Zobrazeno 1 - 10
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pro vyhledávání: '"Börm, Steffen"'
Autor:
Börm, Steffen
The discretization of non-local operators, e.g., solution operators of partial differential equations or integral operators, leads to large densely populated matrices. $\mathcal{H}^2$-matrices take advantage of local low-rank structures in these matr
Externí odkaz:
http://arxiv.org/abs/2403.01566
Autor:
Börm, Steffen, Henningsen, Janne
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 its original form. Algebraic recompression can significantly reduce th
Externí odkaz:
http://arxiv.org/abs/2310.00111
Autor:
Börm, Steffen
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole methods in ord
Externí odkaz:
http://arxiv.org/abs/2309.09061
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 depending on the chosen Bloch boundary conditions. We propose to use
Externí odkaz:
http://arxiv.org/abs/2304.00337
Autor:
Börm, Steffen, Henningsen, Janne
Boundary element methods for elliptic partial differential equations typically lead to boundary integral operators with translation-invariant kernel functions. Taking advantage of this property is fairly simple for particle methods, e.g., Nystrom-typ
Externí odkaz:
http://arxiv.org/abs/2210.16609
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, very often this degeneracy can be broken by virtue of strong interaction
Externí odkaz:
http://arxiv.org/abs/2206.12686
Autor:
Börm, Steffen
Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method or hierarch
Externí odkaz:
http://arxiv.org/abs/2203.05665
Autor:
Börm, Steffen
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 interpolation. In order to improve the efficiency, a multi-level appr
Externí odkaz:
http://arxiv.org/abs/2109.04330
Taking the covering dimension dim as notion for the dimension of a topological space, we first specify thenumber zdim_{T_0}(n) of zero-dimensional T_0-spaces on {1,...,n}$ and the number zdim(n) of zero-dimensional arbitrary topological spaces on {1,
Externí odkaz:
http://arxiv.org/abs/2003.12871