Infinite order-2 digital sequences over F_2 attain the optimal periodic L2-discrepancy bound of order C_d (log N)^{d/2}/N for all N except 1, improving prior order-5 constructions by reducing dimension from 5d to 2d.
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The paper provides sufficient conditions on parametric regularity for QMC error bounds in finite element discretizations of parametric PDEs with Gevrey-regular random fields, achieving faster-than-MC rates when the quantity of interest depends continuously on the solution, flux, or gradient.
MLMC and MLQMC with h- and p-refinement hierarchies achieve significant speedups over standard MC for UQ in cantilever beam problems, with MLQMC showing optimal cost scaling under certain conditions.
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Infinite sequences with optimal diaphony, periodic $L_2$-discrepancy, and beyond
Infinite order-2 digital sequences over F_2 attain the optimal periodic L2-discrepancy bound of order C_d (log N)^{d/2}/N for all N except 1, improving prior order-5 constructions by reducing dimension from 5d to 2d.
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Sufficient conditions for QMC analysis of finite elements for parametric differential equations
The paper provides sufficient conditions on parametric regularity for QMC error bounds in finite element discretizations of parametric PDEs with Gevrey-regular random fields, achieving faster-than-MC rates when the quantity of interest depends continuously on the solution, flux, or gradient.
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h- and p-refined Multilevel Monte Carlo Methods for Uncertainty Quantification in Structural Engineering
MLMC and MLQMC with h- and p-refinement hierarchies achieve significant speedups over standard MC for UQ in cantilever beam problems, with MLQMC showing optimal cost scaling under certain conditions.