Spectral methods for numerical simulation of high-energy particle interactions

The high energy particle interactions are very complex phenomena, characterized by nonlinear, partial differential equations, and require very accurate numerical methods to simulate these phenomena reliably.The efficiency of the spectal methods in representing smooth solution fields, the superior accuracy and the exponential convergence make them very powerful computational tools.A comprehensive overview of the spectral techniques useful for numerical simulation of high energy particle interaction is presented; the Chebyshev and Legendre polynomial based methods are discussed in detail.The numerical stability and the computational efficiency are enhanced by introducing a nonlinear term evaluation, implementing boundary conditions, and physically consistent model parameters in the proposed framework.The validation of the simulation results is carried out for characteristics of the particle field evolution, dynamics of energy transport and interaction between particles, which reduces the discretization errors compared with the results of the use of conventional finite difference methods.The results validate the use of spectral methods in developing efficient, robust and scalable computational tools to study complex phenomena of high energy particles that are relevant to a broad spectrum of scientific and engineering applications.