Efficient Preconditioners for the Triangular Spectral Element Method

Dr. Tony Kwan
Department of Mathematics and Center for Theoretical Biological Physics
UC San Diego


The discretization of partial differential equations (e.g., Navier-Stokes equation, heat equation, convection-diffusion equation) often results in linear systems to solve in each time step. The preconditioned conjugate gradient (PCG) iteration is a popular method to solve the linear system. In this talk, several preconditioners that are suitable for the triangular spectral element method (TSEM) are reviewed and new preconditioners are introduced. Numerical applications are included to illustrate the efficiency of the preconditioners.