The parallel edge-based SUPG/PSPG finite element formulation applied to 3D steady incompressible Navier-Stokes equations is presented. The highly coupled velocitypressure nonlinear system of equations is solved with an inexact Newton-like method. The locally linear system of equations originated by the inexact nonlinear method is solved with a nodal block diagonal preconditioned GMRES solver. M...

In this work, we propose a preconditioned GMRES solver for a Schur complement equation of the linearized fluid-structure interaction problem, with respect to the displacement unknowns only on the interface. The preconditioning for the Schur complement equation requires approximate solutions of the fluid and structure sub-problems with appropriate boundary conditions on the interface, in particu...

A semi-iterative method based on a nested application of Flexible Generalized Minimum Residual(FGMRES) was developed to solve the linear systems resulting from the application of the discretized two-phase hydrodynamics equations to nuclear reactor transient problems. The complex three-dimensional reactor problem is decomposed into simpler, more manageable problems which are then recombined sequ...

A three-dimensional multi-block Newton-Krylov flow solver for the Euler equations has been developed for steady aerodynamic flows. The solution is computed through a Jacobian-free inexact-Newton method with an approximate-Newton method for startup. The linear system at each outer iteration is solved using a Generalized Minimal Residual (GMRES) Krylov subspace algorithm. An incomplete lower/uppe...

[1] We introduce the preconditioned generalized minimum residual (GMRES) method, along with an outer loop (OL) iteration to solve the sea-ice momentum equation. The preconditioned GMRES method is the linear solver. GMRES together with the OL is used to solve the nonlinear momentum equation. The GMRES method has low storage requirements, and it is computationally efficient and parallelizable. It...

An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient method or Generalized Minimum RESidual (GMRES) method, is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models, which are implicitly coupled to anot...

Many scientific libraries are currently based on the GMRES method as a Krylov 7 subspace iterative method for solving large linear systems. The restarted formulation known as 8 GMRES(m) has been extensively studied and several approaches have been proposed to reduce 9 the negative effects due to the restarting procedure. A common effect in GMRES(m) is a slow 10 convergence rate or a stagnation ...

In this report we describe the implementations of the GMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. For the sake of simplicity, exibility and eeciency the GMRES solvers have been implemented using the reverse communication mechanism for the matrix-vector product, the preconditioning and the...

We present a polynomial preconditioner for solving large systems of linear equations. The is derived from the minimum residual (the GMRES polynomial) and more straightforward to compute implement than many previous preconditioners. Our current implementation this using its roots naturally stable methods computing same polynomial. further stability control added roots, allows high degree polynom...