Summary: A Parallel Spectral Fourier Nonlinear Galerkin
Algorithm for Simulation of Turbulence
appeared in Numerical Methods for Partial Differential Equations, pp. 699715, 1997.
A. Averbuch 1 , L. Ioffe 2 , M. Israeli 2 , and L. Vozovoi 1
1 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
2 Faculty of Computer Science, Technion, Haifa 32000, Israel
We present a highorder parallel algorithm which requires only the minimum inter
processor communication dictated by the physical nature of the problem at hand. The
parallelization is achieved by domain decomposition. The discretization in space is
performed using the Local Fourier Basis method. The continuity conditions on the
interfaces are enforced by adding homogeneous solutions. Such solutions often have
fast decay properties which can be utilized to minimize interprocessor communication.
In effect, the predominant part of the computation is performed independently in the
subdomains (processors) or using only local communication.
A novel element of the present parallel algorithm is the incorporation of a Nonlinear
Galerkin strategy to accelerate the computation and stabilize the time integration
process. The basic idea of this approach consists of decomposition of the variables
into large scale and small scale components with different treatment of these large and