Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner.  demonstrate that NKS, combined with a density upwinding continuation strategy for problems with ak shocks, is robust and economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters.  study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.
['Chuan Xiao-Cai', 'William Gropp', 'David E. Keyes', 'Robin G. Melvin', 'and D Young']
I am writing a research paper on a idea PARALLEL NEWTON-KRYLOV-SCHWARZ ALGORITHMS FOR THE TRANSONIC FULL POTENTIAL EQUATION
[{"from": "human", "value": "I am writing a research paper on a idea PARALLEL NEWTON-KRYLOV-SCHWARZ ALGORITHMS FOR THE TRANSONIC FULL POTENTIAL EQUATION"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner.  demonstrate that NKS, combined with a density upwinding continuation strategy for problems with ak shocks, is robust and economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters.  study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer."}]