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math.NA2023
On the nature of the boundary resonance error in numerical homogenization and its reduction
Sean P. Carney, Milica Dussinger, Bjorn Engquist
Numerical homogenization of multiscale equations typically requires taking an average of the solution to a microscale problem. Both the boundary conditions and domain size of the m…
math.NA2022
Physics informed neural networks for elliptic equations with oscillatory differential operators
Arnav Gangal, Luis Kim, Sean P. Carney
Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several auth…