Christoph Schwab

Affiliations:
  • ETH Zurich, Switzerland


According to our database1, Christoph Schwab authored at least 147 papers between 1992 and 2024.

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

Timeline

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Bibliography

2024
Exponential Expressivity of ReLU<sup>k</sup> Neural Networks on Gevrey Classes with Point Singularities.
CoRR, 2024

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

Neural Networks for Singular Perturbations.
CoRR, 2024

2023
Exponential Convergence of \(hp\)-FEM for the Integral Fractional Laplacian in Polygons.
SIAM J. Numer. Anal., December, 2023

De Rham compatible Deep Neural Network FEM.
Neural Networks, August, 2023

Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations.
SIAM J. Numer. Anal., June, 2023

Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities.
Found. Comput. Math., June, 2023

ReLU Neural Network Galerkin BEM.
J. Sci. Comput., May, 2023

Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\).
SIAM/ASA J. Uncertain. Quantification, March, 2023

Exponential convergence of hp FEM for spectral fractional diffusion in polygons.
Numerische Mathematik, 2023

Deep ReLU networks and high-order finite element methods II: Chebyshev emulation.
CoRR, 2023

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

Weighted analytic regularity for the integral fractional Laplacian in polyhedra.
CoRR, 2023

Deep Operator Network Approximation Rates for Lipschitz Operators.
CoRR, 2023

Multilevel Monte Carlo FEM for Elliptic PDEs with Besov Random Tree Priors.
CoRR, 2023

A-posteriori QMC-FEM error estimation for Bayesian inversion and optimal control with entropic risk measure.
CoRR, 2023

2022
Quantized Tensor FEM for Multiscale Problems: Diffusion Problems in Two and Three Dimensions.
Multiscale Model. Simul., September, 2022

Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification.
SIAM/ASA J. Uncertain. Quantification, 2022

Constructive Deep ReLU Neural Network Approximation.
J. Sci. Comput., 2022

Multilevel Domain Uncertainty Quantification in Computational Electromagnetics.
CoRR, 2022

Monte Carlo convergence rates for kth moments in Banach spaces.
CoRR, 2022

Multiresolution kernel matrix algebra.
CoRR, 2022

Neural and gpc operator surrogates: construction and expression rate bounds.
CoRR, 2022

Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D.
CoRR, 2022

Exponential Convergence of hp-Time-Stepping in Space-Time Discretizations of Parabolic PDEs.
CoRR, 2022

De Rham compatible Deep Neural Networks.
CoRR, 2022

Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs.
CoRR, 2022

Tensor rank bounds for point singularities in ℝ<sup>3</sup>.
Adv. Comput. Math., 2022

2021
Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks.
SIAM J. Sci. Comput., 2021

DeepCME: A deep learning framework for computing solution statistics of the chemical master equation.
PLoS Comput. Biol., 2021

Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems.
Math. Comput., 2021

Multilevel Markov Chain Monte Carlo for Bayesian Inversion of Parabolic Partial Differential Equations under Gaussian Prior.
SIAM/ASA J. Uncertain. Quantification, 2021

Weighted analytic regularity for the integral fractional Laplacian in polygons.
CoRR, 2021

Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in L<sup>2</sup>(R<sup>d</sup>, γ<sub>d</sub>).
CoRR, 2021

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

Deep ReLU Neural Network Approximation for Stochastic Differential Equations with Jumps.
CoRR, 2021

Deep ReLU Network Expression Rates for Option Prices in high-dimensional, exponential Lévy models.
CoRR, 2021

2020
Analytic Regularity for the Incompressible Navier-Stokes Equations in Polygons.
SIAM J. Math. Anal., 2020

Exponential convergence in \(H^1\) of <i>hp</i>-FEM for Gevrey regularity with isotropic singularities.
Numerische Mathematik, 2020

Domain Uncertainty Quantification in Computational Electromagnetics.
SIAM/ASA J. Uncertain. Quantification, 2020

hp-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains.
CoRR, 2020

Space-time discontinuous Galerkin approximation of acoustic waves with point singularities.
CoRR, 2020

2019
Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification.
SIAM J. Numer. Anal., 2019

QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights.
Numerische Mathematik, 2019

Uncertainty Quantification for Spectral Fractional Diffusion: Sparsity Analysis of Parametric Solutions.
SIAM/ASA J. Uncertain. Quantification, 2019

Tensor FEM for Spectral Fractional Diffusion.
Found. Comput. Math., 2019

Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion.
Comput. Math. Appl., 2019

2018
Quasi-Monte Carlo Integration for Affine-Parametric, Elliptic PDEs: Local Supports and Product Weights.
SIAM J. Numer. Anal., 2018

