Recent Developments for the PSMG Multiscale Method
COLORADO UNIV AT BOULDER DEPT OF COMPUTER SCIENCE
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In this paper, the authors discuss new developments for the Parallel Superconvergent Multigrid PSMG multiscale method, which they have introduced previously as an efficient Partial Differential Equation PDE solver for massively parallel architectures. After an overview of the algorithm, the authors introduce the fundamental multiscale recursion relation as well as appropriate Fourier space notation. They derive the multiscale recursion as a single functional equation without reference to grids. They prove a sequence of rigorous convergence rate bounds that provide increasingly accurate estimates of the convergence rate for translation invariant problems. They show that in constant coefficient situations the convergence rates for the method may be derived to arbitrary precision, and they develop an efficient numerical scheme for computing such rates. Convergence rates are shown to be faster than reported previously. They then present estimates for the normalized work involved in the PSMG solution the number of parallel arithmetic and communication operations required per digit of error reduction. The work estimates show that the algorithm is highly efficient.
- Numerical Mathematics
- Computer Programming and Software