Accelerated iterative DG finite element solvers for large-scale time-harmonic acoustic problems

Finite element methods are widely used to solve time-harmonic wave propagation problems, but solving large cases can be extremely difficult even with the computational power of parallel computers. In this work, the linear system resulting from the finite element discretization is solved with iterative solution methods, which are efficient in parallel but can require a large number of iterations. In standard discontinuous Galerkin (DG) methods, the numerical solution is discontinuous at the interfaces between the elements. In hybridizable DG methods, additional unknowns are introduced at the interfaces between the finite elements, and the physical unknowns are eliminated from the global system, resulting in a hybridized system. We have recently proposed a new strategy, called CHDG, where the additional unknowns correspond to transmission variables, whereas in the standard approach they are numerical fluxes. This strategy improves the properties of the hybridized system for faster iterative solution procedures. In this talk, we present and study a 3D CHDG implementation with nodal finite element basis functions. The resulting scheme has properties amenable to efficient parallel computing. Numerical results are presented to validate the method, and preliminary 3D computational results are proposed.