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Error analysis of a pressure correction method with explicit time stepping

Autor: Kaya, Utku, Richter, Thomas

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 in the momentum equation e.g. using a backward differentiation formula

Externí odkaz: http://arxiv.org/abs/2407.11159

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An adaptive finite element multigrid solver using GPU acceleration

Autor: Liebchen, Manuel, Kaya, Utku, Lessig, Christian, Richter, Thomas

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. Yet despite their efficiency, computations remain expensive and the simu

Externí odkaz: http://arxiv.org/abs/2405.05047

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Error analysis for hybrid finite element/neural network discretizations

Autor: Kapustsin, Uladzislau, Kaya, Utku, Richter, Thomas

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 scale fluctuations from neural networks in a local manner. The network is

Externí odkaz: http://arxiv.org/abs/2310.11271

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A hybrid finite element/neural network solver and its application to the Poisson problem

Autor: Kapustsin, Uladzislau, Kaya, Utku, Richter, Thomas

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 Network Multigrid Solver (DNN-MG), (Margenberg et al., J Comput Phys 460:11

Externí odkaz: http://arxiv.org/abs/2307.00947

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