Edit Profile (opens in new tab) Harbrecht, Helmut Co-Author Distance Author ID: harbrecht.helmut Published as: Harbrecht, Helmut; Harbrecht, H.; Harbrecht, Helumt; Harbrech, Helmut more...less Homepage: https://cm.dmi.unibas.ch/ External Links: MGP · dblp · GND Documents Indexed: 137 Publications since 2001, including 1 Book and 9 Additional arXiv Preprints 2 Contributions as Editor Co-Authors: 85 Co-Authors with 129 Joint Publications 2,637 Co-Co-Authors all top 5 Co-Authors 9 single-authored 29 Multerer, Michael D. 20 Schneider, Reinhold 18 Eppler, Karsten 9 Dambrine, Marc 9 Dölz, Jürgen 8 Griebel, Michael 8 Schwab, Christoph 6 Puig, Bénédicte 6 Siebenmorgen, Markus 6 Tausch, Johannes 5 Brügger, Rahel 5 Schmidlin, Marc 4 Wendland, Wolfgang L. 4 Zorii, Natalia 3 Randrianarivony, Maharavo 3 Zaspel, Peter 2 Bürli, Christine 2 Chitnis, Nakul 2 Croce, Roberto 2 Dahlke, Stephan 2 Dahmen, Wolfgang A. 2 Greff, Isabelle 2 Hohage, Thorsten 2 Kähler, Uwe 2 Kunoth, Angela 2 Mitrou, Giannoula 2 Moor, Manuela 2 Odermatt, Peter 2 Paiva, Freddy 2 Pérez, Cristian 2 Sayasone, Somphou 2 Stevenson, Rob P. 1 Alm, Daniel 1 Baroli, Davide 1 Ben Bader, Seif 1 Benner, Peter 1 Buffa, Annalisa 1 Bugeanu, Monica 1 Caubet, Fabien 1 Dapogny, Charles 1 Engell, Sebastian 1 Fallahpour, Merlin 1 Gantumur, Tsogtgerel 1 Gatica, Gabriel N. 1 Gerig, Thomas 1 Griewank, Andreas 1 Haji-Ali, Abdul-Lateef 1 Hakula, Harri 1 Herrmann, Lukas 1 Hinze, Michael 1 Ilić, Nikola 1 Jakeman, John Davis 1 Jerez-Hanckes, Carlos 1 Kaarnioja, Vesa 1 Kalmykov, Ilja 1 Kirchner, Kristin 1 Konik, Michael 1 Krämer, Ulf 1 Krause, Rolf H. 1 Kuo, Frances Y. 1 Kurz, Stefan 1 Leugering, Günter 1 Li, Jingzhi 1 Loos, Florian 1 Lüthi, Marcel 1 Mommer, Mario S. 1 Pereverzev, Sergei V. 1 Quaglino, Alessio 1 Quizi, Jacopo 1 Rannacher, Rolf 1 Sangalli, Giancarlo 1 Schenk, Olaf 1 Schlenkrich, Sebastian 1 Schöps, Sebastian 1 Simoncini, Valeria 1 Sloan, Ian Hugh 1 Surowiec, Thomas 1 Ulbrich, Stefan 1 Urban, Karsten 1 Vetter, Thomas 1 von Rickenbach, Remo 1 Walther, Andrea 1 Weimar, Markus 1 Wolf, Felix L. 1 Zank, Marco all top 5 Serials 9 Numerische Mathematik 6 Computer Methods in Applied Mechanics and Engineering 6 Mathematics of Computation 6 SIAM Journal on Control and Optimization 6 Applied Numerical Mathematics 5 Journal of Computational Physics 5 Mathematical Methods in the Applied Sciences 5 SIAM Journal on Numerical Analysis 4 Computational Optimization and Applications 4 SIAM Journal on Scientific Computing 3 Computing 3 Mathematische Nachrichten 3 Engineering Analysis with Boundary Elements 3 Computing and Visualization in Science 2 IMA Journal of Numerical Analysis 2 Journal of Mathematical Analysis and Applications 2 Numerical Functional Analysis and Optimization 2 Journal of Scientific Computing 2 Numerical Linear Algebra with Applications 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Optimization Methods & Software 2 Computational Methods in Applied Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Stochastic and Partial Differential Equations. Analysis and Computations 2 SIAM/ASA Journal on Uncertainty Quantification 1 Inverse Problems 1 Mathematical Biosciences 1 Control and Cybernetics 1 Integral Equations and Operator Theory 1 Journal of Computational and Applied Mathematics 1 Journal of Optimization Theory and Applications 1 Journal of Complexity 1 Constructive Approximation 1 Numerical Methods for Partial Differential Equations 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Integral Equations and Applications 1 SIAM Journal on Applied Mathematics 1 Journal of Mathematical Imaging and Vision 1 Journal of Mathematical Chemistry 1 Journal of Mathematical Study 1 Interfaces and Free Boundaries 1 Optimization and Engineering 1 Foundations of Computational Mathematics 1 Multiscale Modeling & Simulation 1 Oberwolfach Reports 1 ISNM. International Series of Numerical Mathematics 1 Communications in Computational Physics 1 Inverse Problems and Imaging 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 International Journal for Uncertainty Quantification 1 Journal of Theoretical Biology all top 5 Fields 108 Numerical analysis (65-XX) 63 Partial differential equations (35-XX) 44 Calculus of variations and optimal control; optimization (49-XX) 26 Probability theory and stochastic processes (60-XX) 7 Approximations and expansions (41-XX) 7 Mechanics of deformable solids (74-XX) 7 Optics, electromagnetic theory (78-XX) 5 Operator theory (47-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Potential theory (31-XX) 4 Biology and other natural sciences (92-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Functional