A Parallel Spectral Element Method for Acoustic Wave Modeling

The finite element method is well reputed for its great flexibility in solving problems with complex geometries and heterogeneous structures, but, in its classical form, it has fairly low accuracy and poor computational efficiency. This makes an adverse impact on a large-scale numerical simulation of acoustic wavefield propagation. It has been shown by the author and his co-workers that the spectral approach, based on the use of high-order orthogonal interpolating functions (the Spectral Element Method), yields high accuracy with almost no numerical artifacts; it also significantly reduces the simulation computing costs. In this paper, the method is presented in conjunction with an iterative solution technique in such a way that it fully exploits the currently available parallel computers. The underlying algorithm is based on the observations that the assembly of mass and stiffness matrices is not really needed, and that the matrix-vector product required for the iterations can be done concurrently via an element-by-element approach. Moreover, by using a tensor-product sum-factorization scheme, computational and storage requirements can be further reduced as neither element nor global matrices are ever formed. The method is tested on the Cray T3D MPP computer, and its parallel efficiency and speed performance are discussed.