.This project intends to extend the H-matrix based perturbation approach from the mostly academic framework of elliptic equations to the more involved framework of electromagnetism described by Maxwell’s equations, which is an important physical phenomena in engineering to simulate radar waves, radio waves, and microwaves.