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math.NA2025
Numerical reconstruction of Schrödinger equations with quadratic nonlinearities
Khaoula El Maddah, Matti Lassas, Teemu Tyni
We introduce a numerical framework for reconstructing the potential in two dimensional semilinear elliptic PDEs with power type nonlinearities from the nonlinear Dirichlet to Neuma…
math.NA2025
X-ray imaging from nonlinear waves: numerical reconstruction of a cubic nonlinearity
Suvi Anttila, Markus Harju, Teemu Tyni
We study an inverse boundary value problem for the nonlinear wave equation in dimensions. The objective is to recover an unknown potential from the associated Dir…
math.NA2023
A boundary integral equation method for the complete electrode model in electrical impedance tomography with tests on experimental data
Teemu Tyni, Adam R Stinchcombe, Spyros Alexakis
We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, whe…