6 citations · 10 across the 4 of their papers we have counts for
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Error analysis of a pressure correction method with explicit time stepping
Utku Kaya, Thomas Richter
The pressure-correction method is a well established approach for simulating unsteady, incompressible fluids. It is well-known that implicit discretization of the time derivative i…
An adaptive finite element multigrid solver using GPU acceleration
Manuel Liebchen, Robert Jendersie, Utku Kaya +2
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Ye…
Error analysis for hybrid finite element/neural network discretizations
Uladzislau Kapustsin, Utku Kaya, Johannes Pfefferer +1
We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine sca…
A hybrid finite element/neural network solver and its application to the Poisson problem
Uladzislau Kapustsin, Utku Kaya, Thomas Richter
We analyze a hybrid method that enriches coarse grid finite element solutions with fine scale fluctuations obtained from a neural network. The idea stems from the Deep Neural Netwo…