Shape Holomorphy of the Stationary Navier-Stokes Equations.
SIAM J. Math. Anal., 2018

Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions.
Numerische Mathematik, 2018

Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons.
J. Sci. Comput., 2018

Adaptive anisotropic Petrov-Galerkin methods for first order transport equations.
J. Comput. Appl. Math., 2018

Exponential Convergence of hp-FEM for Elliptic Problems in Polyhedra: Mixed Boundary Conditions and Anisotropic Polynomial Degrees.
Found. Comput. Math., 2018

Large deformation shape uncertainty quantification in acoustic scattering.
Adv. Comput. Math., 2018

2017
Symmetric Interior Penalty Discontinuous Galerkin Methods for Elliptic Problems in Polygons.
SIAM J. Numer. Anal., 2017

Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs.
SIAM J. Numer. Anal., 2017

Fractional Space-Time Variational Formulations of (Navier-) Stokes Equations.
SIAM J. Math. Anal., 2017

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

Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations.
Math. Comput., 2017

Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems.
Math. Comput., 2017

QTT-finite-element approximation for multiscale problems I: model problems in one dimension.
Adv. Comput. Math., 2017

2016
Multilevel Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations.
SIAM J. Numer. Anal., 2016

hp-dGFEM for second-order mixed elliptic problems in polyhedra.
Math. Comput., 2016

Numerical Solution of Scalar Conservation Laws with Random Flux Functions.
SIAM/ASA J. Uncertain. Quantification, 2016

Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems.
SIAM/ASA J. Uncertain. Quantification, 2016

Higher Order Quasi-Monte Carlo Integration for Holomorphic, Parametric Operator Equations.
SIAM/ASA J. Uncertain. Quantification, 2016

Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium.
J. Comput. Phys., 2016

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations.
J. Comput. Phys., 2016

2015
Fast QMC Matrix-Vector Multiplication.
SIAM J. Sci. Comput., 2015

Tensor Approximation of Stationary Distributions of Chemical Reaction Networks.
SIAM J. Matrix Anal. Appl., 2015

Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks.
PLoS Comput. Biol., 2015

Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients.
Numerische Mathematik, 2015

Quadrature algorithms for high dimensional singular integrands on simplices.
Numer. Algorithms, 2015

Intrinsic fault tolerance of multilevel Monte Carlo methods.
J. Parallel Distributed Comput., 2015

Finite Elements with mesh refinement for wave equations in polygons.
J. Comput. Appl. Math., 2015

Multi-level Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic PDEs with Random Coefficients.
Found. Comput. Math., 2015

2014
Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities.
SIAM J. Numer. Anal., 2014

Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs.
SIAM J. Numer. Anal., 2014

Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains.
PLoS Comput. Biol., 2014

Optimality of adaptive Galerkin methods for random parabolic partial differential equations.
J. Comput. Appl. Math., 2014

High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs.
Found. Comput. Math., 2014

High-order finite element approximation for partial differential equations.
Comput. Math. Appl., 2014

Computational Higher Order Quasi-Monte Carlo Integration.
Proceedings of the Monte Carlo and Quasi-Monte Carlo Methods, 2014

Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier-Stokes Equations.
Proceedings of the Monte Carlo and Quasi-Monte Carlo Methods, 2014

2013
Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws.
Proceedings of the Uncertainty Quantification in Computational Fluid Dynamics, 2013

hp-DGFEM for Second Order Elliptic Problems in Polyhedra II: Exponential Convergence.
SIAM J. Numer. Anal., 2013

hp-dGFEM for Second-Order Elliptic Problems in Polyhedra I: Stability on Geometric Meshes.
SIAM J. Numer. Anal., 2013

Sparse Tensor Galerkin Discretization of Parametric and Random Parabolic PDEs - Analytic Regularity and Generalized Polynomial Chaos Approximation.
SIAM J. Math. Anal., 2013

Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs.
SIAM J. Control. Optim., 2013

The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem.
Numerische Mathematik, 2013

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data.
Math. Comput., 2013

Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs.
Multiscale Model. Simul., 2013

2012
Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions.
SIAM J. Sci. Comput., 2012

Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients.
SIAM J. Numer. Anal., 2012

Adaptive Petrov-Galerkin Methods for First Order Transport Equations.
SIAM J. Numer. Anal., 2012

Exponential Convergence of Gauss-Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension.
SIAM J. Numer. Anal., 2012

Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data.
Math. Comput., 2012

Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions.
J. Comput. Phys., 2012

Sparse Approximation Algorithms for High Dimensional Parametric Initial Value Problems.
Proceedings of the Modeling, Simulation and Optimization of Complex Processes, 2012

