5 papers · 1 filter
Nemytskii neural operator: a nonlinear model reduction method for parametrized partial differential equations
Jingye Li, Alex Bespalov, Jinglai Li
We introduce a Nemytskii neural operator framework for nonlinear model reduction of parametrized steady-state partial differential equations. The method generalizes reduced basis a…
An adaptive multimesh rational approximation scheme for the spectral fractional Laplacian
Alex Bespalov, Raphaël Bulle
We propose a novel multimesh rational approximation scheme for the numerical solution of the (homogeneous) Dirichlet problem for the spectral fractional Laplacian. The scheme combi…
Goal-Oriented Error Estimation and Adaptivity for Stochastic Collocation FEM
Alex Bespalov, Dirk Praetorius, Thomas Round +1
We propose and analyze a general goal-oriented adaptive strategy for approximating quantities of interest (QoIs) associated with solutions to linear elliptic partial differential e…
Convergence analysis of the adaptive stochastic collocation finite element method
Alex Bespalov, Andrey Savinov
This paper is focused on the convergence analysis of an adaptive stochastic collocation algorithm for the stationary diffusion equation with parametric coefficient. The algorithm e…
Efficient adaptive multilevel stochastic Galerkin approximation using implicit a posteriori error estimation
Adam J. Crowder, Catherine E. Powell, Alex Bespalov
Partial differential equations (PDEs) with inputs that depend on infinitely many parameters pose serious theoretical and computational challenges. Sophisticated numerical algorithm…