analysis (46-XX) 3 Fluid mechanics (76-XX) 2 General and overarching topics; collections (00-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 117 Publications have been cited 1,327 times in 676 Documents Cited by ▼ Year ▼ Compression techniques for boundary integral equations. Asymptotically optimal complexity estimates. Zbl 1113.65114 Dahmen, Wolfgang; Harbrecht, Helmut; Schneider, Reinhold 84 2006 Sparse second moment analysis for elliptic problems in stochastic domains. Zbl 1146.65007 Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph 55 2008 On the low-rank approximation by the pivoted Cholesky decomposition. Zbl 1244.65042 Harbrecht, Helmut; Peters, Michael; Schneider, Reinhold 54 2012 Wavelet Galerkin schemes for boundary integral equations – implementation and quadrature. Zbl 1117.65162 Harbrecht, Helmut; Schneider, Reinhold 47 2006 Analysis of the domain mapping method for elliptic diffusion problems on random domains. Zbl 1479.35969 Harbrecht, H.; Peters, M.; Siebenmorgen, M. 47 2016 An optimal adaptive wavelet method without coarsening of the iterands. Zbl 1115.41023 Gantumur, Tsogtgerel; Harbrecht, Helmut; Stevenson, Rob 46 2007 On convergence in elliptic shape optimization. Zbl 1354.49093 Eppler, Karsten; Harbrecht, Helmut; Schneider, Reinhold 36 2007 BPX-preconditioning for isogeometric analysis. Zbl 1286.65151 Buffa, Annalisa; Harbrecht, Helmut; Kunoth, Angela; Sangalli, Giancarlo 36 2013 Efficient approximation of random fields for numerical applications. Zbl 1349.65048 Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus 31 2015 A regularized Newton method in electrical impedance tomography using shape Hessian information. Zbl 1167.49327 Eppler, Karsten; Harbrecht, Helmut 30 2005 Multilevel frames for sparse tensor product spaces. Zbl 1151.65010 Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph 29 2008 A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems. Zbl 1439.65208 Dölz, Jürgen; Harbrecht, Helmut; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix 26 2018 Biorthogonal wavelet bases for the boundary element method. Zbl 1055.65136 Harbrecht, Helmut; Schneider, Reinhold 25 2004 First order second moment analysis for stochastic interface problems based on low-rank approximation. Zbl 1297.65009 Harbrecht, Helmut; Li, Jingzhi 25 2013 On the construction of sparse tensor product spaces. Zbl 1267.41012 Griebel, Michael; Harbrecht, Helmut 25 2013 Adaptive methods for boundary integral equations: complexity and convergence estimates. Zbl 1129.65090 Dahmen, Wolfgang; Harbrecht, Helmut; Schneider, Reinhold 23 2007 Fast methods for three-dimensional inverse obstacle scattering problems. Zbl 1138.65100 Harbrecht, Helmut; Hohage, Thorsten 22 2007 Efficient treatment of stationary free boundary problems. Zbl 1104.65111 Eppler, Karsten; Harbrecht, Helmut 21 2006 Wavelets with patchwise cancellation properties. Zbl 1112.46012 Harbrecht, Helmut; Stevenson, Rob 20 2006 Approximation of bi-variate functions: Singular value decomposition versus sparse grids. Zbl 1287.65009 Griebel, Michael; Harbrecht, Helmut 20 2014 On the numerical solution of a shape optimization problem for the heat equation. Zbl 1264.65156 Harbrecht, Helmut; Tausch, Johannes 20 2013 Multilevel accelerated quadrature for PDEs with log-normally distributed diffusion coefficient. Zbl 1343.65006 Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus 19 2016 Combination technique based \(k\)-th moment analysis of elliptic problems with random diffusion. Zbl 1349.35441 Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus 17 2013 Tracking Neumann data for stationary free boundary problems. Zbl 1202.49052 Eppler, Karsten; Harbrecht, Helmut 17 2010 On a Kohn-Vogelius like formulation of free boundary problems. Zbl 1258.49069 Eppler, Karsten; Harbrecht, Helmut 17 2012 Covariance regularity and \(\mathcal {H}\)-matrix approximation for rough random fields. Zbl 1362.65124 Dölz, J.; Harbrecht, H.; Schwab, Ch. 16 2017 Novel results for the anisotropic sparse grid quadrature. Zbl 1458.65021 Haji-Ali, A.