Helmut Harbrecht

Orcid: 0000-0003-0093-5706

According to our database1, Helmut Harbrecht authored at least 78 papers between 2002 and 2024.

Collaborative distances:
  • Dijkstra number2 of four.
  • Erdős number3 of four.

Timeline

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Bibliography

2024
Identification of Sparsely Representable Diffusion Parameters in Elliptic Problems.
SIAM J. Imaging Sci., March, 2024

Uncertainty quantification for random domains using periodic random variables.
Numerische Mathematik, February, 2024

Wavelet compressed, modified Hilbert transform in the space-time discretization of the heat equation.
CoRR, 2024

The dimension weighted fast multipole method for scattered data approximation.
CoRR, 2024

2023
Space-time Multilevel Quadrature Methods and their Application for Cardiac Electrophysiology.
SIAM/ASA J. Uncertain. Quantification, December, 2023

Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case.
Comput. Methods Appl. Math., April, 2023

Low-rank approximation of continuous functions in Sobolev spaces with dominating mixed smoothness.
Math. Comput., February, 2023

Analysis of Tensor Approximation Schemes for Continuous Functions.
Found. Comput. Math., February, 2023

The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs.
CoRR, 2023

Solving acoustic scattering problems by the isogeometric boundary element method.
CoRR, 2023

Samplet basis pursuit.
CoRR, 2023

2022
A Wavelet-Based Approach for the Simulation and Optimal Control of NonLocal Operator Equations.
SIAM J. Sci. Comput., August, 2022

On the Reformulation of the Classical Stefan Problem as a Shape Optimization Problem.
SIAM J. Control. Optim., 2022

Samplets: Construction and scattered data compression.
J. Comput. Phys., 2022

Multiresolution kernel matrix algebra.
CoRR, 2022

2021
Sparse Grid Approximation of the Riccati Operator for Closed Loop Parabolic Control Problems with Dirichlet Boundary Control.
SIAM J. Control. Optim., 2021

On the Numerical Solution of a Time-Dependent Shape Optimization Problem for the Heat Equation.
SIAM J. Control. Optim., 2021

A fast direct solver for nonlocal operators in wavelet coordinates.
J. Comput. Phys., 2021

Samplets: A new paradigm for data compression.
CoRR, 2021

Isogeometric shape optimization for scaffold structures.
CoRR, 2021

Multilevel approximation of Gaussian random fields: Covariance compression, estimation and spatial prediction.
CoRR, 2021

2020
Bembel: The fast isogeometric boundary element C++ library for Laplace, Helmholtz, and electric wave equation.
SoftwareX, 2020

Multilevel Quadrature for Elliptic Parametric Partial Differential Equations in Case of Polygonal Approximations of Curved Domains.
SIAM J. Numer. Anal., 2020

Shape Optimization for Composite Materials and Scaffold Structures.
Multiscale Model. Simul., 2020

Isogeometric multilevel quadrature for forward and inverse random acoustic scattering.
CoRR, 2020

2019
On the Best Approximation of the Hierarchical Matrix Product.
SIAM J. Matrix Anal. Appl., 2019

A New Method for the Data Completion Problem and Application to Obstacle Detection.
SIAM J. Appl. Math., 2019

On the Algebraic Construction of Sparse Multilevel Approximations of Elliptic Tensor Product Problems.
J. Sci. Comput., 2019

Error-Controlled Model Approximation for Gaussian Process Morphable Models.
J. Math. Imaging Vis., 2019

2018
A fast sparse grid based space-time boundary element method for the nonstationary heat equation.
Numerische Mathematik, 2018

Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains.
J. Comput. Phys., 2018

Novel results for the anisotropic sparse grid quadrature.
J. Complex., 2018

A scalable H-matrix approach for the solution of boundary integral equations on multi-GPU clusters.
CoRR, 2018

A Digital Edition of Leonhard Euler's Correspondence with Christian Goldbach.
Proceedings of the 13th Annual International Conference of the Alliance of Digital Humanities Organizations, 2018

2017
ℋ-Matrix Based Second Moment Analysis for Rough Random Fields and Finite Element Discretizations.
SIAM J. Sci. Comput., 2017

Uncertainty Quantification for PDEs with Anisotropic Random Diffusion.
SIAM J. Numer. Anal., 2017

Covariance regularity and \(\mathcal {H}\) -matrix approximation for rough random fields.
Numerische Mathematik, 2017

