A hierarchical direct solver for QBX-discretized boundary integral equations using HSS matrices, proxy-based far-field approximations, and ID compression with an error model for automatic parameter selection.
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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.
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A Fast Direct Solver for Boundary Integral Equations Using Quadrature By Expansion
A hierarchical direct solver for QBX-discretized boundary integral equations using HSS matrices, proxy-based far-field approximations, and ID compression with an error model for automatic parameter selection.
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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.