99 citations · 110 across the 10 of their papers we have counts for
10 papers
The regularity of electronic wave functions in Barron spaces
Harry Yserentant
The electronic Schrödinger equation describes the motion of electrons under Coulomb interaction forces in a field of clamped nuclei. It is proved that its solutions for eigenva…
An iterative method for the solution of Laplace-like equations in high and very high space dimensions
Harry Yserentant
This paper deals with the equation on high-dimensional spaces , where the right-hand side is composed of a separable function with an inte…
The Laplace operator, measure concentration, Gauss functions, and quantum mechanics
Harry Yserentant
We represent in this note the solutions of the electronic Schrödinger equation as traces of higher-dimensional functions. This allows to decouple the electron-electron interaction…
A measure concentration effect for matrices of high, higher, and even higher dimension
Harry Yserentant
Let , and let be an -matrix of full rank. Then obviously the estimate holds for the euclidean norm of and and the spectral nor…
Numerical Homogenization of Fractal Interface Problems
Ralf Kornhuber, Joscha Podlesny, Harry Yserentant
We consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular featur…
On the expansion of solutions of Laplace-like equations into traces of separable higher dimensional functions
Harry Yserentant
This paper deals with the equation on high-dimensional spaces where is a positive constant. If the right-hand side is a rapidly converging series…
On the approximation of electronic wavefunctions by anisotropic Gauss and Gauss-Hermite functions
Stephan Scholz, Harry Yserentant
The electronic Schrödinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electroni…
A Note on Approximate Inverse Iteration
Harry Yserentant
Different variants of approximate inverse iteration like the locally optimal block preconditioned conjugate gradient method became in recent years increasingly popular for the solu…
An analysis of a class of variational multiscale methods based on subspace decomposition
Ralf Kornhuber, Daniel Peterseim, Harry Yserentant
Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite elem…
Sparse Approximate Solution of Partial Differential Equations
Sadegh Jokar, Volker Mehrmann, Marc Pfetsch +1
A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work o…