On the quasi-Monte Carlo method with Halton points for elliptic PDEs with log-normal diffusion.
Math. Comput., 2017

Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness.
J. Comput. Phys., 2017

Integrating historical scientific texts into the Bernoulli-Euler Online platform.
Proceedings of the 12th Annual International Conference of the Alliance of Digital Humanities Organizations, 2017

2016
Numerical Solution of the Poisson Equation on Domains with a Thin Layer of Random Thickness.
SIAM J. Numer. Anal., 2016

Analysis of the domain mapping method for elliptic diffusion problems on random domains.
Numerische Mathematik, 2016

Multilevel Accelerated Quadrature for PDEs with Log-Normally Distributed Diffusion Coefficient.
SIAM/ASA J. Uncertain. Quantification, 2016

Optimization of current carrying multicables.
Comput. Optim. Appl., 2016

A Note on Multilevel Based Error Estimation.
Comput. Methods Appl. Math., 2016

2015
Shape Optimization for Quadratic Functionals and States with Random Right-Hand Sides.
SIAM J. Control. Optim., 2015

Efficient approximation of random fields for numerical applications.
Numer. Linear Algebra Appl., 2015

ℋ-matrix Accelerated Second Moment Analysis for Potentials with Rough Correlation.
J. Sci. Comput., 2015

2014
The H<sup>2</sup>-wavelet method.
J. Comput. Appl. Math., 2014

2013
On the Numerical Solution of a Shape Optimization Problem for the Heat Equation.
SIAM J. Sci. Comput., 2013

On the construction of sparse tensor product spaces.
Math. Comput., 2013

Combination technique based k-th moment analysis of elliptic problems with random diffusion.
J. Comput. Phys., 2013

2012
Preconditioning of wavelet BEM by the incomplete Cholesky factorization.
Comput. Vis. Sci., 2012

On a Kohn-Vogelius like formulation of free boundary problems.
Comput. Optim. Appl., 2012

Shape Optimization for Free Boundary Problems - Analysis and Numerics.
Proceedings of the Constrained Optimization and Optimal Control for Partial Differential Equations, 2012

2011
Wavelet BEM on molecular surfaces: solvent excluded surfaces.
Computing, 2011

2010
Wavelet formulation of the polarizable continuum model.
J. Comput. Chem., 2010

From Computer Aided Design to wavelet BEM.
Comput. Vis. Sci., 2010

2009
Tracking Neumann Data for Stationary Free Boundary Problems.
SIAM J. Control. Optim., 2009

Wavelet BEM on molecular surfaces: parametrization and implementation.
Computing, 2009

2008
Sparse second moment analysis for elliptic problems in stochastic domains.
Numerische Mathematik, 2008

Multilevel frames for sparse tensor product spaces.
Numerische Mathematik, 2008

A Newton method for Bernoulli's free boundary problem in three dimensions.
Computing, 2008

A new fictitious domain method in shape optimization.
Comput. Optim. Appl., 2008

Compact gradient tracking in shape optimization.
Comput. Optim. Appl., 2008

2007
On Convergence in Elliptic Shape Optimization.
SIAM J. Control. Optim., 2007

An optimal adaptive wavelet method without coarsening of the iterands.
Math. Comput., 2007

Adaptive methods for boundary integral equations: Complexity and convergence estimates.
Math. Comput., 2007

2006
Wavelet Galerkin Schemes for Boundary Integral Equations-Implementation and Quadrature.
SIAM J. Sci. Comput., 2006

Compression Techniques for Boundary Integral Equations - Asymptotically Optimal Complexity Estimates.
SIAM J. Numer. Anal., 2006

Second-order shape optimization using wavelet BEM.
Optim. Methods Softw., 2006

Coupling of FEM and BEM in Shape Optimization.
Numerische Mathematik, 2006

Wavelets with patchwise cancellation properties.
Math. Comput., 2006

2003
Least Squares Methods for the Coupling of FEM and BEM.
SIAM J. Numer. Anal., 2003

Numerical Solution of Elliptic Shape Optimization Problems using wavelet-based BEM.
Optim. Methods Softw., 2003

Self-regularization by projection for noisy pseudodifferential equations of negative order.
Numerische Mathematik, 2003

Multiscale preconditioning for the coupling of FEM-BEM.
Numer. Linear Algebra Appl., 2003

2002
Biorthogonal wavelet approximation for the coupling of FEM-BEM.
Numerische Mathematik, 2002


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