Analytic sources using polynomial shaped particles in the LTP method

The Local Taylor Polynomial (LTP) method¹ treats fields and sources as local analytic polynomials for rapid numerical solution of PDE´s. Knowledge of the source polynomial would allow analytic treatment in LTP formulas, since the LTP method directly incorporates polynomial coefficients. Aside from idealized cases, such information is seldom available; however, use of macro-particles with finite polynomial shape functions for charge and current deposition can make analytic treatment possible for general cases. The macro-particle polynomial coefficients can be used directly in LTP solution formulas. This scheme allows one to choose a representation of particles that enables high fidelity with fewer particles compared to traditional particle methods, since the polynomials can include information such as transverse profile information from a beam, for example.