-L.; Harbrecht, H.; Peters, M. D.; Siebenmorgen, M. 15 2018 Second-order shape optimization using wavelet BEM. Zbl 1086.49028 Eppler, K.; Harbrecht, H. 15 2006 Comparison of fast boundary element methods on parametric surfaces. Zbl 1286.65175 Harbrecht, H.; Peters, M. 15 2013 Numerical solution of elliptic shape optimization problems using wavelet-based BEM. Zbl 1061.49028 Eppler, K.; Harbrecht, H. 14 2003 On the convergence of the combination technique. Zbl 1316.65054 Griebel, Michael; Harbrecht, Helmut 14 2014 A finite element method for elliptic problems with stochastic input data. Zbl 1237.65009 Harbrecht, Helmut 13 2010 An efficient numerical method for a shape-identification problem arising from the heat equation. Zbl 1219.65132 Harbrecht, Helmut; Tausch, Johannes 13 2011 Fully discrete wavelet Galerkin schemes. Zbl 1035.65138 Harbrecht, Helmut; Konik, Michael; Schneider, Reinhold 13 2003 Shape optimization for quadratic functionals and states with random right-hand sides. Zbl 1326.49070 Dambrine, Marc; Dapogny, Charles; Harbrecht, Helmut 13 2015 Shape optimization for free boundary problems - analysis and numerics. Zbl 1356.49073 Eppler, Karsten; Harbrecht, Helmut 13 2012 A note on the construction of \(L\)-fold sparse tensor product spaces. Zbl 1283.41015 Griebel, Michael; Harbrecht, Helmut 13 2013 From computer aided design to wavelet BEM. Zbl 1213.65146 Harbrecht, H.; Randrianarivony, M. 13 2010 Computing quantities of interest for random domains with second order shape sensitivity analysis. Zbl 1351.60062 Dambrine, Marc; Harbrecht, Helmut; Puig, Bénédicte 12 2015 Self-regularization by projection for noisy pseudodifferential equations of negative order. Zbl 1074.65130 Harbrecht, Helmut; Pereverzev, Sergei; Schneider, Reinhold 12 2003 On output functionals of boundary value problems on stochastic domains. Zbl 1181.35354 Harbrecht, Helmut 11 2010 Coupling of FEM and BEM in shape optimization. Zbl 1104.65065 Eppler, Karsten; Harbrecht, Helmut 11 2006 Analytical and numerical methods in shape optimization. Zbl 1153.49039 Harbrecht, Helmut 11 2008 A Newton method for Bernoulli’s free boundary problem in three dimensions. Zbl 1152.49044 Harbrecht, Helmut 11 2008 Riesz minimal energy problems on \(C^{k-1,1}\)-manifolds. Zbl 1288.31005 Harbrecht, Helmut; Wendland, Wolfgang L.; Zorii, Natalia 11 2014 On the quasi-Monte Carlo method with halton points for elliptic PDEs with log-normal diffusion. Zbl 1355.65010 Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus 10 2017 Wavelet Galerkin schemes for 2D-BEM. Zbl 1005.65133 Harbrecht, Helmut; Schneider, Reinhold 10 2001 Tracking Dirichlet data in \(L^2\) is an ill-posed problem. Zbl 1217.49031 Eppler, K.; Harbrecht, H. 9 2010 Fast wavelet BEM for 3d electromagnetic shaping. Zbl 1114.78017 Eppler, Karsten; Harbrecht, Helmut 9 2005 Improved trial methods for a class of generalized Bernoulli problems. Zbl 1292.35341 Harbrecht, Helmut; Mitrou, Giannoula 9 2014 Trends in PDE constrained optimization. Zbl 1306.49001 9 2014 Multiscale preconditioning for the coupling of FEM-BEM. Zbl 1071.65552 Harbrecht, Helmut; Paiva, Freddy; Pérez, Cristian; Schneider, Reinhold 8 2003 Exterior electromagnetic shaping using wavelet BEM. Zbl 1061.49029 Eppler, K.; Harbrecht, H. 8 2005 On Riesz minimal energy problems. Zbl 1244.49058 Harbrecht, H.; Wendland, W. L.; Zorii, N. 8 2012 Biorthogonal wavelet approximation for the coupling of FEM-BEM. Zbl 1012.65114 Harbrecht, H.; Paiva, F.; Pérez, C.; Schneider, R. 8 2002 Sparse tensor finite elements for elliptic multiple scale problems. Zbl 1230.65127 Harbrecht, Helmut; Schwab, Christoph 7 2011 Wavelet Galerkin BEM on unstructured meshes. Zbl 1512.65283 Harbrecht, H.; Kähler, U.; Schneider, R. 7 2005 The second order perturbation approach for elliptic partial differential equations on random domains. Zbl 1379.65003 Harbrecht, Helmut; Peters, Michael D. 7 2018 Numerical solution of the Poisson equation on domains with a thin layer of random thickness. Zbl 1382.65457 Dambrine, Marc; Greff, Isabelle; Harbrecht, Helmut; Puig, Benedicte 7 2016 \(\mathcal H\)-matrix accelerated second moment analysis for potentials with rough correlation. Zbl 1329.65013 Dölz, J.; Harbrecht, H.; Peters, M. 7 2015 Singular value decomposition versus sparse grids: refined complexity estimates. Zbl 1496.65020 Griebel, Michael; Harbrecht, Helmut 7 2019 Analysis of tensor approximation schemes for continuous functions. Zbl 07654471 Griebel, Michael; Harbrecht, Helmut 7 2023 On the numerical solution of a time-dependent shape optimization problem for the heat equation. Zbl 1461.49051 Brügger, Rahel; Harbrecht, Helmut; Tausch, Johannes 7 2021 Wavelet BEM on molecular surfaces: solvent excluded surfaces. Zbl 1225.92065 Harbrecht, H.; Randrianarivony, M. 5 2011 Adaptive wavelet BEM for boundary integral equations: theory and numerical experiments. Zbl 1388.31008 Dahlke, S.; Harbrecht, H.; Utzinger, M.; Weimar, Markus 5 2018 Wavelet BEM on molecular surfaces: parametrization and implementation. Zbl 1241.65108 Harbrecht, Helmut; Randrianarivony, Maharavo 5 2009 Uncertainty quantification for PDEs with anisotropic random diffusion. Zbl 