@article{north_tsynkov_turkel_2022, title={High-order accurate numerical simulation of monochromatic waves in photonic crystal ring resonators with the help of a non-iterative domain decomposition}, volume={11}, ISSN={["1572-8137"]}, DOI={10.1007/s10825-022-01973-y}, journal={JOURNAL OF COMPUTATIONAL ELECTRONICS}, author={North, Evan and Tsynkov, Semyon and Turkel, Eli}, year={2022}, month={Nov} }
 @article{north_tsynkov_turkel_2022, title={Non-iterative domain decomposition for the Helmholtz equation with strong material discontinuities}, volume={173}, ISSN={["1873-5460"]}, DOI={10.1016/j.apnum.2021.10.024}, abstractNote={Many wave propagation problems involve discontinuous material properties. We propose to solve such problems by non-overlapping domain decomposition combined with the method of difference potentials (MDP). The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with projection on the boundary. The unknowns for the Calderon's equation are the Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered by applying their respective Calderon's equations to the same data at the common interface. Solutions on individual subdomains are computed concurrently using a direct solver. Our method proves to be insensitive to large jumps in the wavenumber for transmission problems, as well as interior cross-points and mixed boundary conditions, which may be a challenge to many other domain decomposition methods.}, journal={APPLIED NUMERICAL MATHEMATICS}, author={North, Evan and Tsynkov, Semyon and Turkel, Eli}, year={2022}, month={Mar}, pages={51–78} }