Parallel Newton-Krylov-Schwarz Solvers for the Full Potential Flow Equation

Date of Award


Document Type


Degree Name

Master of Science (MS)


Computer Science

Committee Director

David E. Keyes

Committee Member

Alex Pothen

Committee Member

Chester Grosch

Committee Member

Mohammad Zubair

Call Number for Print

Special Collections LD4331.C65 Z516


Newton-Krylov-Schwarz methods are increasingly applied in Computational Fluid Dynamics (CFD). We develop a parallel analysis code based on this method for the full potential flow model. The full potential model consists of a single nonlinear second-order partial differential equation of mixed type (elliptic/hyperbolic), which we solve as a steady boundary-value problem.

We use a nine-point finite-difference stencil to discretize the equation. A Newtonlike linearization and correction method is used to solve the resulting set of nonlinear algebraic equations. To solve the inner linear equations, we employ a Krylov space method. Preconditioners are used to improve the convergence rate. In order to preserve the parallelism intrinsic to the Newton-Krylov methods, we use the domain decomposition-based additive Schwarz method as a preconditioner. We compare the performances of various subdomain preconditioners such as Jacobi, SOR, LU, ILU(0), ILU(l), and ILU(2) against each other and against their global counterparts. From the view point of convergence rate and elapsed time, a domain-blocked ILU(n) is a good preconditioner.

We apply these methods in three parallel environments: SUN workstations on Ethernet network, an Intel Paragon (with a 2D interconnected mesh), and an IBM SP2 (with a high-performance multistage switch). Experimental data on sixteen SUN workstations and sixty-four Paragon nodes shows good efficiency for an implicit method.


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