1432.35265 Harbrecht, H.; Peters, M. D.; Schmidlin, M. 5 2017 A new fictitious domain method in shape optimization. Zbl 1152.49043 Eppler, Karsten; Harbrecht, Helmut; Mommer, Mario S. 5 2008 Frames for the solution of operator equations in Hilbert spaces with fixed dual pairing. Zbl 1426.46005 Balazs, Peter; Harbrecht, Helmut 5 2019 Multilevel methods for uncertainty quantification of elliptic PDEs with random anisotropic diffusion. Zbl 1431.35258 Harbrecht, Helmut; Schmidlin, Marc 5 2020 Incorporating knowledge on the measurement noise in electrical impedance tomography. Zbl 1437.78003 Dambrine, Marc; Harbrecht, Helmut; Puig, Benedicte 5 2019 A fast sparse grid based space-time boundary element method for the nonstationary heat equation. Zbl 1403.65059 Harbrecht, Helmut; Tausch, Johannes 5 2018 Mathematical analysis of the transmission dynamics of the liver fluke, Opisthorchis viverrini. Zbl 1397.92619 Bürli, Christine; Harbrecht, Helmut; Odermatt, Peter; Sayasone, Somphou; Chitnis, Nakul 4 2018 Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness. Zbl 1380.65409 Dambrine, M.; Greff, I.; Harbrecht, H.; Puig, B. 4 2017 \(\mathcal{H}\)-matrix based second moment analysis for rough random fields and finite element discretizations. Zbl 1368.60070 Dölz, J.; Harbrecht, H.; Peters, M. D. 4 2017 A fast direct solver for nonlocal operators in wavelet coordinates. Zbl 07511425 Harbrecht, Helmut; Multerer, Michael 4 2021 Multilevel quadrature for elliptic parametric partial differential equations in case of polygonal approximations of curved domains. Zbl 1434.65256 Griebel, Michael; Harbrecht, Helmut; Multerer, Michael D. 4 2020 A Newton method for reconstructing non star-shaped domains in electrical impedance tomography. Zbl 1189.65113 Harbrecht, Helmut; Hohage, Thorsten 3 2009 Least squares methods for the coupling of FEM and BEM. Zbl 1055.65126 Gatica, Gabriel N.; Harbrecht, Helmut; Schneider, Reinhold 3 2003 Second moment analysis for Robin boundary value problems on random domains. Zbl 1326.35370 Harbrecht, Helmut 3 2014 Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data. Zbl 1331.65165 Harbrecht, Helmut; Mitrou, Giannoula 3 2015 Isogeometric multilevel quadrature for forward and inverse random acoustic scattering. Zbl 1507.74529 Dölz, Jürgen; Harbrecht, Helmut; Jerez-Hanckes, Carlos; Multerer, Michael 3 2022 Shape optimization for composite materials and scaffold structures. Zbl 1446.49035 Dambrine, Marc; Harbrecht, Helmut 3 2020 Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains. Zbl 1415.65267 Dölz, Jürgen; Harbrecht, Helmut 3 2018 Wavelet-based boundary element methods for exterior electromagnetic shaping. Zbl 1244.78022 Eppler, K.; Harbrecht, H. 2 2008 The \(\mathcal H^2\)-wavelet method. Zbl 1293.65162 Alm, Daniel; Harbrecht, Helmut; Krämer, Ulf 2 2014 Solution of free boundary problems in the presence of geometric uncertainties. Zbl 1380.49022 Harbrecht, H.; Peters, M. D. 2 2017 A second order convergent trial method for a free boundary problem in three dimensions. Zbl 1331.65170 Bugeanu, Monica; Harbrecht, Helmut 2 2015 Optimization of current carrying multicables. Zbl 1333.49062 Harbrecht, Helmut; Loos, Florian 2 2016 Combination technique based second moment analysis for elliptic PDEs on random domains. Zbl 1339.65015 Harbrecht, Helmut; Peters, Michael 2 2016 Compact gradient tracking in shape optimization. Zbl 1181.90286 Eppler, Karsten; Harbrecht, Helmut 2 2008 A new method for the data completion problem and application to obstacle detection. Zbl 1423.35438 Caubet, Fabien; Dambrine, Marc; Harbrecht, Helmut 2 2019 Rapid computation of far-field statistics for random obstacle scattering. Zbl 1464.76089 Harbrecht, Helmut; Ilić, Nikola; Multerer, Michael D. 2 2019 On Bernoulli’s free boundary problem with a random boundary. Zbl 1498.35366 Dambrine, M.; Harbrecht, H.; Peters, M. D.; Puig, B. 2 2017 Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM. Zbl 07613009 Harbrecht, Helmut; Schmidlin, Marc 2 2022 Low-rank approximation of continuous functions in Sobolev spaces with dominating mixed smoothness. Zbl 07673301 Griebel, Michael; Harbrecht, Helmut; Schneider, Reinhold 2 2023 Shape optimization for 3D electrical impedance tomography. Zbl 1403.49042 Eppler, Karsten; Harbrech, Helmut 2 2007 Finite element based second moment analysis for elliptic problems in stochastic domains. Zbl 1216.65008 Harbrecht, H. 1 2010 Rapid solution of boundary integral equations by wavelet Galerkin schemes. Zbl 1190.65179 Harbrecht, Helmut; Schneider, Reinhold 1 2009 On analytical derivatives for geometry optimization in the polarizable