61 citations · 85 across the 15 of their papers we have counts for
19 papers
Beyond Lipschitz: Data-Driven Robustness via Discrete Modulus of Continuity
Jürgen Dölz, Michael Multerer, Michele Palma
Robustness of neural networks is commonly quantified via local or global Lipschitz constants. However, Lipschitz continuity can be overly coarse or overly restrictive as global rob…
Isogeometric Shape Optimization of Multi-Tapered Coaxial Baluns Simulated by an Integral Equation Method
Boian Balouchev, Jürgen Dölz, Maximilian Nolte +2
We discuss the advantages of a spline-based freeform shape optimization approach using the example of a multi-tapered coaxial balun connected to a spiral antenna. The underlying si…
Shape uncertainty quantification of Maxwell eigenvalues and -modes with application to TESLA cavities
Jürgen Dölz, David Ebert, Sebastian Schöps +1
We consider Maxwell eigenvalue problems on uncertain shapes with perfectly conducting TESLA cavities being the driving example. Due to the shape uncertainty the resulting eigenvalu…
A Low-Frequency-Stable Higher-Order Isogeometric Discretization of the Augmented Electric Field Integral Equation
Maximilian Nolte, Riccardo Torchio, Sebastian Schöps +3
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The…
Solving acoustic scattering problems by the isogeometric boundary element method
Jürgen Dölz, Helmut Harbrecht, Michael Multerer
We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equatio…
Parametric Shape Holomorphy of Boundary Integral Operators with Applications
Jürgen Dölz, Fernando Henríquez
We consider a family of boundary integral operators supported on a collection of parametrically defined bounded Lipschitz boundaries. Consequently, the boundary integral operators…
Data sparse multilevel covariance estimation in optimal complexity
Jürgen Dölz
We consider the $\calH^2$-formatted compression and computational estimation of covariance functions on a compact set in . The classical sample covariance or Monte Carlo es…
On uncertainty quantification of eigenvalues and eigenspaces with higher multiplicity
Jürgen Dölz, David Ebert
We consider generalized operator eigenvalue problems in variational form with random perturbations in the bilinear forms. This setting is motivated by variational forms of partial…
On robustly convergent and efficient iterative methods for anisotropic radiative transfer
Jürgen Dölz, Olena Palii, Matthias Schlottbom
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere.…
A fast and oblivious matrix compression algorithm for Volterra integral operators
Jürgen Dölz, Herbert Egger, Vsevolod Shashkov
The numerical solution of dynamical systems with memory requires the efficient evaluation of Volterra integral operators in an evolutionary manner. After appropriate discretisation…
Isogeometric multilevel quadrature for forward and inverse random acoustic scattering
Jürgen Dölz, Helmut Harbrecht, Carlos Jerez-Hanckes +1
We study the numerical solution of forward and inverse acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary eleme…
A model reduction approach for inverse problems with operator valued data
Jürgen Dölz, Herbert Egger, Matthias Schlottbom
We study the efficient numerical solution of linear inverse problems with operator valued data which arise, e.g., in seismic exploration, inverse scattering, or tomographic imaging…
A convolution quadrature method for Maxwell's equations in dispersive media
Jürgen Dölz, Herbert Egger, Vsevolod Shashkov
We study the systematic numerical approximation of Maxwell's equations in dispersive media. Two discretization strategies are considered, one based on a traditional leapfrog time i…
A higher order perturbation approach for electromagnetic scattering problems on random domains
Jürgen Dölz
We consider time-harmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on th…
A Numerical Comparison of an Isogeometric and a Classical Higher-Order Approach to the Electric Field Integral Equation
Jürgen Dölz, Stefan Kurz, Sebastian Schöps +1
In this paper, we advocate a novel spline-based isogeometric approach for boundary elements and its efficient implementation. We compare solutions obtained by both an isogeometric…
On the best approximation of the hierarchical matrix product
Jürgen Dölz, Helmut Harbrecht, Michael D. Multerer
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the mul…
Recent Advances of Isogeometric Analysis in Computational Electromagnetics
Zeger Bontinck, Jacopo Corno, Herbert De Gersem +8
In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial…
A Fast Isogeometric BEM for the Three Dimensional Laplace- and Helmholtz Problems
Jürgen Dölz, Helmut Harbrecht, Stefan Kurz +2
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compress…
-matrix based second moment analysis for rough random fields and finite element discretizations
Jürgen Dölz, Helmut Harbrecht, Michael D. Peters
We consider the efficient solution of strongly elliptic partial differential equations with random load based on the finite element method. The solution's two-point correlation can…