Related papers: Iso-geometric Integral Equation Solvers and their …
The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but {\em not} differentiable. The need to define physical quantities on this…
We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…
We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
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 basis functions, commonly employed by the classical Finite…
We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the…
Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
In many applications, one encounters signals that lie on manifolds rather than a Euclidean space. In particular, covariance matrices are examples of ubiquitous mathematical objects that have a non Euclidean structure. The application of…
In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry…
This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby…
Complex geometries as common in industrial applications consist of multiple patches, if spline based parametrizations are used. The requirements for the generation of analysis-suitable models are increasing dramatically since isogeometric…
This paper discusses and analyses two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretised by either N\'ed\'elec-type polynomial finite elements or spline-based isogeometric…
Dirac $\delta-$ distributionally sourced differential equations emerge in many dynamical physical systems from machine learning, finance, neuroscience, and seismology to black hole perturbation theory. These systems lack exact analytical…
Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a…
Partial differential equations describing compressible fluids are prone to the formation of shock singularities, arising from faster upstream fluid particles catching up to slower, downstream ones. In geometric terms, this causes the…
We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting their limitations and shortcomings in non-flat (non-Euclidean)…
We introduce manifold-based basis functions for isogeometric analysis of surfaces with arbitrary smoothness, prescribed $C^0$ continuous creases and boundaries. The utility of the manifold-based surface construction techniques in…