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Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs
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On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion
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The uniform sparse FFT with application to PDEs with random coefficients
Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances
Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen and Robert Scheichl SIAM Journal on Numerical Analysis 58(5) 2953 (2020) https://doi.org/10.1137/19M1269877
Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients
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
A mixed ℓ1 regularization approach for sparse simultaneous approximation of parameterized PDEs
Nick Dexter, Hoang Tran and Clayton Webster ESAIM: Mathematical Modelling and Numerical Analysis 53(6) 2025 (2019) https://doi.org/10.1051/m2an/2019048
QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights
Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan
Albert Cohen and Giovanni Migliorati Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan 233 (2018) https://doi.org/10.1007/978-3-319-72456-0_12
Linear Reconstructions and the Analysis of the Stable Sampling Rate
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
Monte Carlo and Quasi-Monte Carlo Methods
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
Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)
Oliver G. Ernst, Björn Sprungk and Lorenzo Tamellini SIAM Journal on Numerical Analysis 56(2) 877 (2018) https://doi.org/10.1137/17M1123079
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
Sparse quadrature for high-dimensional integration with Gaussian measure
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
Sparse polynomial approximation of parametric elliptic PDEs.
Part I: affine coefficients
Markus Bachmayr, Albert Cohen and Giovanni Migliorati ESAIM: Mathematical Modelling and Numerical Analysis 51(1) 321 (2017) https://doi.org/10.1051/m2an/2016045