continuum model. Zbl 1304.82073 Harbrecht, Helmut 1 2011 Analysis of tensor approximation schemes for continuous functions. Zbl 07654471 Griebel, Michael; Harbrecht, Helmut 7 2023 Low-rank approximation of continuous functions in Sobolev spaces with dominating mixed smoothness. Zbl 07673301 Griebel, Michael; Harbrecht, Helmut; Schneider, Reinhold 2 2023 Bernoulli free boundary problems under uncertainty: the convex case. Zbl 1518.35695 Dambrine, Marc; Harbrecht, Helmut; Puig, Benedicte 1 2023 Isogeometric multilevel quadrature for forward and inverse random acoustic scattering. Zbl 1507.74529 Dölz, Jürgen; Harbrecht, Helmut; Jerez-Hanckes, Carlos; Multerer, Michael 3 2022 Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM. Zbl 07613009 Harbrecht, Helmut; Schmidlin, Marc 2 2022 Isogeometric shape optimization of periodic structures in three dimensions. Zbl 1507.49034 Harbrecht, Helmut; Multerer, Michael; von Rickenbach, Remo 1 2022 Boundary integral operators for the heat equation in time-dependent domains. Zbl 1486.35482 Brügger, Rahel; Harbrecht, Helmut; Tausch, Johannes 1 2022 On the reformulation of the classical Stefan problem as a shape optimization problem. Zbl 1481.49042 Brügger, Rahel; Harbrecht, Helmut 1 2022 On the numerical solution of a time-dependent shape optimization problem for the heat equation. Zbl 1461.49051 Brügger, Rahel; Harbrecht, Helmut; Tausch, Johannes 7 2021 A fast direct solver for nonlocal operators in wavelet coordinates. Zbl 07511425 Harbrecht, Helmut; Multerer, Michael 4 2021 Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration. Zbl 1473.62089 Harbrecht, Helumt; Jakeman, John D.; Zaspel, Peter 1 2021 Sparse grid approximation of the Riccati operator for closed loop parabolic control problems with Dirichlet boundary control. Zbl 1480.49005 Harbrecht, Helmut; Kalmykov, Ilja 1 2021 Multilevel methods for uncertainty quantification of elliptic PDEs with random anisotropic diffusion. Zbl 1431.35258 Harbrecht, Helmut; Schmidlin, Marc 5 2020 Multilevel quadrature for elliptic parametric partial differential equations in case of polygonal approximations of curved domains. Zbl 1434.65256 Griebel, Michael; Harbrecht, Helmut; Multerer, Michael D. 4 2020 Shape optimization for composite materials and scaffold structures. Zbl 1446.49035 Dambrine, Marc; Harbrecht, Helmut 3 2020 Solving a Bernoulli type free boundary problem with random diffusion. Zbl 1453.35199 Brügger, Rahel; Croce, Roberto; Harbrecht, Helmut 1 2020 Singular value decomposition versus sparse grids: refined complexity estimates. Zbl 1496.65020 Griebel, Michael; Harbrecht, Helmut 7 2019 Frames for the solution of operator equations in Hilbert spaces with fixed dual pairing. Zbl 1426.46005 Balazs, Peter; Harbrecht, Helmut 5 2019 Incorporating knowledge on the measurement noise in electrical impedance tomography. Zbl 1437.78003 Dambrine, Marc; Harbrecht, Helmut; Puig, Benedicte 5 2019 A new method for the data completion problem and application to obstacle detection. Zbl 1423.35438 Caubet, Fabien; Dambrine, Marc; Harbrecht, Helmut 2 2019 Rapid computation of far-field statistics for random obstacle scattering. Zbl 1464.76089 Harbrecht, Helmut; Ilić, Nikola; Multerer, Michael D. 2 2019 Wavelet boundary element methods: adaptivity and goal-oriented error estimation. Zbl 1431.65243 Harbrecht, Helmut; Moor, Manuela 1 2019 Error-controlled model approximation for Gaussian process morphable models. Zbl 1443.65030 Dölz, Jürgen; Gerig, Thomas; Lüthi, Marcel; Harbrecht, Helmut; Vetter, Thomas 1 2019 On the algebraic construction of sparse multilevel approximations of elliptic tensor product problems. Zbl 1417.65204 Harbrecht, Helmut; Zaspel, Peter 1 2019 On the best approximation of the hierarchical matrix product. Zbl 07011413 Dölz, Jürgen; Harbrecht, Helmut; Multerer, Michael D. 1 2019 A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems. Zbl 1439.65208 Dölz, Jürgen; Harbrecht, Helmut; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix 26 2018 Novel results for the anisotropic sparse grid quadrature. Zbl 1458.65021 Haji-Ali, A.