28 citations · 136 across the 22 of their papers we have counts for
24 papers
Memory-efficient compression of -matrices for high-frequency problems
Steffen Börm, Janne Henningsen
Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but it requires a very large amount of storage in…
Adaptive multiplication of rank-structured matrices in linear complexity
Steffen Börm
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. -matrices refine th…
Computing Maxwell eigenmodes with Bloch boundary conditions
Steffen Börm, Ralf Köhl, Nahid Talebi
Our goal is to predict the band structure of photonic crystals. This task requires us to compute a number of the smallest non-zero eigenvalues of the time-harmonic Maxwell operator…
-matrices for translation-invariant kernel functions
Steffen Börm, Janne Henningsen
Boundary element methods for elliptic partial differential equations typically lead to boundary integral operators with translation-invariant kernel functions. Taking advantage of…
Topological photonics by breaking the degeneracy of line node singularities in semimetal-like photonic crystals
Steffen Börm, Fatemeh Davoodi, Ralf Köhl +1
Degeneracy is an omnipresent phenomenon in various physical systems, which has its roots in the preservation of geometrical symmetry. In electronic and photonic crystal systems, ve…
Distributed -matrices for boundary element methods
Steffen Börm
Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and effic…
On iterated interpolation
Steffen Börm
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by…
Dielectric breakdown prediction with GPU-accelerated BEM
Cedric Münger, Steffen Börm, Jörg Ostrowski
The prediction of a dielectric breakdown in a high-voltage device is based on criteria that evaluate the electric field along field lines. Therefore it is necessary to efficiently…
Semi-Automatic Task Graph Construction for -Matrix Arithmetic
Steffen Börm, Sven Christophersen, Ronald Kriemann
A new method to construct task graphs for \mcH-matrix arithmetic is introduced, which uses the information associated with all tasks of the standard recursive \mcH-matrix algorithm…
Exploiting nested task-parallelism in the factorization
Rocío Carratalá-Sáez, Sven Christophersen, José I. Aliaga +3
We address the parallelization of the LU factorization of hierarchical matrices (-matrices) arising from boundary element methods. Our approach exploits task-paralleli…
Complexity estimates for triangular hierarchical matrix algorithms
Steffen Börm
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices (-matrices). Experiments s…
Variable Order, Directional H2-Matrices for Helmholtz Problems with Complex Frequency
Steffen Börm, Maria Lopez-Fernandez, Stefan Sauter
The sparse approximation of high-frequency Helmholtz-type integral operators has many important physical applications such as problems in wave propagation and wave scattering. The…
Large-scale magnetostatic field calculation in finite element micromagnetics with H2-matrices
Riccardo Hertel, Sven Christophersen, Steffen Börm
Magnetostatic field calculations in micromagnetic simulations can be numerically expensive, particularly in the case of large-scale finite element simulations. The established fini…
GCA- matrix compression for electrostatic simulations
Steffen Börm, Sven Christophersen
We consider a compression method for boundary element matrices arising in the context of the computation of electrostatic fields. Green cross approximation combines an analytic app…
An analysis of a butterfly algorithm
Steffen Börm, Christina Börst, Jens Markus Melenk
Butterfly algorithms are an effective multilevel technique to compress discretizations of integral operators with highly oscillatory kernel functions. The particular version of the…
Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains
Jens Markus Melenk, Markus Faustmann
The hp-version of the finite element method is applied to singularly perturbed reaction-diffusion type equations on polygonal domains. The solution exhibits boundary layers as well…
Approximation of boundary element matrices using GPGPUs and nested cross approximation
Steffen Börm, Sven Christophersen
The efficiency of boundary element methods depends crucially on the time required for setting up the stiffness matrix. The far-field part of the matrix can be approximated by compr…
Approximation of the high-frequency Helmholtz kernel by nested directional interpolation
Steffen Börm, Jens Markus Melenk
We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polyno…
Directional H2-matrix compression for high-frequency problems
Steffen Börm
Standard numerical algorithms like the fast multipole method or -matrix schemes rely on low-rank approximations of the underlying kernel function. For high-frequency p…
Adaptive compression of large vectors
Steffen Börm
Numerical algorithms for elliptic partial differential equations frequently employ error estimators and adaptive mesh refinement strategies in order to reduce the computational cos…
Approximation of integral operators by Green quadrature and nested cross approximation
Steffen Börm, Sven Christophersen
We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations.…
Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum
Peter Benner, Steffen Börm, Thomas Mach +1
The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade. Here we present a new algorit…
An exact solver for simple -matrix systems
Steffen Börm, Jessica Gördes
Hierarchical matrices (usually abbreviated -matrices) are frequently used to construct preconditioners for systems of linear equations. Since it is possible to comput…
Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates
Steffen Börm, Knut Reimer
Many matrices appearing in numerical methods for partial differential equations and integral equations are rank-structured, i.e., they contain submatrices that can be approximated…