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12 papers · 2 filters
Second Kind Integral Equation Formulation for the Mode Calculation of Optical Waveguides
Jun Lai, Shidong Jiang
We present a second kind integral equation (SKIE) formulation for calculating the electromagnetic modes of optical waveguides, where the unknowns are only on material interfaces. T…
Numerical simulation of wave propagation in inhomogeneous media using Generalized Plane Waves
Lise-Marie Imbert-Gerard, Peter Monk
The Trefftz Discontinuous Galerkin (TDG) method is a technique for approximating the Helmholtz equation (or other linear wave equations) using piecewise defined local solutions of…
Fast integrators for dynamical systems with several temporal scales
Yoonsang Lee, Bjorn Engquist
We propose a fast integrator to a class of dynamical systems with several temporal scales. The proposed method is developed as an extension of the variable step size Heterogeneous…
Multiscale numerical methods for passive advection-diffusion in incompressible turbulent flow fields
Yoonsang Lee, Bjorn Engquist
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with mul…
Data-driven prediction strategies for low-frequency patterns of North Pacific climate variability
Darin Comeau, Zhizhen Zhao, Dimitrios Giannakis +1
The North Pacific exhibits patterns of low-frequency variability on the intra-annual to decadal time scales, which manifest themselves in both model data and the observational reco…
A multilevel Monte Carlo method for a class of McKean-Vlasov processes
L. F. Ricketson
We generalize the multilevel Monte Carlo (MLMC) method of Giles to the simulation of systems of particles that interact via a mean field. When the number of particles is large, the…