-L.; Harbrecht, H.; Peters, M. D.; Siebenmorgen, M. 15 2018 The second order perturbation approach for elliptic partial differential equations on random domains. Zbl 1379.65003 Harbrecht, Helmut; Peters, Michael D. 7 2018 Adaptive wavelet BEM for boundary integral equations: theory and numerical experiments. Zbl 1388.31008 Dahlke, S.; Harbrecht, H.; Utzinger, M.; Weimar, Markus 5 2018 A fast sparse grid based space-time boundary element method for the nonstationary heat equation. Zbl 1403.65059 Harbrecht, Helmut; Tausch, Johannes 5 2018 Mathematical analysis of the transmission dynamics of the liver fluke, Opisthorchis viverrini. Zbl 1397.92619 Bürli, Christine; Harbrecht, Helmut; Odermatt, Peter; Sayasone, Somphou; Chitnis, Nakul 4 2018 Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains. Zbl 1415.65267 Dölz, Jürgen; Harbrecht, Helmut 3 2018 Solving a free boundary problem with nonconstant coefficients. Zbl 1397.35082 Brügger, Rahel; Croce, Roberto; Harbrecht, Helmut 1 2018 Analysis of interventions against the liver fluke, Opisthorchis viverrini. Zbl 1405.92249 Bürli, Christine; Harbrecht, Helmut; Odermatt, Peter; Sayasone, Somphou; Chitnis, Nakul 1 2018 Covariance regularity and \(\mathcal {H}\)-matrix approximation for rough random fields. Zbl 1362.65124 Dölz, J.; Harbrecht, H.; Schwab, Ch. 16 2017 On the quasi-Monte Carlo method with halton points for elliptic PDEs with log-normal diffusion. Zbl 1355.65010 Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus 10 2017 Uncertainty quantification for PDEs with anisotropic random diffusion. Zbl 1432.35265 Harbrecht, H.; Peters, M. D.; Schmidlin, M. 5 2017 Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness. Zbl 1380.65409 Dambrine, M.; Greff, I.; Harbrecht, H.; Puig, B. 4 2017 \(\mathcal{H}\)-matrix based second moment analysis for rough random fields and finite element discretizations. Zbl 1368.60070 Dölz, J.; Harbrecht, H.; Peters, M. D. 4 2017 Solution of free boundary problems in the presence of geometric uncertainties. Zbl 1380.49022 Harbrecht, H.; Peters, M. D. 2 2017 On Bernoulli’s free boundary problem with a random boundary. Zbl 1498.35366 Dambrine, M.; Harbrecht, H.; Peters, M. D.; Puig, B. 2 2017 Analysis of the domain mapping method for elliptic diffusion problems on random domains. Zbl 1479.35969 Harbrecht, H.; Peters, M.; Siebenmorgen, M. 47 2016 Multilevel accelerated quadrature for PDEs with log-normally distributed diffusion coefficient. Zbl 1343.65006 Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus 19 2016 Numerical solution of the Poisson equation on domains with a thin layer of random thickness. Zbl 1382.65457 Dambrine, Marc; Greff, Isabelle; Harbrecht, Helmut; Puig, Benedicte 7 2016 Optimization of current carrying multicables. Zbl 1333.49062 Harbrecht, Helmut; Loos, Florian 2 2016 Combination technique based second moment analysis for elliptic PDEs on random domains. Zbl 1339.65015 Harbrecht, Helmut; Peters, Michael 2 2016 A note on multilevel based error estimation. Zbl 1342.65206 Harbrecht, Helmut; Schneider, Reinhold 1 2016 Efficient approximation of random fields for numerical applications. Zbl 1349.65048 Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus 31 2015 Shape optimization for quadratic functionals and states with random right-hand sides. Zbl 1326.49070 Dambrine, Marc; Dapogny, Charles; Harbrecht, Helmut 13 2015 Computing quantities of interest for random domains with second order shape sensitivity analysis. Zbl 1351.60062 Dambrine, Marc; Harbrecht, Helmut; Puig, Bénédicte 12 2015 \(\mathcal H\)-matrix accelerated second moment analysis for potentials with rough correlation. Zbl 1329.65013 Dölz, J.; Harbrecht, H.; Peters, M. 7 2015 Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data. Zbl 1331.65165 Harbrecht, Helmut; Mitrou, Giannoula 3 2015 A second order convergent trial method for a free boundary problem in three dimensions. Zbl 1331.65170 Bugeanu, Monica; Harbrecht, Helmut 2 2015 Approximation of bi-variate functions: Singular value decomposition versus sparse grids. Zbl 1287.65009 Griebel, Michael; Harbrecht, Helmut 20 2014 On the convergence of the combination technique. Zbl 1316.65054 Griebel, Michael; Harbrecht, Helmut 14 2014 Riesz minimal energy problems on \(C^{k-1,1}\)-manifolds. Zbl 1288.31005 Harbrecht, Helmut; Wendland, Wolfgang L.; Zorii, Natalia 11 2014 Improved trial methods for a class of generalized Bernoulli problems. Zbl 1292.35341 Harbrecht, Helmut; Mitrou, Giannoula 9 2014 Trends in PDE constrained optimization. Zbl 1306.49001 9 2014 Second moment analysis for Robin boundary value problems on random domains. Zbl 1326.35370 Harbrecht, Helmut 3 2014 The \(\mathcal H^2\)-wavelet method. Zbl 1293.65162 Alm, Daniel; Harbrecht, Helmut; Krämer, Ulf 2 2014 On shape optimization with parabolic state equation. Zbl 1320.49028 Harbrecht, Helmut; Tausch, Johannes 1 2014 BPX-preconditioning for isogeometric analysis. Zbl 1286.65151 Buffa, Annalisa; Harbrecht, Helmut; Kunoth, Angela; Sangalli, Giancarlo 36 2013 First order second moment analysis for stochastic interface problems based on low-rank approximation. Zbl 1297.65009 