Stability of a fast convolution algorithm for non-reflecting boundary conditions

Achim Schädle, Christian Lubich

Mathematisches Institut, Universität Tübingen, 72076 Tübingen, Germany

achim.schaedle@na.uni-tuebingen.de

http://www.na.uni-tuebingen.de/~schaedle

Contributed talk

Non-reflecting boundary conditions for problems of wave propagation are non-local in time. We present a stability and convergence result for an algorithm using an A-stable integration scheme in the interior domain and a newly developed fast algorithm [1] for the evaluation of the convolution in the boundary condition. To compute a temporal convolution over $N_t$ successive time steps, the convolution algorithm requires ${\cal O}(N_t \log N_t)$ operations and ${\cal O}(log N_t )$ memory.