The aim of this work is a construction of a dual mixed finite element method for a quasi–Newtonian flow obeying the Carreau or power law. This method is based on the introduction of the stress tensor as a new variable and the reformulation of the governing equations as a twofold saddle point problem. The derived formulation possesses local (i.e. at element level) conservation properties (conser...

This paper presents three formulations combining domain decomposition based finite element method with linear preconditioned conjugate gradient (LPCG) technique for solving large-scale problems in structural mechanics on parallel processing machines. In the first formulation called the Global Interface Formulation (GIF), the PCG algorithm is applied on the assembled interface stiffness coeffici...

In this paper we present an efficient adaptive cloth simulation based on the √ 3-refinement scheme. Our adaptive cloth model can handle arbitrary triangle meshes and is not restricted to regular grid meshes which are required by other methods. Previous works on adaptive cloth simulation often use discrete cloth models like mass-spring systems in combination with a specific subdivision scheme. T...

When polymeric liquids undergo large-amplitude shearing oscillations, the shear stress responds as a Fourier series, the higher harmonics of which are caused by fluid nonlinearity. Previous work on large-amplitude oscillatory shear flow has produced analytical solutions for the first few harmonics of a Fourier series for the shear stress response (none beyond the fifth) or for the normal stress...

Large-amplitude oscillatory shear flow (LAOS) is a popular for studying the nonlinear physics of complex fluids. Specifically, the strain rate sweep (also called the strain sweep) is used routinely to identify the onset of nonlinearity. In this paper, we give exact expressions for the nonlinear complex viscosity and the corresponding nonlinear complex normal stress coefficients for the Oldroyd ...

A basic objective in computational uid dynamics is the eecient solution of nonlinear systems of equations that arise in nite element modeling of convective-diiusive ow. The use of implicit Newton-like schemes to solve the coupled system of Navier-Stokes and continuity equations enables rapid convergence, although the well-known diiculty of indirect pressure linkage requires attention when formi...

A basic objective in computational uid dynamics is the eecient solution of nonlinear systems of equations that arise in nite element modeling of convective-diiusive ow. The use of implicit Newton-like schemes to solve the coupled system of Navier-Stokes and continuity equations enables rapid convergence, although the well-known diiculty of indirect pressure linkage requires attention when formi...

Boundary integral equation methods are well suited to represent the Dirichlet to Neumann maps which are required in the formulation of domain decomposition methods. Based on the symmetric representation of the local Steklov– Poincaré operators by a symmetric Galerkin boundary element method, we describe a stabilized variational formulation for the local Dirichlet to Neumann map. By a strong cou...

We present a real-space, non-periodic, finite-element formulation for Kohn–Sham density functional theory (KS-DFT). We transform the original variational problem into a local saddle-point problem, and show its well-posedness by proving the existence of minimizers. Further, we prove the convergence of finite-element approximations including numerical quadratures. Based on domain decomposition, w...