Harbrecht, Helmut; Li, Jingzhi 25 2013 On the construction of sparse tensor product spaces. Zbl 1267.41012 Griebel, Michael; Harbrecht, Helmut 25 2013 On the numerical solution of a shape optimization problem for the heat equation. Zbl 1264.65156 Harbrecht, Helmut; Tausch, Johannes 20 2013 Combination technique based \(k\)-th moment analysis of elliptic problems with random diffusion. Zbl 1349.35441 Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus 17 2013 Comparison of fast boundary element methods on parametric surfaces. Zbl 1286.65175 Harbrecht, H.; Peters, M. 15 2013 A note on the construction of \(L\)-fold sparse tensor product spaces. Zbl 1283.41015 Griebel, Michael; Harbrecht, Helmut 13 2013 On the low-rank approximation by the pivoted Cholesky decomposition. Zbl 1244.65042 Harbrecht, Helmut; Peters, Michael; Schneider, Reinhold 54 2012 On a Kohn-Vogelius like formulation of free boundary problems. Zbl 1258.49069 Eppler, Karsten; Harbrecht, Helmut 17 2012 Shape optimization for free boundary problems - analysis and numerics. Zbl 1356.49073 Eppler, Karsten; Harbrecht, Helmut 13 2012 On Riesz minimal energy problems. Zbl 1244.49058 Harbrecht, H.; Wendland, W. L.; Zorii, N. 8 2012 Preconditioning of wavelet BEM by the incomplete Cholesky factorization. Zbl 1360.65292 Harbrecht, Helmut 1 2012 An efficient numerical method for a shape-identification problem arising from the heat equation. Zbl 1219.65132 Harbrecht, Helmut; Tausch, Johannes 13 2011 Sparse tensor finite elements for elliptic multiple scale problems. Zbl 1230.65127 Harbrecht, Helmut; Schwab, Christoph 7 2011 Wavelet BEM on molecular surfaces: solvent excluded surfaces. Zbl 1225.92065 Harbrecht, H.; Randrianarivony, M. 5 2011 On analytical derivatives for geometry optimization in the polarizable continuum model. Zbl 1304.82073 Harbrecht, Helmut 1 2011 Tracking Neumann data for stationary free boundary problems. Zbl 1202.49052 Eppler, Karsten; Harbrecht, Helmut 17 2010 A finite element method for elliptic problems with stochastic input data. Zbl 1237.65009 Harbrecht, Helmut 13 2010 From computer aided design to wavelet BEM. Zbl 1213.65146 Harbrecht, H.; Randrianarivony, M. 13 2010 On output functionals of boundary value problems on stochastic domains. Zbl 1181.35354 Harbrecht, Helmut 11 2010 Tracking Dirichlet data in \(L^2\) is an ill-posed problem. Zbl 1217.49031 Eppler, K.; Harbrecht, H. 9 2010 Finite element based second moment analysis for elliptic problems in stochastic domains. Zbl 1216.65008 Harbrecht, H. 1 2010 Wavelet BEM on molecular surfaces: parametrization and implementation. Zbl 1241.65108 Harbrecht, Helmut; Randrianarivony, Maharavo 5 2009 A Newton method for reconstructing non star-shaped domains in electrical impedance tomography. Zbl 1189.65113 Harbrecht, Helmut; Hohage, Thorsten 3 2009 Rapid solution of boundary integral equations by wavelet Galerkin schemes. Zbl 1190.65179 Harbrecht, Helmut; Schneider, Reinhold 1 2009 On the numerical solution of Plateau’s problem. Zbl 1178.65069 Harbrecht, Helmut 1 2009 Sparse second moment analysis for elliptic problems in stochastic domains. Zbl 1146.65007 Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph 55 2008 Multilevel frames for sparse tensor product spaces. Zbl 1151.65010 Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph 29 2008 Analytical and numerical methods in shape optimization. Zbl 1153.49039 Harbrecht, Helmut 11 2008 A Newton method for Bernoulli’s free boundary problem in three dimensions. Zbl 1152.49044 Harbrecht, Helmut 11 2008 A new fictitious domain method in shape optimization. Zbl 1152.49043 Eppler, Karsten; Harbrecht, Helmut; Mommer, Mario S. 5 2008 Wavelet-based boundary element methods for exterior electromagnetic shaping. Zbl 1244.78022 Eppler, K.; Harbrecht, H. 2 2008 Compact gradient tracking in shape optimization. Zbl 1181.90286 Eppler, Karsten; Harbrecht, Helmut 2 2008 An optimal adaptive wavelet method without coarsening of the iterands. Zbl 1115.41023 Gantumur, Tsogtgerel; Harbrecht, Helmut; Stevenson, Rob 46 2007 On convergence in elliptic shape optimization. Zbl 1354.49093 Eppler, Karsten; Harbrecht, Helmut; Schneider, Reinhold 36 2007 Adaptive methods for boundary integral equations: complexity and convergence estimates. Zbl 1129.65090 Dahmen, Wolfgang; Harbrecht, Helmut; Schneider, Reinhold 23 2007 Fast methods for three-dimensional inverse obstacle scattering problems. Zbl 1138.65100 Harbrecht, Helmut; Hohage, Thorsten 22 2007 Shape optimization for 3D electrical impedance tomography. Zbl 1403.49042 Eppler, Karsten; Harbrech, Helmut 2 2007 Compression techniques for boundary integral