15 citations · 34 across the 19 of their papers we have counts for
6 papers · 1 filter
Sufficient conditions for QMC analysis of finite elements for parametric differential equations
Vesa Kaarnioja, Andreas Rupp, Jay Gopalakrishnan
Parametric regularity of discretizations of flux vector fields satisfying a balance law is studied under some assumptions on a random parameter that links the flux with an unknown…
On the optimality of dimension truncation error rates for a class of parametric partial differential equations
Philipp A. Guth, Vesa Kaarnioja
In uncertainty quantification for parametric partial differential equations (PDEs), it is common to model uncertain random field inputs using countably infinite sequences of indepe…
New upper and lower bounds on the smallest singular values of nonsingular lower triangular -matrices
Vesa Kaarnioja, André-Alexander Zepernick
Let denote the set of all nonsingular lower triangular -matrices. Hong and Loewy (2004) introduced the number sequence $$ c_n=\min\{λ\midλ~\text{is an eige…
Quasi-Monte Carlo for Bayesian shape inversion governed by the Poisson problem subject to Gevrey regular domain deformations
Ana Djurdjevac, Vesa Kaarnioja, Max Orteu +1
We consider the application of a quasi-Monte Carlo cubature rule to Bayesian shape inversion subject to the Poisson equation under Gevrey regular parameterizations of domain uncert…
Uncertainty quantification for stationary and time-dependent PDEs subject to Gevrey regular random domain deformations
Ana Djurdjevac, Vesa Kaarnioja, Claudia Schillings +1
We study uncertainty quantification for partial differential equations subject to domain uncertainty. We parameterize the random domain using the model recently considered by Chern…
Lattice Rules Meet Kernel Cubature
Vesa Kaarnioja, Ilja Klebanov, Claudia Schillings +1
Rank-1 lattice rules are a class of equally weighted quasi-Monte Carlo methods that achieve essentially linear convergence rates for functions in a reproducing kernel Hilbert space…