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math.NA2026
RUNNs: Ritz-Uzawa Neural Networks for Solving Variational Problems
Pablo Herrera, Jamie M. Taylor, Carlos Uriarte +3
Solving Partial Differential Equations (PDEs) using neural networks presents different challenges, including integration errors and spectral bias, often leading to poor approximati…
math.NA2024
A Shape-Newton Method for Free-boundary Problems Subject to The Bernoulli Boundary Condition
Yiyun Fan, John Billingham, Kristoffer van der Zee
We develop a shape-Newton method for solving generic free-boundary problems where one of the free-boundary conditions is governed by the Bernoulli equation. The Newton-like scheme…