2011
Combining and extending concepts of single display groupware and tangible user interfaces for intuitive collaboration.
PhD thesis, 2011

Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs.
SIAM J. Sci. Comput., 2011

Fast evaluation of nonlinear functionals of tensor product wavelet expansions.
Numerische Mathematik, 2011

Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients.
Numerische Mathematik, 2011

Sparse tensor spherical harmonics approximation in radiative transfer.
J. Comput. Phys., 2011

A multiscale hp-FEM for 2D photonic crystal bands.
J. Comput. Phys., 2011

Sparse Discrete Ordinates Method in Radiative Transfer.
Comput. Methods Appl. Math., 2011

Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs.
Acta Numer., 2011

Static Load Balancing for Multi-level Monte Carlo Finite Volume Solvers.
Proceedings of the Parallel Processing and Applied Mathematics, 2011

2010
On Kolmogorov equations for anisotropic multivariate Lévy processes.
Finance Stochastics, 2010

Convergence Rates of Best <i>N</i>-term Galerkin Approximations for a Class of Elliptic sPDEs.
Found. Comput. Math., 2010

2009
Sparse Tensor Discretization of Elliptic sPDEs.
SIAM J. Sci. Comput., 2009

Space-time adaptive wavelet methods for parabolic evolution problems.
Math. Comput., 2009

Numerical methods for Lévy processes.
Finance Stochastics, 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

Adaptive wavelet algorithms for elliptic PDE's on product domains.
Math. Comput., 2008

Sparse adaptive finite elements for radiative transfer.
J. Comput. Phys., 2008

2006
Wavelet Filtering for Exact Controllability of the Wave Equation.
SIAM J. Sci. Comput., 2006

Linear Complexity Solution of Parabolic Integro-differential Equations.
Numerische Mathematik, 2006

Karhunen-Loève approximation of random fields by generalized fast multipole methods.
J. Comput. Phys., 2006

2005
Fast Numerical Solution of Parabolic Integrodifferential Equations with Applications in Finance.
SIAM J. Sci. Comput., 2005

Multiresolution weighted norm equivalences and applications.
Numerische Mathematik, 2005

High-Dimensional Finite Elements for Elliptic Problems with Multiple Scales.
Multiscale Model. Simul., 2005

Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces.
Multiscale Model. Simul., 2005

2003
Wavelet Discretizations of Parabolic Integrodifferential Equations.
SIAM J. Numer. Anal., 2003

Mixed <i>HP</i>-finite element approximations on geometric edge and boundary layer meshes in three dimensions.
Numerische Mathematik, 2003

Sparse finite elements for elliptic problems with stochastic loading.
Numerische Mathematik, 2003

Boundary Element Methods for Maxwell Transmission Problems in Lipschitz Domains.
Numerische Mathematik, 2003

On some aspects of the discontinuous Galerkin finite element method for conservation laws.
Math. Comput. Simul., 2003

Sparse Finite Elements for Stochastic Elliptic Problems - Higher Order Moments.
Computing, 2003

Higher-Order Convex Approximations of Young Measures in Optimal Control.
Adv. Comput. Math., 2003

2002
Mixed <i>hp</i>-DGFEM for Incompressible Flows.
SIAM J. Numer. Anal., 2002

Discontinuous <i>hp</i>-Finite Element Methods for Advection-Diffusion-Reaction Problems.
SIAM J. Numer. Anal., 2002

Natural Boundary Element Methods for the Electric Field Integral Equation on Polyhedra.
SIAM J. Numer. Anal., 2002

Local Discontinuous Galerkin Methods for the Stokes System.
SIAM J. Numer. Anal., 2002

Boundary element methods for Maxwell's equations on non-smooth domains.
Numerische Mathematik, 2002

Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems.
Math. Comput., 2002

2000
Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method.
SIAM J. Numer. Anal., 2000

Stabilized <i>hp</i>-Finite Element Methods for First-Order Hyperbolic Problems.
SIAM J. Numer. Anal., 2000

Generalized p-FEM in homogenization.
Numerische Mathematik, 2000

Spectral Galerkin Discretization for Hydrodynamic Stability Problems.
Computing, 2000

1999
Wavelet Galerkin Algorithms for Boundary Integral Equations.
SIAM J. Sci. Comput., 1999

Mixed hp-FEM on anisotropic meshes II: Hanging nodes and tensor products of boundary layer meshes.
Numerische Mathematik, 1999

On the extraction technique in boundary integral equations.
Math. Comput., 1999

1996
The p and hp versions of the finite element method for problems with boundary layers.
Math. Comput., 1996

1994
Variable order composite quadrature of singular and nearly singular integrals.
Computing, 1994

1992
Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation.
Computing, 1992


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