equations. Asymptotically optimal complexity estimates. Zbl 1113.65114 Dahmen, Wolfgang; Harbrecht, Helmut; Schneider, Reinhold 84 2006 ...and 17 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 936 Authors 92 Harbrecht, Helmut 38 Schwab, Christoph 26 Multerer, Michael D. 19 Stevenson, Rob P. 18 Griebel, Michael 14 Schneider, Reinhold 13 Dölz, Jürgen 13 Zorii, Natalia 12 Eppler, Karsten 11 Nobile, Fabio 11 Tausch, Johannes 10 Dambrine, Marc 10 Xiao, Jinyou 9 Tempone, Raúl F. 8 Kress, Rainer 8 Kuo, Frances Y. 8 Praetorius, Dirk 8 Schulz, Volker H. 8 Sloan, Ian Hugh 7 Hofreither, Clemens 7 Kressner, Daniel 7 Li, Junpu 7 Rabago, Julius Fergy Tiongson 7 Scacchi, Simone 6 Bachmayr, Markus 6 Balazs, Peter 6 Chernov, Alexey 6 Cho, Durkbin 6 Dahlke, Stephan 6 Dehghan Takht Fooladi, Mehdi 6 Hiptmair, Ralf 6 Pavarino, Luca Franco 6 Scheichl, Robert 6 Siebenborn, Martin 6 Siebenmorgen, Markus 6 Urban, Karsten 6 Wen, Lihua 6 Zech, Jakob 5 Assari, Pouria 5 Chen, Zhongying 5 Dahmen, Wolfgang A. 5 Dinh Dũng 5 Eigel, Martin 5 Fu, Zhuojia 5 Führer, Thomas 5 Gantner, Gregor 5 Gantumur, Tsogtgerel 5 Haji-Ali, Abdul-Lateef 5 Jerez-Hanckes, Carlos 5 Kunoth, Angela 5 Kurz, Stefan 5 Manni, Carla 5 Melenk, Jens Markus 5 Nochetto, Ricardo Horacio 5 Puig, Bénédicte 5 Qin, Qinghua 5 Randrianarivony, Maharavo 5 Rozza, Gianluigi 5 Sangalli, Giancarlo 5 Schmidt, Stephan 5 Speleers, Hendrik 5 Strazzullo, Maria 5 Tamellini, Lorenzo 5 Weimar, Markus 5 Wendland, Wolfgang L. 5 Zapletal, Jan 5 Zhu, Shengfeng 4 Antes, M. Y. 4 Bacani, Jerico B. 4 Ballarin, Francesco 4 Brügger, Rahel 4 Castrillon-Candas, Julio Enrique 4 Chen, Wen 4 Cohen, Albert 4 Dardé, Jérémi 4 Feischl, Michael 4 Fuglede, Bent 4 Garoni, Carlo 4 Gittelson, Claude Jeffrey 4 Hettlich, Frank 4 Hrizi, Mourad 4 Karinski, Yuri S. 4 Kestler, Sebastian 4 Le Louër, Frédérique 4 Merta, Michal 4 Nuyens, Dirk 4 Paganini, Alberto 4 Peichl, Gunther H. 4 Ravnik, Jure 4 Schmidlin, Marc 4 Serra-Capizzano, Stefano 4 Stephan, Ernst Peter 4 Vainikko, Gennadi 4 Welker, Kathrin 4 Yankelevsky, David Z. 4 Zeiser, Andreas 4 Zhang, Duo 4 Zhu, Jialin 4 Zulehner, Walter 3 Ali, Mazen ...and 836 more Authors all top 5 Cited in 146 Serials 52 Computer Methods in Applied Mechanics and Engineering 35 Numerische Mathematik 28 SIAM Journal on Scientific Computing 27 Journal of Computational Physics 25 Journal of Computational and Applied Mathematics 23 Engineering Analysis with Boundary Elements 23 SIAM/ASA Journal on Uncertainty Quantification 22 Computers & Mathematics with Applications 22 Mathematics of Computation 18 Journal of Scientific Computing 17 Advances in Computational Mathematics 16 Applied Numerical Mathematics 15 SIAM Journal on Numerical Analysis 14 Inverse Problems 14 Foundations of Computational Mathematics 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 9 Applied Mathematics and Computation 9 Computational Methods in Applied Mathematics 7 Mathematical Methods in the Applied Sciences 7 SIAM Journal on Control and Optimization 7 Journal of Integral Equations and Applications 7 M\(^3\)AS. 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Neuvième Série 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis ...and 46 more Serials all top 5 Cited in 40 Fields 523 Numerical analysis (65-XX) 272 Partial differential equations (35-XX) 121 Calculus of variations and optimal control; optimization (49-XX) 90 Probability theory and stochastic processes (60-XX) 63 Mechanics of deformable solids (74-XX) 63 Fluid mechanics (76-XX) 48 Approximations and expansions (41-XX) 36 Optics, electromagnetic theory (78-XX) 34 Operator theory (47-XX) 32 Harmonic analysis on Euclidean spaces (42-XX) 30 Integral equations (45-XX) 27 Linear and multilinear algebra; matrix theory (15-XX) 25 Statistics (62-XX) 21 Computer science (68-XX) 20 Potential theory (31-XX) 20 Functional analysis (46-XX) 18 Biology and other natural sciences (92-XX) 11 Operations research, mathematical programming (90-XX) 10 Classical thermodynamics, heat transfer (80-XX) 9 Systems theory; control (93-XX) 9 Information and communication theory, circuits (94-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 General and overarching topics; collections (00-XX) 5 Real functions (26-XX) 5 Statistical mechanics, structure of matter (82-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Ordinary differential equations (34-XX) 3 Manifolds and cell complexes (57-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Measure and integration (28-XX) 2 Differential geometry (53-XX) 2 Quantum theory (81-XX) 2 Geophysics (86-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year