A Modulus-Squared Dirichlet Boundary Condition for Time-Dependent Complex Partial Differential Equations and its Application to the Nonlinear Schrödinger Equation
Provides a practical boundary condition for simulations of complex PDEs, but the improvement is incremental for a specific class of problems.
The paper introduces a modulus-squared Dirichlet (MSD) boundary condition for time-dependent complex PDEs, demonstrating its application to the nonlinear Schrödinger equation. Numerical simulations show it outperforms other simple boundary conditions.
An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a constant modulus-square value of the solution at the boundaries. Application of the MSD boundary condition to the nonlinear Schrödinger equation is shown, and numerical simulations are performed to demonstrate its usefulness and advantages over other simple boundary conditions.