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Exploiting locality in sparse polynomial approximation of parametric elliptic PDEs and application to parameterized domains
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Analyticity of parametric elliptic eigenvalue problems and applications to quasi-Monte Carlo methods
Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs
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Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\)
On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion
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Goal-oriented adaptive finite element multilevel Monte Carlo with convergence rates
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MDFEM: Multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM
Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances
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Robert Calderbank, Anders Hansen, Bogdan Roman and Laura Thesing Applied and Numerical Harmonic Analysis, Compressed Sensing and Its Applications 97 (2019) https://doi.org/10.1007/978-3-319-73074-5_3
Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)
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Sparse quadrature for high-dimensional integration with Gaussian measure
Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan
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Recent Advances in Computational Engineering
Christopher Müller, Sebastian Ullmann and Jens Lang Lecture Notes in Computational Science and Engineering, Recent Advances in Computational Engineering 124 63 (2018) https://doi.org/10.1007/978-3-319-93891-2_5
Representations of Gaussian Random Fields and Approximation of Elliptic PDEs with Lognormal Coefficients
Lukas Herrmann and Christoph Schwab Springer Proceedings in Mathematics & Statistics, Monte Carlo and Quasi-Monte Carlo Methods 241 313 (2018) https://doi.org/10.1007/978-3-319-91436-7_17
Uncertainty Quantification for Low-Frequency, Time-Harmonic Maxwell Equations with Stochastic Conductivity Models
Dimitris Kamilis and Nick Polydorides SIAM/ASA Journal on Uncertainty Quantification 6(4) 1295 (2018) https://doi.org/10.1137/17M1156010
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Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs
Markus Bachmayr, Albert Cohen, Dinh Du͂ng and Christoph Schwab SIAM Journal on Numerical Analysis 55(5) 2151 (2017) https://doi.org/10.1137/17M111626X
Stable splittings of Hilbert spaces of functions of infinitely many variables