A bootstrap method for sum-of-poles approximations

A bootstrap method is presented for finding efficient sum-of-poles approximations of causal functions. The method is based on a recursive application of the nonlinear least squares optimization scheme developed in (Alpert et al. in SIAM J. Numer. Anal. 37:1138–1164, 2000), followed by the balanced truncation method for model reduction in computational control theory as a final optimization step. The method is expected to be useful for a fairly large class of causal functions encountered in engineering and applied physics. The performance of the method and its application to computational physics are illustrated via several numerical examples

Optimal parameter choice for the pole condition

The pole condition is a framework for the derivation of transparent boundary conditions that identifies non-physical modes by the location of the corresponding singularities in the complex plane of the solution's spatial Laplace transform. A complex half-plane is then defined that contains all poles corresponding to non-physical modes. A key parameter in the pole condition arises in the Möbius transformation that maps this half-plane onto the complex unit circle. The effect of variations in this parameter on the quality of the approximate TBC realized by the pole condition is explored here for the two-dimensional drift-diffusion equation with inhomogeneous coefficients