Browsing by Author "Glowinski, R."
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Item Domain Decomposition and Mixed Finite Element Methods for Elliptic Problems(1987-05) Glowinski, R.; Wheeler, M.F.In this paper we describe the numerical solution of elliptic problems with nonconstant coefficients by domain decomposition methods based on a mixed formulation and mixed finite element approximations. Two families of conjugate gradient algorithms taking advantage of domain decomposition will be discussed and their performance will be evaluated through numerical experiments, some of them concerning practical situations arising from flow in porous media.Item Domain Decomposition and Model Reduction of Systems with Local Nonlinearities(2007-11) Sun, K.; Glowinski, R.; Heinkenschloss, M.; Sorensen, D.C.The goal of this paper is to combine balanced truncation model reduction and domain decomposition to derive reduced order models with guaranteed error bounds for systems of discretized partial differential equations (PDEs) with a spatially localized nonlinearities. Domain decomposition techniques are used to divide the problem into linear subproblems and small nonlinear subproblems. Balanced truncation is applied to the linear subproblems with inputs and outputs determined by the original in- and outputs as well as the interface conditions between the subproblems. The potential of this approach is demonstrated for a model problem.Item Fictitious Domain Methods for Viscous Flow Simulation(1995-05) Glowinski, R.; Kearsley, A.J.; Pan, T.W.; Periaux, J.We discuss the fictitious domain solution of the Navier-Stokes equations modeling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary conditions to be satisfied and is particularly well suited to the treatment of no-slip boundary conditions. This approach allows the use of structured meshes and fast specialized solvers for problems on complicated geometries. Another interesting feature of the fictitious domain approach is that it allows the solution of optimal shape problems without regridding. The resulting methodology is applied to the solution of flow problems including external viscous flow past oscillating rigid body and vortex dynamics of two-dimensional flow modeled by the incompressible Navier-Stokes equations and then to an optimal shape problem for Stokes and Navier-Stokes flows.Item Mixed Finite Element Methods for Time Dependent Problems: Application to Control(1989-09) Dupont, T.; Glowinski, R.; Kinton, W.; Wheeler, M.F.