Implementation of Local, High-Order Accurate Boundary Conditions for Time-Dependent Acoustic Scattering

Abstract

A sequence of high-order accurate radiation boundary conditions involving local differential operators of auxiliary functions on a circular boundary are implemented in a spectral finite element method with mixed time integration. The semi-discrete finite element equations are integrated explicitly in time while the auxiliary functions on the circular boundary are integrated using a semi-implicit time-integration method. An efficient algorithm results which avoids the need to update either the solutions for the field variable or the boundary functions at intermediate time steps. Using this mixed time integration approach, a very natural and efficient implementation of the high-order accurate, local boundary conditions is obtained without altering the local/sparse character of the finite element equations. Numerical studies of time-dependent scattering from an elliptic object demonstrate the rapid convergence and accuracy of the implementation.